Question

1. In order to determine whether or not the sales volume of a company (y in millions of dollars) is related to advertising expenditures (x₁ in millions of dollars) and the number of salespeople (x₂), data were gathered for 10 years. Part of the Excel output is shown below.

ANOVA
	df	SS	MS	F
Regression		321.11
Residual		63.39
	Coefficients	Standard Error
Intercept	7.0174	1.8972
x1	8.6233	2.3968
x2	0.0858	0.1845

a.	Use the above results and write the regression equation that can be used to predict sales.
b.	Estimate the sales volume for an advertising expenditure of 3.5 million dollars and 45 salespeople. Give your answer in dollars.
c.	At a = 0.01, test to determine if the fitted equation developed in Part a represents a significant relationship between the independent variables and the dependent variable.
d.	At a = 0.05, test to see if b1 is significantly different from zero.
e.	Determine the multiple coefficient of determination.
f.	Compute the adjusted coefficient of determination.

Answer 1

ANOVA
	df	SS	MS	F
Regression	2	321.11	160.5550	17.7297
Residual	7	63.39	9.0557

	Coefficients	Standard Error	t stat	p value
Intercept	7.0174	1.8972	3.6988	0.0077
x1	8.6233	2.3968	3.5978	0.0088
x2	0.0858	0.1845	0.4650	0.6560

a) Y=7.0174+8.6233*x1+0.0858*x2

b) Y=7.0174+8.6233*3.5+0.0858*45 = 41.06
c)

F=17.7297

p value=0.0018

since, p value <α=0.01, so test is significant

Part a represents a significant relationship between the independent variables and the dependent variable.

d)

test stat, t=3.5978

p value=0.0088

since, p value <α=0.01, reject Ho

and conclude that b1 is significantly different from zero.

e) R² = SSR/SST = 321.11/(321.11 + 63.39 ) = 0.8351 or 83.51%
f) adjusted coefficient of determination = 1 - (1-R²)(N-1)/(N-p-1)=   0.7880