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GPU COMPUTING WITH R GPU Computing with R. Statistics is computationally intensive. Routine statistical tasks such as data extraction, graphical summary, and technical interpretation all require pervasive use of modern computing machinery. Obviously, these tasks can benefit greatly from a parallel computing environment where extensive calculations can be performed RSTANDARD | R TUTORIAL An R introduction to statistics. Explain basic R concepts, and illustrate with statistics textbook homework exercise. EXPONENTIAL DISTRIBUTION The exponential distribution describes the arrival time of a randomly recurring independent event sequence. If μ is the mean waiting time for the next event recurrence, its probability density function is: . Here is a graph of the exponential distribution with μ = 1.. Problem. Suppose the mean checkout time of a supermarket cashier is three minutes. Find the probability of a customerFACTORIAL DESIGN
KURTOSIS | R TUTORIAL An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the RANDOMIZED BLOCK DESIGNF DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F SKEWNESS | R TUTORIAL Skewness. The skewness of a data population is defined by the following formula, where μ2 and μ3 are the second and third central moments . Intuitively, the skewness is a measure of symmetry. As a rule, negative skewness indicates that the mean of the data values is less than the median, and the data distribution is left-skewed. INTEGER | R TUTORIALVARIANCESTANDARD DEVIATION A discussion of the integer data type in R. And we can parse a string for decimal values in much the same way. DATA FRAME ROW SLICE Data Frame Row Slice. We retrieve rows from a data frame with the single square bracket operator, just like what we did with columns. However, in additional to an index vector of row positions, we append an extra comma character. This is important, as the extra comma signals a wildcard match for the second coordinate for columnpositions.
GPU COMPUTING WITH R GPU Computing with R. Statistics is computationally intensive. Routine statistical tasks such as data extraction, graphical summary, and technical interpretation all require pervasive use of modern computing machinery. Obviously, these tasks can benefit greatly from a parallel computing environment where extensive calculations can be performed RSTANDARD | R TUTORIAL An R introduction to statistics. Explain basic R concepts, and illustrate with statistics textbook homework exercise. EXPONENTIAL DISTRIBUTION The exponential distribution describes the arrival time of a randomly recurring independent event sequence. If μ is the mean waiting time for the next event recurrence, its probability density function is: . Here is a graph of the exponential distribution with μ = 1.. Problem. Suppose the mean checkout time of a supermarket cashier is three minutes. Find the probability of a customerFACTORIAL DESIGN
KURTOSIS | R TUTORIAL An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the RANDOMIZED BLOCK DESIGNF DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F SKEWNESS | R TUTORIAL Skewness. The skewness of a data population is defined by the following formula, where μ2 and μ3 are the second and third central moments . Intuitively, the skewness is a measure of symmetry. As a rule, negative skewness indicates that the mean of the data values is less than the median, and the data distribution is left-skewed.QUANTITATIVE DATA
Quantitative data, also known as continuous data, consists of numeric data that support arithmetic operations. This is in contrast with qualitative data, whose values belong to pre-defined classes with no arithmetic operation allowed.We will explain how to apply some of the R tools for quantitative data analysis with examples. The tutorials in this section are based on a built-in data frame RANDOMIZED BLOCK DESIGN Randomized Block Design. In a randomized block design, there is only one primary factor under consideration in the experiment. Similar test subjects are grouped into blocks. Each block is tested against all treatment levels of the primary factor at random order. This is intended to eliminate possible influence by other extraneous factors.RESID | R TUTORIAL
A tutorial on the residual of a simple linear regression model. Tags: Elementary Statistics with R. fitted value. linear regression. residual. abline. lm. plot.MTCARS | R TUTORIAL
Hierarchical Cluster Analysis. With the distance matrix found in previous tutorial, we can use various techniques of cluster analysis for relationship discovery. For example, in the data set mtcars, we can run the distance matrix with hclust, and plot a dendrogram thatdisplays a
SIGNIFICANCE TEST FOR MLR Answer. As the p-values of Air.Flow and Water.Temp are less than 0.05, they are both statistically significant in the multiple linear regression model of stackloss.. Note. Further detail of the summary function for linear regression model can be found in the Rdocumentation.
SKEWNESS | R TUTORIAL An R tutorial on computing the skewness of an observation variable in statistics. The skewness of a data population is defined by the following formula, where μ 2 and μ 3 are the second and third central moments.. Intuitively, the skewness is a measure of symmetry. As a rule, negative skewness indicates that the mean of the data values is less than the median, and the data distribution is CORRELATION COEFFICIENT The correlation coefficient of two variables in a data set equals to their covariance divided by the product of their individual standard deviations.It is a normalized measurement of how the two are linearly related. Formally, the sample correlation coefficient is defined by the following formula, where s x and s y are the sample standard deviations, and s xy is the sample covariance. PREDICTION INTERVAL FOR MLR Then we wrap the parameters inside a new data frame variable newdata . > newdata = data.frame (Air.Flow=72, + Water.Temp=20, + Acid.Conc.=85) We now apply the predict function and set the predictor variable in the newdata argument. We also set the interval type as "predict", and use the default 0.95 confidence level. COMPARISON OF TWO POPULATION PROPORTIONS Comparison of Two Population Proportions. A survey conducted in two distinct populations will produce different results. It is often necessary to compare the survey response proportion between the two populations. Here, we assume that the data populations follow the normal distribution . LOWER TAIL TEST OF POPULATION MEAN WITH KNOWN VARIANCE The null hypothesis of the lower tail test of the population mean can be expressed as follows: . where μ 0 is a hypothesized lower bound of the true population mean μ.. Let us define the test statistic z in terms of the sample mean, the sample size and the population standard deviation σ : . Then the null hypothesis of the lower tail test is to be rejected if z ≤− z α, where z α is LIST | R TUTORIALSTANDARD DEVIATIONMATRIX An R tutorial on the concept of lists in R. Discussion on list creation, retrieving list slices with the single square bracket operator, and accessing a list member directly with the double squarebracket operator.
QUALITATIVE DATA
The tutorials in this section are based on an R built-in data frame named painters. It is a compilation of technical information of a few eighteenth century classical painters. The data set belongs to the MASS package, and has to be pre-loaded into the R workspace prior to its use. > library (MASS) # load the MASS package. > painters. DATA FRAME ROW SLICE Data Frame Row Slice. We retrieve rows from a data frame with the single square bracket operator, just like what we did with columns. However, in additional to an index vector of row positions, we append an extra comma character. This is important, as the extra comma signals a wildcard match for the second coordinate for columnpositions.
FACTORIAL DESIGN
BAYESIAN INFERENCE USING OPENBUGS CORRELATION COEFFICIENT The correlation coefficient of two variables in a data set equals to their covariance divided by the product of their individual standard deviations.It is a normalized measurement of how the two are linearly related. Formally, the sample correlation coefficient is defined by the following formula, where s x and s y are the sample standard deviations, and s xy is the sample covariance. STUDENT T DISTRIBUTION Student t Distribution. Assume that a random variable Z has the standard normal distribution , and another random variable V has the Chi-Squared distribution with m degrees of freedom. Assume further that Z and V are independent, then the following quantity follows a Student t distribution with m degrees of freedom. Here is a graph ofthe
KURTOSIS | R TUTORIAL An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the CHI-SQUARED DISTRIBUTION Chi-squared Distribution. If X1,X2,,Xm are m independent random variables having the standard normal distribution, then the following quantity follows a Chi-Squared distribution with m degrees of freedom. Its mean is m, and its variance is 2m . Here is a graph of the Chi-Squared distribution 7 degrees of freedom.KRUSKAL-WALLIS TEST
A collection of data samples are independent if they come from unrelated populations and the samples do not affect each other. Using the Kruskal-Wallis Test, we can decide whether the population distributions are identical without assuming them to follow the normal distribution.. Example. In the built-in data set named airquality, the daily air quality measurements in New York, May to LIST | R TUTORIALSTANDARD DEVIATIONMATRIX An R tutorial on the concept of lists in R. Discussion on list creation, retrieving list slices with the single square bracket operator, and accessing a list member directly with the double squarebracket operator.
QUALITATIVE DATA
The tutorials in this section are based on an R built-in data frame named painters. It is a compilation of technical information of a few eighteenth century classical painters. The data set belongs to the MASS package, and has to be pre-loaded into the R workspace prior to its use. > library (MASS) # load the MASS package. > painters. DATA FRAME ROW SLICE Data Frame Row Slice. We retrieve rows from a data frame with the single square bracket operator, just like what we did with columns. However, in additional to an index vector of row positions, we append an extra comma character. This is important, as the extra comma signals a wildcard match for the second coordinate for columnpositions.
FACTORIAL DESIGN
BAYESIAN INFERENCE USING OPENBUGS CORRELATION COEFFICIENT The correlation coefficient of two variables in a data set equals to their covariance divided by the product of their individual standard deviations.It is a normalized measurement of how the two are linearly related. Formally, the sample correlation coefficient is defined by the following formula, where s x and s y are the sample standard deviations, and s xy is the sample covariance. STUDENT T DISTRIBUTION Student t Distribution. Assume that a random variable Z has the standard normal distribution , and another random variable V has the Chi-Squared distribution with m degrees of freedom. Assume further that Z and V are independent, then the following quantity follows a Student t distribution with m degrees of freedom. Here is a graph ofthe
KURTOSIS | R TUTORIAL An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the CHI-SQUARED DISTRIBUTION Chi-squared Distribution. If X1,X2,,Xm are m independent random variables having the standard normal distribution, then the following quantity follows a Chi-Squared distribution with m degrees of freedom. Its mean is m, and its variance is 2m . Here is a graph of the Chi-Squared distribution 7 degrees of freedom.KRUSKAL-WALLIS TEST
A collection of data samples are independent if they come from unrelated populations and the samples do not affect each other. Using the Kruskal-Wallis Test, we can decide whether the population distributions are identical without assuming them to follow the normal distribution.. Example. In the built-in data set named airquality, the daily air quality measurements in New York, May to AN R INTRODUCTION TO STATISTICS Deep Learning in R. Deep learning has a wide range of applications, from speech recognition, computer vision, to self-driving cars and mastering the game of Go. While the concept is intuitive, the implementation is often tedious and heuristic. We will take a stab at simplifying the process, and make the technology more accessible.August 14, 2016.
R INTRODUCTION
An introduction to R, discuss on R installation, R session, variable assignment, applying functions, inline comments, installing add-on packages, R help and documentation. GPU COMPUTING WITH R GPU Computing with R. Statistics is computationally intensive. Routine statistical tasks such as data extraction, graphical summary, and technical interpretation all require pervasive use of modern computing machinery. Obviously, these tasks can benefit greatly from a parallel computing environment where extensive calculations can be performedFACTORIAL DESIGN
In a factorial design, there are more than one factors under consideration in the experiment.The test subjects are assigned to treatment levels of every factor combinations at random. Example. A fast food franchise is test marketing 3 new menu items in both East and West Coasts of continental United States. DATA FRAME ROW SLICE Data Frame Row Slice. We retrieve rows from a data frame with the single square bracket operator, just like what we did with columns. However, in additional to an index vector of row positions, we append an extra comma character. This is important, as the extra comma signals a wildcard match for the second coordinate for columnpositions.
BAYESIAN INFERENCE USING OPENBUGS Bayesian Inference Using OpenBUGS. We will use the data set survey for our first demonstration of OpenBUGS . Although the example is elementary, it does contain all the essential steps. There are more advanced examples along with necessary background materials in the R Tutorial eBook . The central concept of OpenBUGS is the BUGS model.NORMAL DISTRIBUTION
The normal distribution is defined by the following probability density function, where μ is the population mean and σ 2 is the variance.. If a random variable X follows the normal distribution, then we write: . In particular, the normal distribution with μ = 0 and σ = 1 is called the standard normal distribution, and is denoted as N (0, 1).It can be graphed as follows. DATA FRAME COLUMN SLICE To retrieve a data frame slice with the two columns mpg and hp, we pack the column names in an index vector inside the single square bracket operator. > mtcars mpg hp. Mazda RX4 21.0 110. Mazda RX4 Wag 21.0 110. Datsun 710 22.8 93. NORMAL PROBABILITY PLOT OF RESIDUALS AnR tutorial on the normal probability plot for the residual of a simple linear regression model. WILCOXON SIGNED-RANK TEST Two data samples are matched if they come from repeated observations of the same subject. Using the Wilcoxon Signed-Rank Test, we can decide whether the corresponding data population distributions are identical without assuming them to follow the normal distribution.. Example. In the built-in data set named immer, the barley yield in years 1931 and 1932 of the same field are recorded.BASIC DATA TYPES
Basic Data Types. There are several basic R data types that are of frequent occurrence in routine R calculations. Though seemingly innocent, they can still deliver surprises. Instead of chewing through the language specification, we will try to understand them better by direct experimentation with the R code. For simplicity, we deferdiscussing
FACTORIAL DESIGN
RSTANDARD | R TUTORIAL An R introduction to statistics. Explain basic R concepts, and illustrate with statistics textbook homework exercise. GPU COMPUTING WITH R GPU Computing with R. Statistics is computationally intensive. Routine statistical tasks such as data extraction, graphical summary, and technical interpretation all require pervasive use of modern computing machinery. Obviously, these tasks can benefit greatly from a parallel computing environment where extensive calculations can be performed COMPLETELY RANDOMIZED DESIGN KURTOSIS | R TUTORIAL An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the RANDOMIZED BLOCK DESIGN CUMULATIVE FREQUENCY DISTRIBUTION The cumulative frequency distribution of a quantitative variable is a summary of data frequency below a given level.. Example. In the data set faithful, the cumulative frequency distribution of the eruptions variable shows the total number of eruptions whose durations are less than or equal to a set of chosen levels.. Problem. Find the cumulative frequency distribution of the eruptionF DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F SKEWNESS | R TUTORIAL Skewness. The skewness of a data population is defined by the following formula, where μ2 and μ3 are the second and third central moments . Intuitively, the skewness is a measure of symmetry. As a rule, negative skewness indicates that the mean of the data values is less than the median, and the data distribution is left-skewed.BASIC DATA TYPES
Basic Data Types. There are several basic R data types that are of frequent occurrence in routine R calculations. Though seemingly innocent, they can still deliver surprises. Instead of chewing through the language specification, we will try to understand them better by direct experimentation with the R code. For simplicity, we deferdiscussing
FACTORIAL DESIGN
RSTANDARD | R TUTORIAL An R introduction to statistics. Explain basic R concepts, and illustrate with statistics textbook homework exercise. GPU COMPUTING WITH R GPU Computing with R. Statistics is computationally intensive. Routine statistical tasks such as data extraction, graphical summary, and technical interpretation all require pervasive use of modern computing machinery. Obviously, these tasks can benefit greatly from a parallel computing environment where extensive calculations can be performed COMPLETELY RANDOMIZED DESIGN KURTOSIS | R TUTORIAL An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the RANDOMIZED BLOCK DESIGN CUMULATIVE FREQUENCY DISTRIBUTION The cumulative frequency distribution of a quantitative variable is a summary of data frequency below a given level.. Example. In the data set faithful, the cumulative frequency distribution of the eruptions variable shows the total number of eruptions whose durations are less than or equal to a set of chosen levels.. Problem. Find the cumulative frequency distribution of the eruptionF DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F SKEWNESS | R TUTORIAL Skewness. The skewness of a data population is defined by the following formula, where μ2 and μ3 are the second and third central moments . Intuitively, the skewness is a measure of symmetry. As a rule, negative skewness indicates that the mean of the data values is less than the median, and the data distribution is left-skewed. INTEGER | R TUTORIAL A discussion of the integer data type in R. And we can parse a string for decimal values in much the same way. RANDOMIZED BLOCK DESIGN Randomized Block Design. In a randomized block design, there is only one primary factor under consideration in the experiment. Similar test subjects are grouped into blocks. Each block is tested against all treatment levels of the primary factor at random order. This is intended to eliminate possible influence by other extraneous factors.F DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the FHYPOTHESIS TESTING
An R tutorial on statistical hypothesis testing based on criticalvalue approach.
CUMULATIVE FREQUENCY DISTRIBUTION The cumulative frequency distribution of a quantitative variable is a summary of data frequency below a given level.. Example. In the data set faithful, the cumulative frequency distribution of the eruptions variable shows the total number of eruptions whose durations are less than or equal to a set of chosen levels.. Problem. Find the cumulative frequency distribution of the eruptionRESID | R TUTORIAL
A tutorial on the residual of a simple linear regression model. Tags: Elementary Statistics with R. fitted value. linear regression. residual. abline. lm. plot. PREDICTION INTERVAL FOR LINEAR REGRESSION Answer. The 95% prediction interval of the eruption duration for the waiting time of 80 minutes is between 3.1961 and 5.1564 minutes. Note. Further detail of the predict function for linear regression model can be found in the R documentation. WILCOXON SIGNED-RANK TEST Two data samples are matched if they come from repeated observations of the same subject. Using the Wilcoxon Signed-Rank Test, we can decide whether the corresponding data population distributions are identical without assuming them to follow the normal distribution.. Example. In the built-in data set named immer, the barley yield in years 1931 and 1932 of the same field are recorded. CORRELATION COEFFICIENT The correlation coefficient of two variables in a data set equals to their covariance divided by the product of their individual standard deviations.It is a normalized measurement of how the two are linearly related. Formally, the sample correlation coefficient is defined by the following formula, where s x and s y are the sample standard deviations, and s xy is the sample covariance. DENDROGRAM | R TUTORIAL With the distance matrix found in previous tutorial, we can use various techniques of cluster analysis for relationship discovery. For example, in the data set mtcars, we can run the distance matrix with hclust, and plot a dendrogram that displays a hierarchical relationship among the vehicles.DATA IMPORT
It is often necessary to import sample textbook data into R before you start working on your homework. Excel File. Quite frequently, the sample data is in Excel format, and needs to be imported into R prior to use. For this, we can use the function read.xls from the gdata package. It reads from an Excel spreadsheet and returns a data frame.The following shows how to load an Excel spreadsheet COMPLETELY RANDOMIZED DESIGN RSTANDARD | R TUTORIAL An R introduction to statistics. Explain basic R concepts, and illustrate with statistics textbook homework exercise.MATRIX | R TUTORIAL
Matrix. A matrix is a collection of data elements arranged in a two-dimensional rectangular layout. The following is an example of a matrix with 2 rows and 3 columns. We reproduce a memory representation of the matrix in R with the matrix function. The data elements must beHYPOTHESIS TESTING
An R tutorial on statistical hypothesis testing based on criticalvalue approach.
CORRELATION COEFFICIENT The correlation coefficient of two variables in a data set equals to their covariance divided by the product of their individual standard deviations.It is a normalized measurement of how the two are linearly related. Formally, the sample correlation coefficient is defined by the following formula, where s x and s y are the sample standard deviations, and s xy is the sample covariance. BAYESIAN INFERENCE USING OPENBUGS WILCOXON SIGNED-RANK TEST Two data samples are matched if they come from repeated observations of the same subject. Using the Wilcoxon Signed-Rank Test, we can decide whether the corresponding data population distributions are identical without assuming them to follow the normal distribution.. Example. In the built-in data set named immer, the barley yield in years 1931 and 1932 of the same field are recorded.F DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F LOWER TAIL TEST OF POPULATION MEAN WITH KNOWN VARIANCE The null hypothesis of the lower tail test of the population mean can be expressed as follows: . where μ 0 is a hypothesized lower bound of the true population mean μ.. Let us define the test statistic z in terms of the sample mean, the sample size and the population standard deviation σ : . Then the null hypothesis of the lower tail test is to be rejected if z ≤− z α, where z α isDATA IMPORT
It is often necessary to import sample textbook data into R before you start working on your homework. Excel File. Quite frequently, the sample data is in Excel format, and needs to be imported into R prior to use. For this, we can use the function read.xls from the gdata package. It reads from an Excel spreadsheet and returns a data frame.The following shows how to load an Excel spreadsheet COMPLETELY RANDOMIZED DESIGN RSTANDARD | R TUTORIAL An R introduction to statistics. Explain basic R concepts, and illustrate with statistics textbook homework exercise.MATRIX | R TUTORIAL
Matrix. A matrix is a collection of data elements arranged in a two-dimensional rectangular layout. The following is an example of a matrix with 2 rows and 3 columns. We reproduce a memory representation of the matrix in R with the matrix function. The data elements must beHYPOTHESIS TESTING
An R tutorial on statistical hypothesis testing based on criticalvalue approach.
CORRELATION COEFFICIENT The correlation coefficient of two variables in a data set equals to their covariance divided by the product of their individual standard deviations.It is a normalized measurement of how the two are linearly related. Formally, the sample correlation coefficient is defined by the following formula, where s x and s y are the sample standard deviations, and s xy is the sample covariance. BAYESIAN INFERENCE USING OPENBUGS WILCOXON SIGNED-RANK TEST Two data samples are matched if they come from repeated observations of the same subject. Using the Wilcoxon Signed-Rank Test, we can decide whether the corresponding data population distributions are identical without assuming them to follow the normal distribution.. Example. In the built-in data set named immer, the barley yield in years 1931 and 1932 of the same field are recorded.F DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F LOWER TAIL TEST OF POPULATION MEAN WITH KNOWN VARIANCE The null hypothesis of the lower tail test of the population mean can be expressed as follows: . where μ 0 is a hypothesized lower bound of the true population mean μ.. Let us define the test statistic z in terms of the sample mean, the sample size and the population standard deviation σ : . Then the null hypothesis of the lower tail test is to be rejected if z ≤− z α, where z α isMATRIX | R TUTORIAL
Matrix. A matrix is a collection of data elements arranged in a two-dimensional rectangular layout. The following is an example of a matrix with 2 rows and 3 columns. We reproduce a memory representation of the matrix in R with the matrix function. The data elements must be of the same basic type. > A = matrix (.NORMAL DISTRIBUTION
A tutorial on computing the interval estimate of population mean at given confidence level. The variance of the population is assumed tobe known.
BAYESIAN INFERENCE USING OPENBUGS Bayesian Inference Using OpenBUGS. We will use the data set survey for our first demonstration of OpenBUGS . Although the example is elementary, it does contain all the essential steps. There are more advanced examples along with necessary background materials in the R Tutorial eBook . The central concept of OpenBUGS is the BUGS model.F DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F KURTOSIS | R TUTORIAL An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the SIMPLE LINEAR REGRESSION An R tutorial for performing simple linear regression analysis. FREQUENCY DISTRIBUTION OF QUALITATIVE DATA The frequency distribution of a data variable is a summary of the data occurrence in a collection of non-overlapping categories.. Example. In the data set painters, the frequency distribution of the School variable is a summary of the number of painters in each school.. Problem. Find the frequency distribution of the painter schools in thedata set painters.
CHI-SQUARED DISTRIBUTION Chi-squared Distribution. If X1,X2,,Xm are m independent random variables having the standard normal distribution, then the following quantity follows a Chi-Squared distribution with m degrees of freedom. Its mean is m, and its variance is 2m . Here is a graph of the Chi-Squared distribution 7 degrees of freedom. POISSON DISTRIBUTION The Poisson distribution is the probability distribution of independent event occurrences in an interval. If λ is the mean occurrence per interval, then the probability of having x occurrences within a given interval is: . Problem. If there are twelve cars crossing a bridge per minute on average, find the probability of having seventeen or more cars crossing the bridge in a particularminute.
BINOMIAL DISTRIBUTION The binomial distribution is a discrete probability distribution. It describes the outcome of n independent trials in an experiment. Each trial is assumed to have only two outcomes, either success or failure. If the probability of a successful trial is p, then the probability of having x successful outcomes in an experiment of n independent trialsis as follows.
DATA IMPORT
It is often necessary to import sample textbook data into R before you start working on your homework. Excel File. Quite frequently, the sample data is in Excel format, and needs to be imported into R prior to use. For this, we can use the function read.xls from the gdata package. It reads from an Excel spreadsheet and returns a data frame.The following shows how to load an Excel spreadsheet COMPLETELY RANDOMIZED DESIGN RSTANDARD | R TUTORIAL An R introduction to statistics. Explain basic R concepts, and illustrate with statistics textbook homework exercise.MATRIX | R TUTORIAL
Matrix. A matrix is a collection of data elements arranged in a two-dimensional rectangular layout. The following is an example of a matrix with 2 rows and 3 columns. We reproduce a memory representation of the matrix in R with the matrix function. The data elements must beHYPOTHESIS TESTING
An R tutorial on statistical hypothesis testing based on criticalvalue approach.
CORRELATION COEFFICIENT The correlation coefficient of two variables in a data set equals to their covariance divided by the product of their individual standard deviations.It is a normalized measurement of how the two are linearly related. Formally, the sample correlation coefficient is defined by the following formula, where s x and s y are the sample standard deviations, and s xy is the sample covariance. BAYESIAN INFERENCE USING OPENBUGS WILCOXON SIGNED-RANK TEST Two data samples are matched if they come from repeated observations of the same subject. Using the Wilcoxon Signed-Rank Test, we can decide whether the corresponding data population distributions are identical without assuming them to follow the normal distribution.. Example. In the built-in data set named immer, the barley yield in years 1931 and 1932 of the same field are recorded.F DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F LOWER TAIL TEST OF POPULATION MEAN WITH KNOWN VARIANCE The null hypothesis of the lower tail test of the population mean can be expressed as follows: . where μ 0 is a hypothesized lower bound of the true population mean μ.. Let us define the test statistic z in terms of the sample mean, the sample size and the population standard deviation σ : . Then the null hypothesis of the lower tail test is to be rejected if z ≤− z α, where z α isDATA IMPORT
It is often necessary to import sample textbook data into R before you start working on your homework. Excel File. Quite frequently, the sample data is in Excel format, and needs to be imported into R prior to use. For this, we can use the function read.xls from the gdata package. It reads from an Excel spreadsheet and returns a data frame.The following shows how to load an Excel spreadsheet COMPLETELY RANDOMIZED DESIGN RSTANDARD | R TUTORIAL An R introduction to statistics. Explain basic R concepts, and illustrate with statistics textbook homework exercise.MATRIX | R TUTORIAL
Matrix. A matrix is a collection of data elements arranged in a two-dimensional rectangular layout. The following is an example of a matrix with 2 rows and 3 columns. We reproduce a memory representation of the matrix in R with the matrix function. The data elements must beHYPOTHESIS TESTING
An R tutorial on statistical hypothesis testing based on criticalvalue approach.
CORRELATION COEFFICIENT The correlation coefficient of two variables in a data set equals to their covariance divided by the product of their individual standard deviations.It is a normalized measurement of how the two are linearly related. Formally, the sample correlation coefficient is defined by the following formula, where s x and s y are the sample standard deviations, and s xy is the sample covariance. BAYESIAN INFERENCE USING OPENBUGS WILCOXON SIGNED-RANK TEST Two data samples are matched if they come from repeated observations of the same subject. Using the Wilcoxon Signed-Rank Test, we can decide whether the corresponding data population distributions are identical without assuming them to follow the normal distribution.. Example. In the built-in data set named immer, the barley yield in years 1931 and 1932 of the same field are recorded.F DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F LOWER TAIL TEST OF POPULATION MEAN WITH KNOWN VARIANCE The null hypothesis of the lower tail test of the population mean can be expressed as follows: . where μ 0 is a hypothesized lower bound of the true population mean μ.. Let us define the test statistic z in terms of the sample mean, the sample size and the population standard deviation σ : . Then the null hypothesis of the lower tail test is to be rejected if z ≤− z α, where z α isMATRIX | R TUTORIAL
Matrix. A matrix is a collection of data elements arranged in a two-dimensional rectangular layout. The following is an example of a matrix with 2 rows and 3 columns. We reproduce a memory representation of the matrix in R with the matrix function. The data elements must be of the same basic type. > A = matrix (.NORMAL DISTRIBUTION
A tutorial on computing the interval estimate of population mean at given confidence level. The variance of the population is assumed tobe known.
BAYESIAN INFERENCE USING OPENBUGS Bayesian Inference Using OpenBUGS. We will use the data set survey for our first demonstration of OpenBUGS . Although the example is elementary, it does contain all the essential steps. There are more advanced examples along with necessary background materials in the R Tutorial eBook . The central concept of OpenBUGS is the BUGS model.F DISTRIBUTION
F Distribution. If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom. Here is a graph of the F KURTOSIS | R TUTORIAL An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the SIMPLE LINEAR REGRESSION An R tutorial for performing simple linear regression analysis. FREQUENCY DISTRIBUTION OF QUALITATIVE DATA The frequency distribution of a data variable is a summary of the data occurrence in a collection of non-overlapping categories.. Example. In the data set painters, the frequency distribution of the School variable is a summary of the number of painters in each school.. Problem. Find the frequency distribution of the painter schools in thedata set painters.
CHI-SQUARED DISTRIBUTION Chi-squared Distribution. If X1,X2,,Xm are m independent random variables having the standard normal distribution, then the following quantity follows a Chi-Squared distribution with m degrees of freedom. Its mean is m, and its variance is 2m . Here is a graph of the Chi-Squared distribution 7 degrees of freedom. POISSON DISTRIBUTION The Poisson distribution is the probability distribution of independent event occurrences in an interval. If λ is the mean occurrence per interval, then the probability of having x occurrences within a given interval is: . Problem. If there are twelve cars crossing a bridge per minute on average, find the probability of having seventeen or more cars crossing the bridge in a particularminute.
BINOMIAL DISTRIBUTION The binomial distribution is a discrete probability distribution. It describes the outcome of n independent trials in an experiment. Each trial is assumed to have only two outcomes, either success or failure. If the probability of a successful trial is p, then the probability of having x successful outcomes in an experiment of n independent trialsis as follows.
R Tutorial
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DEEP LEARNING IN R
Deep learning has a wide range of applications, from speech recognition, computer vision, to self-driving cars and mastering the game of Go. While the concept is intuitive, the implementation is often tedious and heuristic. We will take a stab at simplifying the process, and make the technology moreaccessible.
August 14, 2016
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HIERARCHICAL LINEAR MODELLinear regression
probably is the
most familiar technique in data analysis, but its application is often hamstrung by model assumptions. For instance, if the data has a hierarchical structure, quite often the assumptions of linear regression are feasible only at local levels. We will investigate an extension of the linear model to bi-level hierarchies.July 22, 2013
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BAYESIAN CLASSIFICATION WITH GAUSSIAN PROCESS Despite prowess of the support vector machine , it is not specifically designed to extract features relevant to the prediction. For example, in network intrusion detection, we need to learn relevant network statistics for the network defense. In consumer credit rating, we would like to determine relevant financial records for the credit score. As for medical genetics research, we aim to identify genes relevant to the illness.January 6, 2013
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BAYESIAN INFERENCE USING OPENBUGS In our previous statistics tutorials, we have treated population parameters as fixed values, and provided point estimates and confidence intervals for them. An alternative approach is the Bayesian statistics. It treats population parameters as random variables. Probability becomes a measure of our belief in possible outcomes. With new tools like OpenBUGS, tackling new problems requires building new models, instead of creating yetanother R command.
July 22, 2012
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SIGNIFICANCE TEST FOR KENDALL'S TAU-BA variation of the
standard definition of Kendall correlation coefficientis necessary in
order to deal with data samples with tied ranks. It known as the Kendall’s tau-b coefficient and is more effective in determining whether two non-parametric data samples with ties are correlated.April 15, 2012
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SUPPORT VECTOR MACHINE WITH GPU, PART II In our last tutorial on SVM training with GPU, we mentioned a necessary step to pre-scale the data with rpusvm-scale, and to reverse scaling the prediction outcome. This cumbersome procedure is now simplified with the latest RPUSVM .October 21, 2011
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HIERARCHICAL CLUSTER ANALYSISWith the
distance matrix found in previous tutorial, we can use various techniques of cluster analysis for relationship discovery. For example, in the data set mtcars , we can run the distance matrix with hclust, and plot a dendrogram that displays a hierarchical relationship among the vehicles.November 25, 2010
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R TUTORIAL EBOOK
R TUTORIALS
* R Introduction
* Basic Data Types
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* Numeric Index Vector * Logical Index Vector * Named Vector Members* Matrix
* Matrix Construction* List
* Named List Members* Data Frame
* Data Frame Column Vector * Data Frame Column Slice * Data Frame Row Slice* Data Import
* Elementary Statistics with R* Qualitative Data
* Frequency Distribution of Qualitative Data * Relative Frequency Distribution of Qualitative Data* Bar Graph
* Pie Chart
* Category Statistics* Quantitative Data
* Frequency Distribution of Quantitative Data* Histogram
* Relative Frequency Distribution of Quantitative Data * Cumulative Frequency Distribution * Cumulative Frequency Graph * Cumulative Relative Frequency Distribution * Cumulative Relative Frequency Graph * Stem-and-Leaf Plot* Scatter Plot
* Numerical Measures* Mean
* Median
* Quartile
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* Interquartile Range* Box Plot
* Variance
* Standard Deviation* Covariance
* Correlation Coefficient* Central Moment
* Skewness
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* Probability Distributions * Binomial Distribution * Poisson Distribution * Continuous Uniform Distribution * Exponential Distribution * Normal Distribution * Chi-squared Distribution * Student t Distribution* F Distribution
* Interval Estimation * Point Estimate of Population Mean * Interval Estimate of Population Mean with Known Variance * Interval Estimate of Population Mean with Unknown Variance * Sampling Size of Population Mean * Point Estimate of Population Proportion * Interval Estimate of Population Proportion * Sampling Size of Population Proportion * Hypothesis Testing * Lower Tail Test of Population Mean with Known Variance * Upper Tail Test of Population Mean with Known Variance * Two-Tailed Test of Population Mean with Known Variance * Lower Tail Test of Population Mean with Unknown Variance * Upper Tail Test of Population Mean with Unknown Variance * Two-Tailed Test of Population Mean with Unknown Variance * Lower Tail Test of Population Proportion * Upper Tail Test of Population Proportion * Two-Tailed Test of Population Proportion* Type II Error
* Type II Error in Lower Tail Test of Population Mean with KnownVariance
* Type II Error in Upper Tail Test of Population Mean with KnownVariance
* Type II Error in Two-Tailed Test of Population Mean with KnownVariance
* Type II Error in Lower Tail Test of Population Mean with UnknownVariance
* Type II Error in Upper Tail Test of Population Mean with UnknownVariance
* Type II Error in Two-Tailed Test of Population Mean with UnknownVariance
* Inference About Two Populations * Population Mean Between Two Matched Samples * Population Mean Between Two Independent Samples * Comparison of Two Population Proportions* Goodness of Fit
* Multinomial Goodness of Fit * Chi-squared Test of Independence * Analysis of Variance * Completely Randomized Design * Randomized Block Design* Factorial Design
* Non-parametric Methods* Sign Test
* Wilcoxon Signed-Rank Test * Mann-Whitney-Wilcoxon Test * Kruskal-Wallis Test * Simple Linear Regression * Estimated Simple Regression Equation * Coefficient of Determination * Significance Test for Linear Regression * Confidence Interval for Linear Regression * Prediction Interval for Linear Regression* Residual Plot
* Standardized Residual * Normal Probability Plot of Residuals * Multiple Linear Regression * Estimated Multiple Regression Equation * Multiple Coefficient of Determination * Adjusted Coefficient of Determination * Significance Test for MLR * Confidence Interval for MLR * Prediction Interval for MLR * Logistic Regression * Estimated Logistic Regression Equation * Significance Test for Logistic Regression * GPU Computing with R * Distance Matrix by GPU * Hierarchical Cluster Analysis * Kendall Rank Coefficient * Significance Test for Kendall's Tau-b * Support Vector Machine with GPU * Support Vector Machine with GPU, Part II * Bayesian Classification with Gaussian Process * Hierarchical Linear Model * Installing GPU Packages * Installing CUDA Toolkit 7.5 on Fedora 21 Linux * Installing CUDA Toolkit 7.5 on Ubuntu 14.04 LinuxRECENT ARTICLES
*
Deep Learning in R
August 14, 2016
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Installing CUDA Toolkit 7.5 on Fedora 21 LinuxSeptember 10, 2015
*
Installing CUDA Toolkit 7.5 on Ubuntu 14.04 LinuxSeptember 10, 2015
*
Hierarchical Linear ModelJuly 22, 2013
QUOTES
" How happy is the blameless vestal's lot! The world forgetting, by the world forgot. Eternal sunshine of the spotless mind! Each pray'r accepted, and each wish resign'd. "ALEXANDER POPE
_Eloisa to Abelard_
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