MTB > execute 'aa-467.mtb'
MTB > Note. Bill Qualls - Multiple Regression Example
MTB > Note. Source: Amir Aczel, Complete Business Statistics,
MTB > Note. 2ed, Irwin Publishing, Page 467, Example (a)
MTB > Note. This is file AA-467.MTB
MTB >
MTB >
MTB > Note. "Alka-Seltzer recently embarked on an in-store
MTB > Note. promotional campaign, with displays of its antacid
MTB > Note. featured prominently in supermarkets. The company
MTB > Note. also ran its usual radio and television commercials.
MTB > Note. Over a period of 10 weeks, the company kept track of
MTB > Note. its expenditure on radio and television advertising,
MTB > Note. variable X1, and well as its spending on in-store
MTB > Note. displays, variable X2. The resulting sales for each
MTB > Note. week in the area studied were recorded as the
MTB > Note. dependent variable, Y."
MTB >
MTB >
MTB > read c1-c3
DATA> 12 5 72
DATA> 11 8 76
DATA> 15 6 78
DATA> 10 5 70
DATA> 11 3 68
DATA> 16 9 80
DATA> 14 12 82
DATA> 8 4 65
DATA> 8 3 62
DATA> 18 10 90
DATA> end
10 ROWS READ
MTB >
MTB >
MTB > name c1 'RadioTV' c2 'InStore' c3 'Sales'
MTB >
MTB >
MTB > Note. First, let's try using Radio/TV (only) as a predictor...
MTB > regr c3 1 c1
The regression equation is
Sales = 45.0 + 2.38 RadioTV
Predictor Coef Stdev t-ratio p
Constant 45.014 3.909 11.52 0.000
RadioTV 2.3810 0.3076 7.74 0.000
s = 3.108 R-sq = 88.2% R-sq(adj) = 86.7%
Analysis of Variance
SOURCE DF SS MS F p
Regression 1 578.82 578.82 59.92 0.000
Error 8 77.28 9.66
Total 9 656.10
MTB >
MTB >
MTB > Note. Next, let's try using In-store displays (only)...
MTB > regr c3 1 c2
The regression equation is
Sales = 58.5 + 2.43 InStore
Predictor Coef Stdev t-ratio p
Constant 58.482 3.253 17.98 0.000
InStore 2.4335 0.4559 5.34 0.000
s = 4.240 R-sq = 78.1% R-sq(adj) = 75.3%
Analysis of Variance
SOURCE DF SS MS F p
Regression 1 512.26 512.26 28.49 0.000
Error 8 143.84 17.98
Total 9 656.10
MTB >
MTB >
MTB > Note. Finally, let's use both (combined) as a predictor...
MTB > regr c3 2 c1 c2
The regression equation is
Sales = 47.2 + 1.60 RadioTV + 1.15 InStore
Predictor Coef Stdev t-ratio p
Constant 47.165 2.470 19.09 0.000
RadioTV 1.5990 0.2810 5.69 0.000
InStore 1.1487 0.3052 3.76 0.007
s = 1.911 R-sq = 96.1% R-sq(adj) = 95.0%
Analysis of Variance
SOURCE DF SS MS F p
Regression 2 630.54 315.27 86.34 0.000
Error 7 25.56 3.65
Total 9 656.10
SOURCE DF SEQ SS
RadioTV 1 578.82
InStore 1 51.72
MTB > stop
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