# 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%

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