14.3 - A shoe manufacturer is considering developing a new brand of running shoes. The business...

14.3 - A shoe manufacturer is considering developing a new brand of running shoes. The business problem facing the marketing analyst is to determine which variables should be used to predict durability (i.e., the effect of long-term impact). Two independent variables under consideration are X₁ (FOREIMP), a measurement of the forefoot shock-absorbing capability, and X₂ (MIDSOLE), a measurement of the change in impact properties over time. The dependent variable Y is LTIMP, a measure of the shoe's durability after a repeated impact test. Data are collected from a random sample of 15 types of currently manufactured running shoes, with the following results:

Variable	Coefficients	Standard Error	t Statistic	p-Value
Intercept	-0.02686	0.06905	-0.39	0.7034
FOREIMP	0.79116	0.06295	12.57	0.0000
MIDSOLE	0.60484	0.07174	8.43	0.0000

A) State the regression equation.

B) Interpret the meaning of the slopes, b₁ and b₂, in this problem.

C) What conclusions can you reach concerning durability?

Please show all work.

Next question is the main one I need answered.

14.12 - In problem 14.3 on page 548, you predicted the durability of a brand of running shoe, based of the forefoot shock-absorbing capability and the change in impact properties over time. The regression analysis resulted in the following ANOVA summary table:

Source	Degrees of Freedom	Sum of Squares	Mean Squares	F	p-Value
Regression	2	12.61020	6.30510	97.69	0.0001
Error	12	0.77453	0.06454
Total	14	13.38473

A) Determine whether there is a significant relationship between durability and the two independent variables at the 0.05 level of significance.

B) Interpret the meaning of the p-value.

C) Compute the coefficient of multiple determination, r², and interpret its meaning.

Please show all work.

Solutions

Expert Solution

orchestra answered 1 year ago

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