A microcomputer manufacturer has developed a regression model relating his sales

Question

A microcomputer manufacturer has developed a regression model relating his sales (Y in $10,000 s) 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 1.1211 22.8752 Price -0.1924 0.1411 ADV 0.7849 0.2886 Lines -0.1663 1.5340 Analysis of variance Source of Variation Degrees of freedom Sum of squares Regression Error(Residuals) 21 2708.61 2840.51 a. 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. b Compute the coefficient of determination and fully interpret its meaning. c. At alpha = 0.01, perform and F-1est to see if there is a significant relationship between sales and all independent variables. d. At alpha = 0.05, test to see if there is a significant relationship between sales and the number of product lines. e. Fully interpret the meaning of the regression (coefficient of price) per unit that is, the slope for the price per unit.

Explanation / Answer

Part-a

Sales=1.1211-0.1924*30+0.7849*40-0.1663*10

=25.0821

=$250821 as sales inn 10,000

Part-b

Total sum of squares SST=SSR+SSE

=2708.61+2840.51

=5549.12

Coefficient of determination =SSR/SST

=2708.61/5549.12

=0.4881

This means that regression model explained 48.81% of the variability in sales

Part-c

Regression degree of freedom =3

Error df=21

MSR=2708.61/3=902.87

MSE=2840.51/21=135.262381

So, F=902.87/135.262381 =6.6749

Critical F(0.01,3,21)= 4.8740

As calculated F>4.8740, we conclude that there is significant relationship between sales and all independent variables

Part-d

Calculated test statistic t=-0.1663/1.5340=-0.1084

Critical t(0.05,21)=2.0796

As calculated |t|<2.0796, we conclude that lines is not a significant predictor of sales.

Part-e

Corresponding to $100 increase in price per unit there is on an average a decrease of $1924 in the sales, holding other predictors fixed.

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