Question

A computer 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		-0.1524	0.1411
ADV		0.8849	0.2886
Lines		-0.1463	1.5340
Analysis of Variance
Source of Variation		Degrees of Freedom	Sum of Squares
Regression			2708.61
Error (Residuals) Required:		14	2840.51
a.	Use the above results and write the regression equation that can be used to predict sales.
b.	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?
c.	Compute the coefficient of determination and fully interpret its meaning.
d.	At a = 0.05, test to see if there is a significant relationship between sales and unit price.
e.	At a = 0.05, test to see if there is a significant relationship between sales and the number of product lines.
f.	Is the regression model significant?
g.	Fully interpret the meaning of the regression (coefficient of price) per unit that is, the slope for the price per unit.

.

Note: Please write in computer typing please

Answer 1

The fitted regression model is

a )

Sales_hat = 1.0211 - 0.1524* price + 0.8849 * ADV - 0.1463 * Lines

b )

Here product lines = 10

Advertising = $ 40000 and price per unit = $ 3000

the estimate of sale is

Substitute this values in fitted regression equation,we get

Sales_ hat = 1.0211 - 0.1524 * 3000 + 0.8849 * 40000 - 0.1463 * 10

= 1.0211 - 457.2 + 35396 - 1.463

Sales _ hat = 34938.36

c )

We want to find

Here given that

SSR = 2708.61

SSRes =2840.51

SST = SSR + SSRes

SST = 2708.61 + 2840.51

SST = 5549.12

= 0.49

Meaning 49% variability explain due to the regressor price , advertising and product lines

In short 49% model is good fit.

d)

To test

Ho : vs Ha:

Or

Ho There is no linear relationship between sales and price

Vs

Ha There is linear relationship between sales and price

Test statistic

​​​​

Where  

And

t = - 1.08008

Here

=2.22814

= 2.22814. By using t table

|t| <

That is 1.08008 < 2.22814

Price does not contribute significantly to the model

e)

To test

Ho There is no linear relationship between sales and number of products lines

Vs

Ha There is no linear relationship between sales and number of products lines

Test statistic

Standard error beta3 hat = 1.5340

t= - 0.095371

|t |< talpha/2,10

That is  

0.095371 < 2.22814

Product of lines does contribute significantly to the model

g)

When one unit change in price the average change in sales all other regressor variable kept constant