# Regression analysis

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.