Q. 4.72 - Elementary Statistics

Question

Movie Grosses. Box Office Mojo collects and posts data on movie grosses. For a random sample of 50 movies, we obtained both the domestic (U.S.) and overseas grosses, in millions of dollars. The data are presented on the Weiss Stats site.

a. Obtain a scatterplot for the data.

b. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f).

Step-by-Step Solution

Answer

a. Obtained scatterplot for the data is,

b. The regression line does not make sense because the data has a large curvature.

Part (a) Step 1: Given Information

The number sample of movies are $n=50$

Make a scatter plot with the data obtained from the box office mojo.

Part (a) Step 2: Explanation

Based on the question, let's look at an international and domestic movie collection of 50 movies each.

MATLAB will then create a scatterplot with data collection on the $x-$axis and overseas data collection on the $y-$axis.

Program:

clc

clear

close all

$n=50;$

domestic $=$randi $(500, n, 1);$

overseas $=$randi $(700, n, 1);$

scatter $(domestic, overseas,\text{'}linewidth\text{'}, 1.2)$

set$(gca,\text{'}linewidth\text{'}, 1.2,\text{'}fontsize\text{'}, 12)$

box on

xlabel $(\text{'}domestic collection (million\$)\text{'})$

ylabel $(\text{'}overseas collection (million\$)\text{'})$

title $(\text{'}N=50\text{'})$

axis square

The scatterplot representation is,

Query:

As a first step, we have defined the sample size of 50 movies at home and abroad.

After that, create a scatter plot.

$X$ represents the domestic collection axis.

$Y$represents the overseas collection.

Part (b) Step 1: Given Information

Draw a regression line and show whether or not it is realistic. 

Part (b) Step 2: Explanation

If the data does not have a strong curvature, the regression line is plausible. 

Let's take a 50 movie collection from both domestic and international sources, as suggested in the question.

Then create a scatter plot in MATLAB. 

Domestic data gathering is on the x-axis, whereas abroad data collection is on the y-axis.

If the data collection has a higher curvature, the regression line will be useless.

Program:

Clc

clear

close all

$n=50 ;$

domestic$=randi (500, n, 1)$

overseas $= randi (700, n, 1)$

$[\mathrm{p},\mathrm{s}]=\text{ polyfit (domestic, overseas, }1)\text{; }$

$\left[\mathrm{y}\text{ \_fit, delta] = polyval }\right(\mathrm{p},\text{ domestic, }\mathrm{s})\text{; }$

scatter$(domestic, overseas, \text{'}linewidth\text{'} , 1.2)$

hold on

plot$(domestic,y\_fit,\text{'}r-\text{'},\text{'}linewidth\text{'},1.2)$

set$(gca,\text{'}linewidth\text{'},1.2,\text{'}fontsize\text{'}, 12)$

box on

xlabel$(\text{'}Domestic collection (million\$)\text{'})$

ylabel $(\text{'}Overseas collection (million\$)\text{'})$

title $(\text{'}N = 50\text{'} )$

axis square

The data has a high curvature, as shown in the figure, so the regression line isn't plausible. 

Query:

• First, we established the data collection of 50 example movies from both domestic and international locations. 
• After that, make a scatter plot.
• After that, draw a regression line.
• Domestic collection is shown on the x-axis.
• Overseas collection identifier on the Y-axis.