Question

A regression Study involving 32 convenience stores was undertaken to examine the relationship between monthly newspaper advertising expenditures (X) and the number of the customers shopping at the store (Y). A partial ANOVA table is below.

Source	SS	DF	MS	F
Regression	2850
Error			1260
Total

Complete the mission parts of the table.

Test whether or not X and Y are linearly related using the correlation coefficient. Use alpha = .01

What proportion of the variation in the number of customers is left UNEXPLAINED by this model?

At the 1% level of significance, what is the critical value to test the explanatory power of the model?

Answer 1

Source	SS	DF	MS	F
Regression	2850	1	2850	2.2619
Error	37800	30	1260
Total	40650	31

R²=SSR/SST=0.07011

r = √R² = 0.26478

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correlation hypothesis test                              
Ho:   ρ = 0                          
Ha:   ρ ╪ 0                          
                              
n=   32                          
alpha,α =    0.01                          
correlation , r =   0.2648                          
                              
Df =    n-2 =   30                      
t-test statistic = r*√(n-2)/√(1-r²) =        0.2648   * √    30   / √ ( 1 -    0.2648   ² ) =   1.504
                              
p-value =    0.1430   [excel function: =t.dist.2t(t-stat,df) ]                       
decision:   p value > α , so, do not reject the null hypothesis                          
so,  X and Y are not linearly related

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0.9299 proportion of the variation in the number of customers is left UNEXPLAINED by this model

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critical value=F(0.01,1,30) = 7.5625