Use computer software packages, such as Minitab or Excel, to solve this problenm
ID: 3363896 • Letter: U
Question
Use computer software packages, such as Minitab or Excel, to solve this problenm 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 Television Advertising ($1,000s) 5.0 2.0 Weekly Gross Revenue ($1,000s) 95 90 95 92 93 94 94 93 Newspaper Advertising ($1,000s) 1.5 2.0 2.5 3.0 3.5 2.5 3.0 2.5 3.3 2.3 4.2 2.5 a. Develop an estimated regression equation with the amount of television advertising as the independent variable (to 1 decimal) Revenue TVAdv b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables (to 2 decimals) Revenue NewsAdv c. Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? Select d. Predict weekly gross revenue for a week when $3.2 thousand is spent on television advertising and $2 thousand is spent on newspaper advertising? in thousandsExplanation / Answer
USing R studio:
code:
Revenue <- c(95,90,95,92,93,94,94,93)
TvAdv <- c(5,2,4,2.5,3,3.5,2.5,3)
NewsAdv <- c(1.5,2,1.5,2.5,3.3,2.3,4.2,2.5)
mod1 <- lm(Revenue~TvAdv)
summary(mod1)
Call:
lm(formula = Revenue ~ TvAdv)
Residuals:
Min 1Q Median 3Q Max
-1.57488 -0.41184 0.01449 0.38285 1.71981
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 88.7536 1.3686 64.849 9.04e-10 ***
TvAdv 1.4106 0.4132 3.414 0.0143 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.051 on 6 degrees of freedom
Multiple R-squared: 0.6601, Adjusted R-squared: 0.6035
F-statistic: 11.65 on 1 and 6 DF, p-value: 0.01426
Revenue=88.8+1.4 TvAdv
Solutionb:
mod2 <- lm(Revenue~TvAdv+NewsAdv)
summary(mod2)
Call:
lm(formula = Revenue ~ TvAdv + NewsAdv)
Residuals:
1 2 3 4 5 6 7
-0.78863 -0.51486 1.12969 0.04479 -0.68428 0.31894 0.40873
8
0.08563
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 84.7534 1.8684 45.362 9.83e-08 ***
TvAdv 1.9183 0.3610 5.314 0.00315 **
NewsAdv 0.9624 0.3807 2.528 0.05267 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7628 on 5 degrees of freedom
Multiple R-squared: 0.8508, Adjusted R-squared: 0.7911
F-statistic: 14.25 on 2 and 5 DF, p-value: 0.0086
Revenue=84.75+1.92TvAdv+0.96 News Adv
Solutionc:
For 1 case coeff for Tv Adv is 1.4
For 2 case coeff for Tva dv is 1.92
NO
Solutiond:
use the second reg equation
Revenue=84.75+1.92TvAdv+0.96 News Adv
Tv adv=3.2
NewsAdv=2
substitue in the above Reg eq
Revenue=84.75+1.92(3.2)+0.96 (2)
Revenue=$92.814
if we need to round to nearest integer it will be
Revenue=$93
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