Question

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. Weekly Gross Televison Newspaper Advertising ($1000s) Advertising ($1000s) Revenue ($1000s) 97 5 1.5 2 06 96 4 2.5 93 3.5 2.5 96 4 3.3 94 3.5 3.3 94 2.5 5.2 95 4 2,5 a. Use o 0.01 to test the hypotheses H8 and/or B is not equal to zero for the model y = Bo +B1 B22, where television advertising ($1000s) 2newspaper advertising ($1000a) Compute the F test statistic (to 2 decimals). Use F table. What is the p-value? - Select your answer What is your conclusion? Select your answer b. Use a 0.05 to test the significance of B. Compute the t test statistic (to 2 decimals). Use t table. What is the p-value? - Select your answer What is your conclusion? - Select your answer Should1 be dropped from the model? - Select your answer- c. Use a 0.05 to test the significance of B. Compute the t test statistic (to 2 decimals). Use t table. what is the p-value? Select your answer What is your conclusion? - Select your answer Should 22 be dropped from the model? - Select your answer st st

Answer 1

Hi,

Just run the below code in R,

y <- c(97,90,96,93,96,94,94,95)
x1 <- c(5,2,4,3.5,4,3.5,2.5,4)
x2<- c(1.5,2,2.5,2.5,3.3,3.3,5.2,2.5)
model <- lm(y~x1+x2)
model
summary(model)

You'll get,

> y <- c(97,90,96,93,96,94,94,95)
> x1 <- c(5,2,4,3.5,4,3.5,2.5,4)
> x2<- c(1.5,2,2.5,2.5,3.3,3.3,5.2,2.5)
> model <- lm(y~x1+x2)
> model

Call:
lm(formula = y ~ x1 + x2)

Coefficients:
(Intercept) x1 x2
82.9754 2.5085 0.8642

> summary(model)

Call:
lm(formula = y ~ x1 + x2)

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 82.9754 1.4926 55.593 3.56e-08 ***
x1 2.5085 0.2902 8.643 0.000343 ***
x2 0.8642    0.2434 3.550 0.016386 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6517 on 5 degrees of freedom
Multiple R-squared: 0.9373,   Adjusted R-squared: 0.9122
F-statistic: 37.37 on 2 and 5 DF, p-value: 0.0009843

From this,

a.

F-statistic: 37.37

p-value: 0.0009843

Here, the p-value is less than 0.01 hence we reject the null hypothesis.

b.

t-statistics: 8.643

p-value: 0.000343

Here, the p-value is less than 0.05, hence beta1 is significant.

x1 shouldn't drop from the model.

c.

t-statistics: 3.550

p-value: 0.016386

Here, the p-value is greater than 0.05, hence beta2 is not significant.

x2 should drop from the model.