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 
R^{2} = 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 
R^{2} = 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, R^{2 }, 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 
R^{2} = 93.9% 
= 92.2% 
Subject  General 
Due By (Pacific Time)  10/25/2013 12:37 pm 
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