2. Suppose that a simple linear regression of Y on X is performed. va. Fill in t
ID: 3043812 • Letter: 2
Question
2. Suppose that a simple linear regression of Y on X is performed.
va. Fill in the blanks in the following ANOVA table for the regression:
Source DF SS MS F P-value
Regression 1 250 250 12.5
Error 10 200 20
Total 11 450
b. Is there a significant linear association between Y and X, at the a = 0.05 level? Explain.
c. What is the R2 value for the regression? Interpret the value you get.
d. What is the absolute value of the estimated sample (Pearson’s) correlation between X and Y? Interpret the magnitude of the value you get. What important detail about the estimated sample correlation, if any, are you unable to determine from the information provided?
Explanation / Answer
Ans:
a)
b)
p-value=Fdist(12.5,1,10)=0.0054
As,p-value<0.05,we reject null hypothesis.
There is sufficient evidence to conclude that there is a significant linear association between Y and X.
c)
SSR=250
SSE=200
SST=450
R2=SSR/SST=1-(SSE/SST)=250/450=0.556
The proportion of total variation (SST) that is explained by the regression (SSR) is known as the Coefficient of Determination, and is often referred to as R2
So,R2=0.556,indicates that 55.6% of the linear varition is explained by the regression.
d)
r=sqrt(0.556)=0.745
Strength of association between X and Y is r=0.745 (moderately correlated)
We are not able to determine the sign of pearson cofficient i.e whether there is positive or negative correlation between X and Y,it can not be retrieved from above.
Source df SS MS F p-value critical F Regression 1 250 250 12.5 0.0054 4.965 Error 10 200 20 Total 11 450Related Questions
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