basic operation of r-16!2!2016

8/16/2019 Basic Operation of R-16!2!2016

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Department of Mathematics, Statistics &Computer Sc. 1

Learning R

Laboratory Exercise-III

BPS651 Research MethodologyR.S.Rajput, Assistant Professor (Computer Science)

Laboratory Instructor

BPS651


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Department of Mathematics, Statistics &Computer Sc. 2

Laboratory Exercise -III

Correlation

Regression

Analysis of Variance

BPS651


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Correlation

Correlation is used to test for a relationship between two

numerical variables or two ranked (ordinal) variables.

Correlation is a bi variants analysis that measures the strengths

of association between two variables. In statistics, the value of

the correlation coefficient varies between +1 and -1. Usually, in statistics, we measure three types of correlations:

Pearson correlation

Kendall rank correlation

Spearman correlation

BPS651 Department of Mathematics, Statistics &Computer Sc. 3


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Pearson Correlation

Pearson r co rrelat ion : Pearson r correlation is widely used in

statistics to measure the degree of the relationship between

linear related variables. Pearson r correlation, both variables

should be normally distributed.

The following formula is used to calculate the Pearson rcorrelation:-

Where:

r = Pearson r correlation coefficient

N = number of value in each data

∑xy = sum of the products of paired scores

∑x = sum of x scores

∑y = sum of y scores

∑x2= sum of squared x scores

∑y2= sum of squared y scores



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Kendall rank Correlation

Kendall rank correlation is a non-parametric test that measures

the strength of dependence between two variables. If we

consider two samples, a and b, where each sample size is n, we

know that the total number of pairings with a b is n(n-1)/2. The

following formula is used to calculate the value of Kendall rank

correlation:

Where:

Nc= number of concordant

Nd= Number of discordant

Concordant: Ordered in the same way Discordant: Ordered differently



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Spearman Correlation

Spearman rank correlation is a non-parametric test that is used to

measure the degree of association between two variables. Spearman

rank correlation test does not assume any assumptions about the

distribution of the data and is the appropriate correlation analysis when

the variables are measured on a scale that is at least ordinal.

The following formula is used to calculate the Spearman rankcorrelation:

Where:

P= Spearman rank correlation di= the difference between the ranks of corresponding values Xi and Yi

n= number of value in each data set



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The cor( ) function

The cor( ) function to produce correlations .A simplified format is

cor(X , use=, method= )

where

X: Matrix or data frame

Use:Specifies the handling of missing data. Options are

all.obs (assumes no missing data, * missing data will

produce an error), complete.obs (listwise deletion), and

pairwise.complete.obs (pairwise deletion)

Method: Specifies the type of correlation. Options are

pearson, spearman or kendall.



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Visualizing Correlations

plot(), abline(), lowess() ,line(), pairs()

plot(): The basic function is plot(), denoting the (x,y) points to plot

>plot(x, y)

pairs() to create scatterplot matrices

>pairs(y~ x)

lines() use to point match

> lines(x, y, col="black")

abline() use to print regression line (y~ x)

>abline(lm(x~ y), h=0,v=0,col="red") lowess line function

> lines(lowess(x, y), col="blue")



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Exercise 10

Protein intake X and fat intake Y (in gm) for ten old

women given as

X 56,47,33,39,42,38,46,47,38,32

Y 56,83,49,52,65,52,56,48,59,70 Calculate correlation Coefficient (Pearson)

Draw scatter plot matrix, scatter plot



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Exercise 11

Find correlation coefficient (Pearson) between the

sales and expenses from the data given below:Firm: 1 2 3 4 5 6 7 8 9 10

Sales (Rs Lakhs): 50 50 55 60 65 65 65 60 60 50

Expenses (Rs Lakhs):11 13 14 16 16 15 15 14 13 13

Draw scatter plot matrix, scatter plot



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Simple Linear Regression

A simple linear regression model that describes the relationship

between two variables x and y can be expressed by the

following equation. The numbers α and β are called parameters,

and ϵ is the error term.

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



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Simple Linear Regression cont.

Estimated Simple Regression Equation

>W=lm(y~x)

Where

X

Y

w



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Multiple Linear Regressions

Estimated Multiple Regression Equation

Multiple Coefficient of Determination

Adjusted Coefficient of Determination

Significance Test for MLR

Confidence Interval for MLR

Prediction Interval for MLR



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Logistic Regression

Estimated Logistic Regression Equation

Significance Test for Logistic Regression

BPS651Department of Mathematics, Statistics &

Computer Sc.

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Exercise 11

Geographical area x and area under paddy

cultivated y ( in hectares) for 15 villages of a

district are given below-

X 103,106,120,120,100,151,160,155,136,178,196,140,160,166,112 Y 041,033,087,078,035,081,090,085,070,100,102,070,082,085,050

Calculate correlation coefficient

Calculate regression equation of y on x

Estimate paddy cultivation whore geograhicalarea is 136 hater

BPS651Department of Mathematics, Statistics &

Computer Sc.

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Exercise 12

Calculate correlation coefficient between

marks obtained in 1st prefinal and 2nd prefinal

examination on the basis of the following data

collected for a sample of 12 students I 12,14,9.5,10.5,8,11.5,10,14,8,9.5,11,12

II 11.5,13.5,12,14,7,14,8,12.5,6.5,10,9,12

Calculate correlation coefficients Calculate regression equation of y on x

BPS651 Department of Mathematics, Statistics &

Computer Sc.

16


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Exercise 10

Protein intake X and fat intake Y (in gm) for

ten old women given as

X 56,47,33,39,42,38,46,47,38,32

Y 56,83,49,52,65,52,56,48,59,70

Calculate correlation Coefficient

Calculate regression equation of y on x

Estimate fat intake of a women whose proteinintake is 38 gm.


Computer Sc.

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Exercise 13

Twelve students for the following percentage

of makes in physics & statistics calculate:-

Correlation coefficient

Linear regression equation of y on x

Calculate predicted values & residual value

for x=80, for the given data below

X 73,42,88,38,68,75,80,54,64,48,35,37 Y 73,48,86,58,65,60,76,54,50,38,32,30


Computer Sc.

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Exercise 14


Computer Sc.

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Exercise 15


Computer Sc.

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Exercise 16


Computer Sc.

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Exercise 17


Computer Sc.

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Exercise 18


Computer Sc.

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Exercise 19


Computer Sc.

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Exercise 20


Computer Sc.

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Analysis of Variance


Computer Sc.

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Completely Randomized Design


Computer Sc.

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Randomized Block Design


Computer Sc.

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Factorial Design


Computer Sc.

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basic operation of r-16!2!2016

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