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In: Statistics and Probability

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.

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Expert Solution

orchestra answered 2 years ago
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