The price of the “Spirit of the Devil” brand beer fluctuates from month to month
ID: 3181935 • Letter: T
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. The data is in spirit.sav . Please see data table below.
sales price ads 159.14 0.8 13 33.08 0.75 3 156.04 0.9 13 93.86 1 8 27.02 1.1 3 130.69 1 11 104.17 1.2 9 117.84 1.25 10 32.88 0.9 3 145.77 1.5 12 91.65 1 8 94.03 1.25 8Explanation / Answer
Solution:
Here, we have to find the regression equation for the prediction of the dependent variable or response variable as the sales based on the independent variables or predictors such as advertisements and coupon value. The regression model (by using excel) for the prediction of the sales is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.920374554
R Square
0.84708932
Adjusted R Square
0.813109169
Standard Error
21.3830988
Observations
12
ANOVA
df
SS
MS
F
Significance F
Regression
2
22796.86777
11398.434
24.928945
0.000213782
Residual
9
4115.132227
457.23691
Total
11
26912
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-52.02936652
20.66052304
-2.518299
0.03286026
-98.76671659
-5.292016438
Ads
7.644673824
1.311440785
5.8292177
0.00025016
4.677988665
10.61135898
Coupon Value
28.87526149
5.532146356
5.2195404
0.00054953
16.36067701
41.38984597
The multiple correlation coefficient between the dependent variable or response variable sales and the independent variables or predictors such as ads and coupon value is given as R = 0.9204 approximately. This means there is a strong positive correlation or association exists between the dependent variable or response variable sales and the independent variables or predictors such as ads and coupon value. The value of the R square or coefficient of determination is given as 0.8471 which means about 84.71% of the variation in the dependent variable sales is explained by the independent variables ads and coupon value. The p-value for this regression model is given as 0.00 approximately, this means the given regression model is statistically significant. The required regression equation is given as below:
Sales = -52.03 + 7.64*Ads + 28.88*Coupon value
Now, we have to find the predicted value for sales for ads = 8 and coupon value = $3
Sales = -52.03 + 7.64*8 + 28.88*3
Sales = $95.73
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.920374554
R Square
0.84708932
Adjusted R Square
0.813109169
Standard Error
21.3830988
Observations
12
ANOVA
df
SS
MS
F
Significance F
Regression
2
22796.86777
11398.434
24.928945
0.000213782
Residual
9
4115.132227
457.23691
Total
11
26912
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-52.02936652
20.66052304
-2.518299
0.03286026
-98.76671659
-5.292016438
Ads
7.644673824
1.311440785
5.8292177
0.00025016
4.677988665
10.61135898
Coupon Value
28.87526149
5.532146356
5.2195404
0.00054953
16.36067701
41.38984597
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