Question

A regression analysis is performed to predict the durability of a brand of running shoe, based on the shock-absorbing capability and the change in impact properties over time. The resulting ANOVA table is below. Complete parts (a) through (d). Degrees of Sum of Freedom Squares Regression Error Total 10.45577 6.46314 16.91891 Mean Square 5.22789 0.28101 p-value 0.00002 18.60 2 23 25 a. Determine whether there is a significant relationship between durability and the two independent variables at the 0.05 level of significance. Choose the correct answer belovw. A. Reject Ho There is is insufficient evidence of a significant linear relationship ○ B. Do not reject Ho . There iS is insufficient evidence of a signicant linear relationship. O C. Do not reject Ho. There is sufficient evidence of a significant linear relationship 0 D. Reject Ho There is sufficient evidence of a significant linear relationship b. Interpret the meaning of the p-value. O A The p value 0.00002 is the probability of getting an overall test statistic of 1860 or less, assuming there is no linear relationship between the dependent variable and the independent variables O B. The p-value 0.00002 is the probability of getting an overall test statistic of 18.60 or greater, assuming there is no linear relationship between the dependent variable and the independent variables. ° C. The p-value 0.00002 is the probability that there is a linear relationship between the dependent vanable and at least one of the independent variables C. Compute the coefficient of multiple determination, ґ, and interpret its meaning. 宀□ (Round to four decimal places as needed.) Interpret the meaning of r The coefficient of multiple determination indicates that | | % of the vanation in V can be explained by the variation in Round to two decimal places as needed.) d. Compute the adjusted r2 radi-L (Round to four decimal places as needed.)

Drop down options are durability, impact properties, shock absorbing capabilities, the two independent variables.

Answer 1

a) As p-value = 0.00002 < 0.05, we reject the null hypothesis.

Answer D : Reject Ho. There is sufficient evidence of a significant linear relationship.

b) Answer B

c) Coefficient of determination , r² =

$r^2 = \frac{SS_{regression}}{SS_{total}} =\frac{10.45577}{16.91891} =\textbf{0.6180}$

The Coefficient of multiple determination indicates that 61.80% of the variation in durability can be explained by the variation in the two independent variables.

d) Adjusted r²=

$r^2_{adj} = 1-\frac{(1-r^2)(n-1)}{N-k-1}= 1-\frac{(1-0.618)(25)}{23} = \textbf{0.5848}$