The price of the “Spirit of the Devil” brand beer fluctuates from month to month

Question

The price of the “Spirit of the Devil” brand beer fluctuates from month to month due to the change in raw material prices and other factors. The company that sells this beer also advertises several times a month. The company wishes to investigate the impact of price and advertising on beer sales and collects monthly sales data (in thousands of dollars), number of advertisements per month and the average monthly price of beer (in dollars). The company suspects that higher prices lead to lower sales and more advertising leads to greater sales. In addition, the company also expects that the negative impact of prices on sales is affected by the level of advertising such that higher levels of advertising may lower the negative effect of price. Express the regression model that the company must estimate to test their intuition, state the relevant hypothesis, estimate the model and provide interpretation. Given the results of your estimation, predict the beer sales when the company spends on 12 advertisements and prices the beer at $1.25.

Sales   Price    Ads

159.14 .80     13

33.08   .75     3

156.04 .90     13

93.86   1.00   8

27.02   1.10   3

130.69 1.00   11

104.17 1.20   9

117.84 1.25   10

32.88   .90     3

145.77 1.50   12

91.65   1.00   8

94.03   1.25   8

Explanation / Answer

Ho: = 0 versus Ha: 0

The regression model is Sales = -2.8703 Price + 12.6737 Ads

Correlation coefficient is r = 0.999 (High positive correlation)

Coefficient of determination is r^2 = 0.998 (99.8% of the variation is Sales is explained by the variation in Price and Ads.

When Price = 1.25 and Ads = 12, Sales = 143.70

Regression Analysis R² 0.998 Adjusted R² 0.998 n   12 R   0.999 k   2 Std. Error   2.096 Dep. Var. Sales   ANOVA table Source SS   df   MS F p-value Regression 24,407.4941 2   12,203.7471 2778.09 2.75E-13 Residual 39.5357 9   4.3929 Total 24,447.0298 11   Regression output confidence interval variables coefficients std. error    t (df=9) p-value 95% lower 95% upper std. coeff. Intercept -4.7969 0.000 Price    -2.8703 3.0213 -0.950 .3669 -9.7050 3.9643 -0.013 Ads 12.6737 0.1749 72.473 9.17E-14 12.2781 13.0693 1.002 Predicted values for: Sales   95% Confidence Interval 95% Prediction Interval Price    Ads Predicted lower upper lower upper Leverage 1.25 12 143.69943 141.52229 145.87656 138.48217 148.91668 0.211

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