Question

A regression analysis relating a company’s sales, their advertising expenditure, price, and time resulted in the following.

Regression Statistics
Multiple R	0.8800
R Square	0.7744
Adjusted R Square	0.7560
Standard Error	232.29
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	3	53184931.86	17728310.62	328.56	0.0000
Residual	21	1133108.30	53957.54
Total	24	54318040.16
	Coefficients	Standard Error	t Stat	P-value
Intercept	927.23	1229.86	0.75	0.4593
Advertising (X1)	1.02	3.09	0.33	0.7450
Price (X2)	15.61	5.62	2.78	0.0112
Time (X3)	170.53	28.18	6.05	0.0000

a.	At 95% confidence, determine whether or not the regression model is significant. Fully explain how you arrived at your conclusion (give numerical reasoning) and what your answer indicates.
b.	At 95% confidence determine which variables are significant and which are not. Explain how you arrived at your conclusion (Give numerical reasoning).
c.	Fully explain the meaning of R-square, which is given in this model. Be very specific and give numerical explanation.

Answer 1

a) Significance F = 0.0000

And since Significance F= 0.0000 < = 0.05, we can say that the regression model is significant.

b) From the variables, Advertising, time and price, Only price and time has p-value less than 0.05, we can say that only price and time are significant variables.

Advertising -- p-value = 0.7450 > 0.05, This is not significant .

Price -- p-value = 0.0112 < 0.05, This is significant.

Time -- p-value = 0.0000 < 0.05, This is significant.

c) R-squqre = 0.7744

This indicates that 77.44% of variation in sales is explained by variation in Price, Time and Adevertising. There is 22.56% unexplained variation.