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# 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

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

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

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
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.