Regression analysis
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A,B,C Inc. produces fresh, a brand of liquid laundry detergent. In order to more effectively manage its inventory and make revenue projections, the company would like to like to better predict demand for Fresh. The company has established the flowing demand equation:
Demand = Bo + B1FreshPrice + B2ComPrice + B3AdvExpend
Your Minitab Output follows:
Regression Analysis: Demand versus FreshPrice, ComPrice, AdvExpend
The regression equation is
Demand = 7.59 - 2.36 FreshPrice + 1.61 ComPrice + 0.501 AdvExpend
Predictor Coef SE Coef T stat Pvalue
Constant 7.589 2.445 3.10 0.005
FreshPrice -2.3577 0.6379 -3.70 0.001
ComPrice 1.6122 0.2954 5.46 0.000
AdvExpend 0.5012 0.1259 3.98 0.000
S = 0.234669 R-Sq = 89.4% R-Sq(adj) = 88.1%
Analysis of Variance
Source DF SS MS F Sign F
Regression 3 12.0268 4.0089 72.80 0.000
Residual Error 26 1.4318 0.0551
Total 29 13.4586
Source DF Seq SS
FreshPrice 1 2.9631
ComPrice 1 8.1907
AdvExpend 1 0.8729
Unusual Observations
Obs FreshPrice Demand Fit SE Fit Residual St Resid
5 3.60 9.3300 8.8164 0.0864 0.5136 2.35R
R denotes an observation with a large standardized residual.
Predicted Values for New Observations
New
Obs Fit SE Fit 95% CI 95% PI
1 8.4107 0.0469 (8.3143, 8.5070) (7.9188, 8.9025)
Values of Predictors for New Observations
New
Obs FreshPrice ComPrice AdvExpend
1 3.70 3.90 6.50
a. Write out the regression equation.
b. Predict the Demand when FreshPrice is 3.70, ComPrice is 3.90 and AdvExpend is 6.50.
c. Using the data from #1 above:
1. Report R-Sq and Adj R-SQ. Explain there differences and explain their meaning in the context of this problem.
2. Test the entire Model for significance. That is, the F test. Let alpha equal .05.
d. Using the t tests on each of the independent variables and also the p values.
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Solution Summary
Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.
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