A liquor wholesaler is interested in assessing the effect of the price of a prem

Question

A liquor wholesaler is interested in assessing the effect of the price of a premium scotch whiskey on the quantity sold. The results in the accompanying table on price, in dollars, and sales, in cases, were obtained from a sample of 8 weeks of sales records.

Price 19.1 20.5 19.8 21.2 20.9 19.7 17.9 17.1

Sales 25.6 15.1 19.1 11.3 11.6 15.9 29.7 35.1

a. Estimate by least squares the linear regression of increase in sales on increase in price. b. Find a 95% confidence interval for the slope of the population regression line

b. Find a 95% confidence interval for the slope of the population regression line.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Sales
Independent Variable: Price
Sales = 137.43317 - 5.9927361 Price
Sample size: 8
R (correlation coefficient) = -0.98057213
R-sq = 0.96152171
Estimate of error standard deviation: 1.8607452

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) The least square regression line is:

Sales = 137.43 - 5.99 Price

b) The 95% confidence interval for the slope of the population regression line is:

(-7.19, -4.80)

Parameter Estimate Std. Err. DF 95% L. Limit 95% U. Limit Intercept 137.43317 9.5784599 6 113.99553 160.87082 Slope -5.9927361 0.48941567 6 -7.190293 -4.7951791

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