In order to solve this question I used R software.
R codes and output:
> d=read.table('data.csv',header=T,sep=',')
> head(d)
Revenue TV Newspaper
1 101.3 4.9 1.4
2 52.9 3.1 3.2
3 75.8 4.2 1.5
4 127.2 4.5 4.3
5 137.8 3.6 4.0
6 102.4 3.5 2.3
> attach(d)
> fit=lm(Revenue ~ TV)
> summary(fit)
Call:
lm(formula = Revenue ~ TV)
Residuals:
Min 1Q Median 3Q Max
-49.221 -28.623 -7.739 17.779 82.130
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -52.783 70.89 -0.745 0.4847
TV 41.491 15.47 2.682 0.0364 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 47.79 on 6 degrees of freedom
Multiple R-squared: 0.5452, Adjusted R-squared: 0.4694
F-statistic: 7.192 on 1 and 6 DF, p-value: 0.03645
> fit2=lm(Revenue ~ TV + Newspaper)
> summary(fit2)
Call:
lm(formula = Revenue ~ TV + Newspaper)
Residuals:
1 2 3 4 5 6 7 8
5.858 -34.433 -5.100 -13.891 23.540 22.755 6.147 -4.875
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -46.208 33.678 -1.372 0.22841
TV 23.485 8.302 2.829 0.03672 *
Newspaper 18.980 4.081 4.651 0.00558 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 22.68 on 5 degrees of freedom
Multiple R-squared: 0.9146, Adjusted R-squared: 0.8804
F-statistic: 26.78 on 2 and 5 DF, p-value: 0.002131
a.
y = -52.783 + 41.491 x
Since p-value for testing slope coefficient of TV is 0.0364, which is less than 0.05, hence we conclude that Slope coefficient is statistically significant. Which ultimately implies that there is significant relationship between television advertising and weekly gross revenue.
b.
54.52% variation.
c.
y = -46.208 + 23.485 x1 + 18.980 x2
P-value for intercept is greater than 0.05, hence intercept is not statistically significant. P-value for slope coefficient and are less that 0.05, hence these variables are statistically significant.
d.
91.46% variation.
e.
R^{2} and adjusted R^{2} both are high for second model, it means second model will explain more variation in the weekly gross revenue. Hence we choose second model for prediction.
f.
Manager would prefer model 2.
Problem 7-9 Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several...
12.3 A statistical program is recommended. The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let x, represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) Develop an estimated...
The owner ot Showtime Movie Theaters, Inc., would ike to prodict wecey grosa revenue as a function of advertising expenditures. Historical data for a sample of cight weeks tollow. Weekly Television Newspaper Advertising Advertising ($1,000s)(1,000s) (1,000s) 5.0 2.0 96 1.5 2.0 1.5 90 3.5 2.5 3.0 94 (a) Develop an etimated regression equation with the amount of television adwartising as the indapendent variable. (Round your numerical values to two decimal places. Lot x represent the amount of television advertising in...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks are entered into the Microsoft Excel Online file below. Use the XLMiner Analysis ToolPak to perform your regression analysis in the designated areas of the spreadsheet. Open spreadsheet a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 2 decimals). Revenue = TVAdv b. Develop...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks are entered into the Microsoft Excel Online file below. Use the XLMiner Analysis ToolPak to perform your regression analysis in the designated areas of the spreadsheet Open spreadsheet a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 2 decimals). Revenue = + TVAdv b....
Repair Time in Months Since Last Hours 2.9 3.0 Service 2 6 8 3 2 7 Type of Repair Repairperson Electrical Mechanical Electrical Mechanical Electrical Electrical Mechanical Mechanical Electrical Electrical Donna Newton Donna Newton Bob Jones Donna Newton Donna Newton Bob Jones Bob Jones Bob Jones Bob Jones Donna Newton 1.8 2.9 4.9 4.2 8 4 6 d Create a new dummy variable that is equal to。if the repairperson s Bob ones and 1 the repairperson s or na Newton...
The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (1) and newspaper advertising (C2). Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 2.5 The estimated regression equation was y = 85.5+ 2.0621 -0.37x2. The computer solution provided SST = 26, SSR = 24.356. a. Compute RP (to 3 decimals). Compute RX (to 3 decimals). b. When television advertising was the only independent variable, R2 =...
Question 1The owner of Showtime Movie Theaters, Inc. would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. (6 points) Weekly Gross Revenue Newspaper Advertising Advertising ($1000s) Televison ($1000s) (s1000s) 96 5.0 1.5 2.0 2.0 90 95 4.0 1.5 92 2.5 2.5 3.3 95 3.0 3.5 2.3 94 2.5 4.2 94 94 3.0 2.5 b. Develop an estimated regression equation with both television advertising and news- paper advertising...
The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (1) and newspaper advertising (2). Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 2.5 لما الما ا ل The estimated regression equation was y = 84.6 + 1.38001 - 1.29.02. The computer solution provided SST = 17.5, SSR = 16.412. a. Compute R (to 3 decimals). Compute R (to 3 decimals). = 0.475. Are the multiple...
The owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (1) and newspaper advertising (22) Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 1.5 البة بة جة The estimated regression equation was y = 88.4 +1.85&1 - 0.1722 The computer solution provided SST = 23.5, SSR = 22.035. a. Compute R2 (to 3 decimals). Compute R2 (to 3 decimals). Compute RX (to 3 decimals). b. When...
Question 1The owner of Showtime Movie Theaters, Inc. would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. (6 points) Weekly Gross Revenue Newspaper Advertising Advertising ($1000s) Televison ($1000s) (s1000s) 96 5.0 1.5 2.0 2.0 90 95 4.0 1.5 92 2.5 2.5 3.3 95 3.0 3.5 2.3 94 2.5 4.2 94 94 3.0 2.5 Question 2: In Question 1, the owner of Showtime Movie Theaters, Inc. used multiple...