Project #15327 - Mutiple Regression

Multiple Regression. Kitchen Products, Ltd., is a regional distributor of  the Kitchen Regal Bread Making Machine. The company wishes to assess the relative importance of price reductions versus an increase in personal selling efforts as means for enhancing product promotion. To this end, the company recently used a regression analysis approach to study the following monthly unit sales, price, and personal selling expense information for the Bozeman, Montana market:

 

Unit Sales

Price

Personal Selling Expenses

132

$74

$1,140

203

  74

  1,400

217

  55

  1,160

255

  53

  1,210

252

  64

  1,490

239

  70

  1,460

152

  75

  1,200

197

  58

  1,020

230

  65

  1,390

154

  61

  1,040

 

As a first step in the analysis, the company ran simple regressions of unit sales on each of the potentially important independent variables of price and personal selling expenses:

 

The first simple regression equation is:

 

 Equation 1.  SALES = 371 - 2.59 PRICE

 

Predictor

Coef

Stdev

t ratio

p

Constant

371.0

109.5

3.39

0.010

PRICE

-2.587

1.676

-1.54

0.161

 

 

 

 

 

SEE = 40.94

R2 = 22.9%

 = 13.3%

 

As a second step in the analysis, the company ran a second simple regression equation;  the second equation is:

 

Equation 2  SALES = 5.9 + 0.158 SELLEXP

 

Predictor

Coef

Stdev

t ratio

p

Constant

5.89

90.10

0.07

0.949

SELLEXP

0.15764

0.07142

2.21

0.058

 

 

 

 

 

SEE = 36.77

R2 = 37.8%

 = 30.1%

 

A.

Based on these simple regression model results, does the potentially important independent variable affect unit sales?

What does each of the SEEs, R2 , numbers  indicate?  What share of overall variation in sales is explained by the regression equation?  What share is left unexplained? 

B

Characterize the differences between each simple regression model coefficient estimates above from part A with those estimated using the following multiple regression equation below.  Using equation 3 below, determine the range of the expected level of sales with a confidence of 95 percent if the price was lowered to $60 and personal selling expenses were $1000.  What would the range of total revenue be in this case.  Suggest other variables that we might add to our analysis that may improve the predictability of our equations.

C.

 

The multiple regression equation is:

 

Equation 3.  SALES = 195 - 4.33 PRICE + 0.231 SELLEXP

 

Predictor

Coef

Stdev

t ratio

p

Constant

194.92

38.27

5.09

0.000

PRICE

-4.3296

0.5396

-8.02

0.000

SELLEXP

0.23115

0.02560

9.03

0.000

 

 

 

 

 

SEE = 12.31

R2 = 93.9%

 = 92.2%

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Due By (Pacific Time) 10/25/2013 12:37 pm
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