Question

As a manager, you have been provided the following regression summery output for a regression model of a new product.

PLEASE PROVIDE STEP BY STEP INSTRUCTIONS TO SOLVE THIS. THANK YOU

	df	SS		MS		F	Significance F
Regression	3	156.4823		52.16077		28.01892	0.000002177
Residual	26	48.4023		1.861627
Total	29	204.8846
	Coefficients	P-value
Intercept	23.8163	9.24E-07
Price	-0.3035	0.001925
Price other	-0.342937	0.112442
Income	0.23406	0.033889

a. What is the percent risk of the coefficients really being zero? In other words, are the individual coefficients statistically significant using the 95 percent confidence level?   

b. Using the regression summary, compute R² and interpret its meaning.  

c. Is the “Price other” coefficient referring to a complement or a substitute (motivate)?

d. Is the “Income” coefficient referring to a normal good or inferior good (motivate)?   

Answer 1

a. The coefficients “Price” and Income are statistically significant as the p-value is less than 0.05
b. R^2= 1-SSE/SST = 1-(156.4823/204.8846) = 0.236241
It means that the model is able to capture 23.62 percent variation or the variables like Price, Price other and Income are able to explain 23.62 percent only.
c. Since the value is negative an increase in price other would lead to decrease in quantity hence the price other is a complement
d. Since the coefficient value is positive and less than 1 it is a normal good which means with the increase in income by 1 unit there would be increase in quantity demand by 0.234 units