time series. 4. A marketing research trainee in the national office of a chain o

Question

time series.

4. A marketing research trainee in the national office of a chain of shoe stores used the following response function to study seasonal (winter, spring, summer, fall) effects on sale of a certain line of shoes: E(Y) = 0 + 1X1-82X2 + 3X3, where {o, other X2-(0, ifthe ringe, X3-6: 1, if fall 1, if winter 0, otherwise, X- x, I, if spring 0, otherwise, , After fitting the model, the trainee tested the regression coefficients k 0,1,2,3 and came to the following set of conclusions at a 0.05 family level of significance: 00, ! = 0, B20, 3 0. In the report the trainee then wrote: "Results of regression analysis show that climatic and other seasonal factors have no influence in determining sales of this shoe line in the winter. Seasonal influences do exist in the other seasons." Do you agree with this interpretation of the test results? Discuss.

Explanation / Answer

False - The coefficients for the indicator variables are relative to the category left out. Since Summer does NOT have an indicator variable assigned to it, the other indicator coefficients are relative to summer.

Beta1 is 0 <-- This indicates that effect of Winter is NOT significantly different than the effect of Summer.

** We are NOT saying that there is no Winter effect.

Note:

Beta2 is not 0 <-- This indicates that effect of Spring IS significantly different than the effect of Summer.

Beta3 is not 0 <-- This indicates that effect of Fall IS significantly different than the effect of Summer.

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