2. A regression analysis is performed to predict the durability of a brand of ru
ID: 3257274 • Letter: 2
Question
2. 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 Mean Square F p-value Source 7.05963 3.52982 9.58 0.0012 Regression 7.36802 0.36840 Error 20 Total 22 14.42765 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 below. O A. Reject Ho. There is is insufficient evidence of a significant linear relationship. O B. Do not reject Ho. There is is insufficient evidence of a significant linear relationship. O C. Reject Ho. There is sufficient evidence of a significant linear relationship O D. Do not reject Ho. There is sufficient evidence of a significant linear relationship b. Interpret the meaning of the p-value. O A. The p-value 0.0012 is the probability that there is a linear relationship between the dependent variable and at least one of the independent variables. O B. The p-value 0.0012 is the probability of getting an overall test statistic of 9.58 or less, assuming there is no linear relationship between the dependent variable and the independent variables. O C. The p-value 0.0012 is the probability of getting an overall test statistic of 9.58 or greater, assuming there is no linear relationship between the dependent variable and the independent variables. c. Compute the coefficient of multiple determination, r and interpret its meaning (Round to four decimal places as needed.) Interpret the meaning of r The coefficient of multiple determination indicates that of the variation in (1 can be explained by the variation in (2) (Round to two decimal places as needed.)Explanation / Answer
a) Correct option is C because p value is so less (0.0012)
b) Correct option is C because p value denote the rejecting the null hypothesis when it is actually true
c) Coefficient of determination will be = 7.05963/14.42765 = 0.4893
The coefficient of determination indicates that 48.93% of variation in dependent can be explained by the variation in independent variable
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