Question

Problem. Chris Pratt is almost ready to pop the question to the girl of his dreams. He collected the data on the sizes (xi) and the prices (x) of diamond rings from online jewelry stores and obtained the following ANOVA table for a simple linear regression model, yi Bo+ Boxi+E df Sum of Squares Mean Square F Significance F Regression 2300 ? 1 2300 Residual 500 14 7000 Total 15 9300

Find the sample variance of the dependent variable y_i.

What fraction of the sample variance in y_i can be explained by the linear regression model? Find the coefficient of determination, r².

Find the adjusted r² value.

Do we have enough evidence to conclude that there exists a strong linear relationship between x_i and y_i? Find the p-value for the test.

Answer 1

1) sample variance of the dependent variable =SST/df(total) =9300/15 =620

2) fraction of the sample variance in y_i can be explained by the linear regression model:

R2=SSR/SST=

0.2473

3)

here k= number of independent variables =1

and n=sample size =15+1 =16

R2adj=

1-(n-1)*SSE/(SST(n-k-1)) =

0.1935

4)

test statistic F =(MSR/MSE )=2300/500 =4.6

for above test statistic and (1,14) degree of freedom , p value =0.0500

as p value <=0.0500, we have sufficient evidence that there exist a strong linear relationship