5. A bookstore chain sees its annual revenue as well as annual advertising expen
ID: 3277782 • Letter: 5
Question
5. A bookstore chain sees its annual revenue as well as annual advertising expenditure (both in millions of dollars) grow as follows:
Year 1 2 3 4 5
Revenues 18 21 25 30 33
Adv. Exp. 0.12 0.15 0.18 0.24 0.29
a. Develop a time series Regression to forecast revenue for year 6. What do the regression parameters represent in this situation?
b. Develop a causal Regression model and forecast revenue if advertising expenditure is expected to be 0.35 (in millions of dollars). What do the regression parameters represent here?
Please show step by step solution
Explanation / Answer
Part a
Here, we have to develop a time series regression equation for the estimation of revenue for year 6. For this regression model, the response variable represents the revenue and explanatory variable represent the year. The required regression model is given as below:
Regression Statistics
Multiple R
0.996403454
R Square
0.992819843
Adjusted R Square
0.990426458
Standard Error
0.605530071
Observations
5
ANOVA
df
SS
MS
F
Significance F
Regression
1
152.1
152.1
414.8182
0.000258778
Residual
3
1.1
0.366667
Total
4
153.2
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
13.7
0.635085296
21.57191
0.000218
11.67887515
15.7211249
Year
3.9
0.191485422
20.36709
0.000259
3.290607928
4.50939207
The required regression model or equation is given as below:
Revenue = 13.7 + 3.9*Year
Where Y-intercept is given as 13.7 which indicate the value of revenue at base year and slope is given as 3.9 which indicate per year increment in the revenue. Positive slope indicates a positive linear relationship.
Now, we have to find estimate for revenue for year 6.
Revenue = 13.7 + 3.9*Year
Revenue = 13.7 + 3.9*6
Revenue = $37.1 million
Part b
In this part we have to develop the regression model for the estimation of revenue for the given advertisement expenditure. For this regression model, response variable is given as revenue and explanatory variable is given as advertisement expenditure. The required regression model is given as below:
Regression Statistics
Multiple R
0.991476657
R Square
0.983025961
Adjusted R Square
0.977367947
Standard Error
0.931025032
Observations
5
ANOVA
df
SS
MS
F
Significance F
Regression
1
150.5995772
150.5996
173.7405
0.000943393
Residual
3
2.600422833
0.866808
Total
4
153.2
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
7.913319239
1.390455254
5.691171
0.010754
3.488270054
12.3383684
Adv. Exp.
89.21775899
6.768630272
13.18107
0.000943
67.67695659
110.758561
Regression equation is given as below:
Revenue = 7.91 + 89.22*Adv. Exp.
Where y-intercept is given as 7.91 which represent the revenue when advertising expenditure is zero, slope for this regression equation is given as 89.22 which indicate per unit increase in revenue.
Now, we have to find revenue for adv. Exp. = 0.35
Revenue = 7.91 + 89.22*Adv. Exp.
Revenue = 7.91 + 89.22*0.35
Revenue = $39.137 million
Regression Statistics
Multiple R
0.996403454
R Square
0.992819843
Adjusted R Square
0.990426458
Standard Error
0.605530071
Observations
5
ANOVA
df
SS
MS
F
Significance F
Regression
1
152.1
152.1
414.8182
0.000258778
Residual
3
1.1
0.366667
Total
4
153.2
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
13.7
0.635085296
21.57191
0.000218
11.67887515
15.7211249
Year
3.9
0.191485422
20.36709
0.000259
3.290607928
4.50939207
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