1. ] Below is the output of a multiple linear regression model. The dependent va
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Question
1. ] Below is the output of a multiple linear regression model. The dependent variable was Total Gross Revenue. This model looked at the Total Gross Revenue (in millions of dollars) of many different movies to try and determine which factors played a role in the movie’s earnings.
Coefficients
Estimate
Std. Error
t-statistic
p-value
Intercept
7.6760
6.7602
1.135
0.2995
Book Sales
0.8285
0.5394
1.536
0.1754
Production Cost
3.6616
1.1178
3.276
0.0169
Promotional Cost
7.6211
1.6573
4.598
0.0037
Adjusted R-Squared
0.95
a.) a. Write an interpretation for each of the coefficients (including the intercept). The intercept is in millions of dollars; Book Sales are in tens-of-thousands of books sold; Production Cost and Promotional Cost are both in millions of dollars (e.g., a Production Cost of $3 million implies x = 3).
b.) b. Do you think this model adequately describes the data? Why or why not?
c.) c. Suppose Movie X has sold 100,000 books, spent $10 million on production, and $5 million on promotion. What is the projected revenue for Movie X? Note the units here- books are measured in tens of thousands, so 100,000 books = 10. Production is in millions, so $10 million = 10, and 5 million = 5. You do NOT have to do any kind of unit conversion! Use 10 for books, 10 for production, and 5 for promotion.
d.) d. According to the model, which variable is the most important predictor of revenue for any given movie? Why?
e.) e. According to the model, which variable is the least important predictor of revenue for any given movie? Why?
Coefficients
Estimate
Std. Error
t-statistic
p-value
Intercept
7.6760
6.7602
1.135
0.2995
Book Sales
0.8285
0.5394
1.536
0.1754
Production Cost
3.6616
1.1178
3.276
0.0169
Promotional Cost
7.6211
1.6573
4.598
0.0037
Adjusted R-Squared
0.95
Explanation / Answer
Dependent variable : Total Gross Revenue
Independent variables : Book Sales, Production Cost and Promotional Cost.
a)Intercept is interpreted as the amount of total gross revenue in millions of dollars when all the independent variables are fixed at zero, i.e in this case 7.676 millions of dollars is the total gross revenue when no books are sold and both the costs are zero.
The coefficient for book sales is interpreted as the increase in the amount of total gross revenue in millions of dollars when book sales are increased by 10,000 and other variables are kept fixed, i.e if the book sales are increased by 10,000 the total gross revenue increases by 0.8285 millions of dollars provided other variables are kept fixed.
The coefficient for production cost is interpreted as the increase in the amount of total gross revenue in millions of dollars when production cost is increased by 1 million dollars and other variables are kept fixed, i.e if the production cost is increased by 1 million dollars the total gross revenue increases by 3.6616 millions of dollars provided other variables are kept fixed.
The coefficient for promotional cost is interpreted as the increase in the amount of total gross revenue in millions of dollars when promotional cost is increased by 1 million dollars and other variables are kept fixed, i.e if the promotional cost is increased by 1 million dollars the total gross revenue increases by 7.6211 millions of dollars provided other variables are kept fixed.
b)Yes this model adequately describes the data.
Adjusted R-square = 0.95 means that 95% of the total variability is explained by the regression fitted to the data which is quite a good amount.
c)Books sold = 10 (in 10-thousands)
Production Cost = 10 (in million dollars)
Promotional Cost = 5 ( in million dollars)
Regression Equation :
Total Gross Revenue = 7.676 + 0.8285*10 + 3.6616*10 + 7.6211*5
= 90.6825 million dollars
d) Promotional cost is the most important predictor for any movie since it has the lowest p-value.
Here, the null hypothesis is the particular variable is statistically insignificant and low p-value implies rejection of the null hypothesis which in turn implies the statistical significance of the variable.
e) Book Sales is the least important predictor since it has a large p-value ( >0.1) so by the same argument stated above, the variable book sales is statistically insignificant.
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