A detergent manufacturer wants to predict demand for its brand "CLEAN" to manage its inventory more effectively and to make revenue projections. The company has gathered the following data taken over the last 30 sales periods (each sales period is defined to be a four week period) to develop a prediction model for demand of "CLEAN".

y = demand for the large sized bottle of CLEAN (in hundreds of thousands of bottles) in the

sales period

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x1 = the price (in $) of CLEAN as offered by the company in the sales period

x2 = the average industry price (in $) (IndPrice) of competitors' similar detergents in the sales period

x3 = company's advertising expenditure (in hundreds of thousands of dollars) to promote CLEAN

in the sales period

After carrying out some preliminary analysis as shown above, the company has used simple regression model for predicting demand (y) on the basis of price (x1) of the product and the following results are obtained. The data is shred in the spreadsheet.

Answers to the following questions:

a) Obtain 95% confidence interval for the regression coefficient.

b) What does R-Sq = 22.0% mean?

c) How do you interpret Std Error?

d) How do you interpret p-value of the explanatory variable "price"?

e) Do you feel any need for the improvement of the model? Justify your answer.

The company also wants to use the other variables x2 and x3 along with x1 to predict demand and hence uses multiple regression analysis.

Answers to the following questions:

f) Interpret the coefficients (regression coefficients) of each of the explanatory variables along

with the intercept.

g) What does the F test carry out?

h) Is there any improvement taken place in the regression model? Explain.

i) What will the predicted demand for "CLEAN" be when price=3.55, IndPrice=3.52 and

AdvExp=0.22 in respective units. Hence calculate the residual and standardized residual.