Question

1. The president of a national real estate company wanted to know why certain branches of the company outperformed others. He felt that the key factors in determining total annual sales ($ in millions) were the advertising budget (in $1000s) X₁ and the number of sales agents X₂. To analyze the situation, he took a sample of 25 offices and ran the following regression. The computer output is below.

          PREDICTOR           COEF           STDEV                   P-VALUE

          Constant                 -19.47           15.84                      0.2422

          X₁                           0.1584          .0561                      0.0154

          X₂                           0.9625          .7781                      0.2386

          S_e = 7.362                        R squared = .524                        Sig F = 0.0116

1. What is the residual associated with office #13, an office with $24 million in sales, that spends $256000 on advertising and has 20 agents?

2. Interpret the coefficient of determination.

3. Create the ANOVA table appropriate for this situation.

Answer 1

The estimated regression equation is,

ŷ = -19.47 + 0.1584 X1 + 0.9625 X2

n = 25

e) For X1 = 256, X2 = 20

ŷ = -19.47 + 0.1584 * 256  + 0.9625 * 20 = 40.3304

Residual = Observed - Predicted = 24 - 40.3304 = -$16.3304 million

(f) Coefficient of determination = R squared = 0.524

52.4 % of the variation in sales can be explained by the relationship between advertising cost , number of agent and sales.

g) df(Regression) = number of independent variable = 2

df(residual) = n-3 = 22

df(total) = n-1 = 24

MSE = se² = (7.362)² = 54.1990

SSE = MSE*df(residual) = 54.1990 * 22 = 1192.3790

R² = 1 - SSE/SST

SST = SSE/(1-R²) = 1192.3790/(1-0.524) = 2504.9978

SSR = SST -SSE = 1312.6189

MSR = SSR/2 = 656.3094

F = MSR/MSE = 12.1092

p-value = F.DIST.RT(12.1092, 2, 22) = 0.0003

ANOVA
	df	SS	MS	F	Significance F
Regression	2	1312.6189	656.3094	12.1092	0.0003
Residual	22	1192.3790	54.1990
Total	24	2504.9978