39 A researcher intends to conduct a multiple regression on the following data s

Question

39 A researcher intends to conduct a multiple regression on the following data set where Y is the dependent variable. X, X, Y| 45.9 61 53 45.9 | 26.7 57.1 75.1 44.9 63.5 79.4 63.6 69.4 85.1 52.8 44 60.2 54.6 59.7 61.1 53 45.9 59.9. 65.4 41.4 51.447.6 42.5 49.9 58 64.9 72.7 | 58.9 69.7 55.3 51.9 49.1 54.7 58.4 | 78.7 59.6 | 37.9 8.3 83.4 | 43.8 | 65.750.8 | 47 | 59.2 49.2 | 55.2 | 63.6 51 | 53.3 74.1 54.7 | 60.5 77.3 | 44.2 | 43.6 68.1 45.5 52 Calculate the following correlations and semipartial correlations with the dependent variable. Report all answers accurate to 3 decimal places. ry1 = Ty(1-2) = 0 ry2 = Ty(2-1) =

Explanation / Answer

#library required for semi-partial correlations
> library(ppcor)
Loading required package: MASS
> data1=read.csv(file.choose(),header=T) #importing the saved file in .csv format into R
> attach(data1)
> names(data1)
[1] "X1" "X2" "Y"

a)> cor(Y,X1)
[1] -0.07258168 : r y1

c)> cor(Y,X2)
[1] -0.5539815 : r y2

b)> spcor.test(Y,X1,X2)

estimate p.value statistic n gp Method
1 0.3289304 0.1567552 1.477765 21 1 pearson
ry(1.2) = 0.3289304

d)> spcor.test(Y,X2,X1)
estimate p.value statistic n gp Method
1 -0.6401739 0.002363206 -3.535435 21 1 pearson
r y(2.1) = -0.6401739

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