Question

The district manager of Jasons, a large 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 results of a multiple regression analysis, using Minitab, follow: Analysis of Variance Source Regression Error Total df MS 1016.67 84.62 3050 2200 5250 26 29 Coefficient 14.00 1.00 30.00 0.20 SE Coefficient 7.00 0.70 5.20 0.08 Predictor Constant 2.00 1.43 5.77 2.50 X2 X3 a.)What are the estimated sales for the Bryne store, which has four competitors, a regional population 0.4 (400,000), and an advertising expense of 30 ($30,000)? b.) Compute the coefficient of determination and comment on how well this model fits the data c.) Conduct a global test of the hypothesis to determine whether any of the regression coefficients are not equal to zero. Use a 5% level of significance. Show your computed F and the corresponding p value.

Answer 1

a)

Regression equation is given by

Y=14-1.00X₁+30X₂+0.20X₃

Given

X₁=4

X₂=0.4

X₃=30

Y=14-1.00*4+30*0.40+0.20*30=$28 K

b)

Coefficient of determination=SSR/SST=3050/5250=0.58

It means that 58% of variations in Y are explained by regression model.

Since R² is more than 0.50, we can say that model fits the data in a good way.

c)

In global test, we see that if model as whole is significant.

Ho:β1 = β2 = β3 = 0

Ho : atleast one 0

Let us calculate F statistics

F=MSR/MSE=1016.67/84.62=12.01

Critical value of F is found by MS Excel or other calculators with 3 numerator and 26 denominator degrees at 5% significance level.

Fc=2.98

Observed value of F is larger than Fc, we can say that regression as a whole is significant.

p-value is 0.000040

(we can calculate this number by MS Excel or any calculator with 3 degrees in numerator and 26 degrees in denominator with observes F=12.01)

Since p is less than our significance level i,e 0.05. We can say that regression model as a whole is significant.