The district manager of Jasons, a large discount electronics chain, is investigating why certain stores in her region are performing better than others. She believes that three factors are related to total sales: the number of competitors in the region, the population in the surrounding area, and the amount spent on advertising. From her district, consisting of several hundred stores, she selects a random sample of 30 stores. For each store she gathered the following information
Y = total sales last year (in $ thousands).
X1 = number of competitors in the region.
X2 = population of the region (in millions).
X3 = advertising expense (in $ thousands).
The sample data were run on MINITAB, with the following results.
Analysis of variance
SOURCE DF SS MS
Regression 3 3050.00 1016.67
Error 26 2200.00 84.62
Total 29 5250.00
Predictor Coef StDev t-ratio
Constant 14.00 7.00 2.00
X1 -1.00 0.70 -1.43
X2 30.00 5.20 5.77
X3 0.20 0.08 2.50
a. What are the estimated sales for the Bryne store, which has four competitors, a regional population of 0.4 (400,000), and advertising expense of 30 ($30,000)?
b. Compute the R2 value.
c. Compute the multiple standard error of estimate.
d. Conduct a global test of hypothesis to determine whether any of the regression coefficients are not equal to zero. Use the .05 level of significance.
e. Conduct tests of hypotheses to determine which of the independent variables have significant regression coefficients. Which variables would you consider eliminating? Use the .05 significance level.
The solution provides step by step method for the calculation of multiple regression model. Formula for the calculation and Interpretations of the results are also included.