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

Question

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 and a dependent variable under consideration are: FOREIMP (x_1) = a measurement of the forefoot shock-absorbing capability, MIDSOLD (x_2) = a measurement of the change in impact properties over Time, and LTIMP(y) = 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. The regression analysis resulted in the following ANOVA summary table: 1) Complete the ANOVA table above. 2) Determine whether there is a significant relationship between durability and the two independent variables at the 0.05 level of significance.

Explanation / Answer

1) Regression degrees of freedom = Number of independent variables = 2

Total degrees of freedom = 2 + 12 = 14

Error sum of squares = 13.38473 - 12.61020 = 0.77453

Regression mean sum of squares = 12.61020 / 2 = 6.3051

F Value = 6.3051 / 0.06454 = 97.69

Hence,

The complete ANOVA table will be:

2) Since p - value is less than 0.05, we reject Ho and hence,

There is sufficient evidence to conclude that there is a significant relationship between durability and the two independent variables.

Source Degrees of Freedom Sum of squares Mean Squares F P Value Regression 2 12.61020 6.3051 97.69 0.0001 Error 12 0.77453 0.06454 - - Total 14 13.38473 - - -

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