Question

2.) The data set named "HW 6.2" contains a random sample of 35 movies released in 2008 collected from the Internet Movie Database (IMDb). The goal of this problem is to explore if the information available soon after a movie's theatrical release can successfully predict total revenue. All dollar amounts (i.e., variables "Budget", "Opening", and "USRevenue") are measured in millions of dollars. . Investigate the relationship between the explanatory variable "Budget" and response variable "USRevenue" by doing the following: a. i. Make a scatterplot. - ii. Calculate the correlation coefficient. - ii. Interpret the scatterplot and correlation coefficient in terms of trend, strength, and shape. - Repeat part (a) for the explanatory variable "Opening". Repeat part (a) for the explanatory variable "Theaters". . Based on your findings in parts (a) through (c), which of the three explanatory variables would be most appropriate for predicting the response variable "USRevenue"? Justify your choice in a few sentences. » For the "most appropriate" variable identified in part (d), run a Simple Linear Regression analysis. Please include: b. c. d. e. i. The regression equation. . ii. iii. Interpret the slope of the regression line (in context of this data set). - Is it meaningful to interpret the y-intercept? why or why not? ' iv. State r-squared (i.e., the coefficient of determination) and explain what this value means (in context of the data set). f. Use the regression equation from part (e) to predict the total US revenue for the movie "Get Smart". (Note: Get Smart is not included in the dataset, but it's Budget was 80 million dollars; it was shown in 3911 theaters; and its opening weekend revenue was 38.7 million dollars.) State your predicted value in a sentence that is in context of the data including units Note: You can do this calculation "by hand" or using Mintab Is your prediction in part (e) an example of extrapolation? Why or why not?. RatingGenre Budget USRevenu Opening Theaters 180 152.6 4056 3285 2812 1291 2988 1379 1591 4114 2986 2735 2466 2700 4366 2543 3175 1850 3434 2808 2030 3760 3510 2651 3060 1185 3560 808 3428 3965 3606 2436 2532 2123 1690 4105 2464 2 |Madagasc PG 3 ISex and th R 4 The Ruins R Animation Comedy Horror Drama 8 6 The Curiou PG-13 Drama 7 Redbelt R 8 The Secret PG-13 Drama 127.5 Action 130 Animation Dram Comedy Horror 215.4 10 The HappeR 11 Zach and IR 12 The Strang R 13 Prom Nigh PG-13 Horro 14 The Dark k PG-13 Action 15 Baby Mam PG-13 Comedy 16 Wanted R 17 Changelin R 18 Yes Man PG-13 Comedy 19 The Expres PG 158.4 533.3 185 Action Drama 134.3 Drama PG-13 Drama 21 The Mumr PG-13 Action 22 Eagle Eye PG-13 Action 102.2 101.1 Comedy Horror Action 25 Miracle an R 26 The Day th PG-13 Drama 27 Be Kind Re PG-13 Comedy 28 Jumper PG-13 Action 29 Hancock PG-13 Action 30 Speed Rac PG 227.9 Action Drama Action Comedy Drama 120 32 |Death Rac R 33 College R 34 |Blindness R 35 Iron Man PG-13 Action 36 |Lakeview 1PG-13 Drama 318.3 102.1

Answer 1

Solved by using R-software

a)

Analysis for the explanatory variable x= 'Budget' and response variable y= 'USRevenue'

> x=scan("clipboard")
Read 35 items
> y=scan("clipboard")
Read 35 items

i)

> plot(x,y)

髦3 髦3 9 08 oo 100 50 150 0

ii)

> cor(x,y)
[1] 0.791832

iii)

Correlation coefficient indicates that Budget and USRevenue are 79% correlated with each other, and from scatter plot we see there is no linear trend.

b)

Analysis for the explanatory variable x1= 'Opening' and response variable y= 'USRevenue'

> y=scan("clipboard")
Read 35 items
> x1=scan("clipboard")
Read 35 items

> plot(x1,y)

髦3 髦3 150 100 50 0 r1

> cor(x1,y)
[1] 0.9840788

From the scatter plot we see that the Opening and USRevenue are linearly related with each other. Correlation coefficient shows that 98% correlation is there.

c)

Analysis for the explanatory variable x2= 'Theaters' and response variable y= 'USRevenue'

> x2=scan("clipboard")
Read 35 items
> y=scan("clipboard")
Read 35 items

> plot(x2,y)

髦3 o O 髦3 1000 1500 2000 2500 3000 3500 4000 4500

> cor(x2,y)
[1] 0.7152985

From scatter plot we see that there is no linear relationship between Theaters and USRevenue. Correlation coefficient shows that 71% correlation is there.

d)

From the findings of a,b,c the explanatory variable 'Opening' is most appropriate for predicting response variable 'USRevenue'. The scatter plot of Opening and USRevenue shows linear trend.

e)

> m=lm(y~x1)
> summary(m)

Call:
lm(formula = y ~ x1)

Residuals:
Min 1Q Median 3Q Max
-35.038 -11.898 1.720 7.827 46.250

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -6.918 4.378 -1.58 0.124
x1 3.278 0.103 31.81 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 19.17 on 33 degrees of freedom
Multiple R-squared: 0.9684, Adjusted R-squared: 0.9675
F-statistic: 1012 on 1 and 33 DF, p-value: < 2.2e-16

i)

Regression equation is

USRevenue = -6.918 + 3.728 Opening

ii)

As the Hypothesis of slope is rejected, the slope of the line is not zero. i.e. the variable Opening is may not be zero in the regression model.

iii)

As the Hypothesis of slope is accepted, the y-intercept of the regression line may be zero.

iv)

Multiple R-squared = 0.9684

It shows that 96% variability in the USRevenue was explained by the variable Opening.