Question

A microcomputer manufacturer has developed a regression model relating his sales (Y in $10,000s) with three independent variables. The three independent variables are price per unit (Price in $100s), advertising (ADV in $1,000s) and the number of product lines (Lines). Part of the regression results is shown below.

	Coefficient	Standard Error
Intercept	1.0211	22.8752
Price (X1)	-.1523	-.1411
ADV (X2)	.8849	.2886
Lines(X3)	-.1463	1.5340

Source	D.F.	S.S.
Regression	3	2708.651
Error	14	2840.51
Total	17	5549.12

(a) What has been the sample size (n) for this analysis?

(b) Use the above results to find the estimated multiple regression equation that can be used to predict sales.

(c) Interpret the meaning of the coefficient of X2.

(d) If the manufacturer has 10 product lines, advertising of $40,000, and the price per unit is $3,000, what is your estimate of their sales? Give your answer in dollars.

Answer 1

Here in our case, p=3.

(a)

The sample size (n) for this analysis is 18 because it is given in ANOVA of Regression that D.F. for TSS (Total sum of square) is 17 which should be n-1.

so, n - 1 = 18

n=18.

(b) Estimated multiple regression equation or Regression model will be:

Y= 1.0211 - 0.1523*X1 + 0.8849*X2 - 0.1463*X3

(c) The coefficient of Xi2 = b2 = 0.8849: Generally the Coefficient value measures a unit change in the dependent variable when x_i2 changes

i.e. The coefficient indicates that for every additional unit in ADV (Advertising) we can expect sales to increase by an average of 0.8849 times.

(d) given that

X1= 30(in $100s) , X2 = 40(in $1000s), X3=10(in lines)

so Y =  1.0211 -0.1523*30 + 0.8849*40 - 0.1463*10

Y= 30.3851 (in $10000s)

Y = $303851s ( Estimate of sales)