91Ó°ÊÓ

Do Movies with Larger Budgets Get Higher Audience Ratings? The dataset HollywoodMovies2011 is introduced on page \(93,\) and includes many variables for movies that were produced in Hollywood in 2011, including Budget and AudienceScore. (a) Use technology to create a scatterplot to show the relationship between the budget of a movie, in millions of dollars, and the audience score. We want to see if the budget has an effect on the audience score. (b) Is there a linear relationship? How strong is it? Give your answer in the context of movies. (c) There is an outlier with a very large budget. What is the audience rating for this movie and what movie is it? There is another data value with a budget of about 125 million dollars and an audience score over 90 . To what movie does that dot correspond? (d) Use technology to find the correlation between these two variables.

Step by step solution

01

Creating a scatterplot

Using your preferred technology tool (like Python's matplotlib, Excel, etc.), plot a scatterplot with Budget (in million dollars) on the x-axis and Audience Score on y-axis.

02

Analyzing relationship

Observe the plot and analyze if there's a linear relationship between variables. A close to upward sloping straight line would indicate a positive relationship. The stronger the relationship the closer data points are to that line. Give your observation in context of movies, i.e., if higher budget movies tend to have higher audience scores or not.

03

Identifying the outlier

Identify the movie with the highest budget (outlier) and note its audience score. Similarly, identify the movie with a budget of about 125 million dollars and an audience score over 90. Find out their names in the given dataset.

04

Finding correlation

Calculate the correlation coefficient (r) between the two variables using technology (this function is available in Excel, Python's numpy etc.). Correlation coefficient r ranges from -1 to +1. It measures the strength and direction of the linear relationship, with -1 indicating a strong negative linear correlation, +1 indicating a strong positive linear correlation, and 0 indicating no correlation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Scatterplot Analysis

Scatterplot analysis is a powerful way to visualize the relationship between two variables. In the context of our movie dataset, we plot the movie budget on the x-axis and the audience score on the y-axis. Each point on the scatterplot represents a movie, showing both its budget and how it was rated by the audience.

Creating a scatterplot involves following some simple steps:

• Select the data: movie budgets and their corresponding audience scores.
• Choose your preferred technology or tool, such as Excel or Python's Matplotlib, to create the plot.
• Label the axes appropriately - "Budget ($ million)" and "Audience Score".

Once your scatterplot is ready, it provides an instant visual snapshot and makes it easier to identify trends, clusters, and outliers in the data. Looking at the dots can help us understand if there's a visible trend between how much is spent on a movie and how well it is received by the audience. Although scatterplots do not provide numerical values for correlation, they set the groundwork for further analysis.

Linear Relationship

In statistics, a linear relationship occurs when changes in one variable directly correlate to changes in another, and this relationship can often be represented as a straight line in a scatterplot. For our exercise, we want to determine if higher movie budgets are linked to higher audience scores.

To assess the linear relationship in our scatterplot, you should:

• Examine the scatterplot to see if the data points form a pattern resembling a straight line.
• Check the slope of this line – an upward slope suggests a positive correlation where higher budgets lead to higher scores.
• Look at the proximity of the data points to the line – the closer they are, the stronger the linear relationship.

A strong linear relationship implies that variations in one variable predict variations in the other. The next step typically involves calculating the correlation coefficient, which quantifies the linear relationship's strength and direction between budget and audience score.

Outlier Identification

Identifying outliers is crucial since they can significantly affect the results of your analysis. An outlier is a data point that differs significantly from other observations. In a scatterplot of movie budgets and audience ratings, an outlier might be a movie that had either an exceptionally high budget or an unusually high or low audience score.

To identify outliers in your scatterplot:

• Look for points that stand apart from the dense clusters of data.
• Note particularly high or low values on either the x-axis or y-axis.

In our exercise, one outlier was identified with a very large budget not matched by a proportional audience score. Another point corresponds to a movie with a budget around 125 million dollars, achieving an audience score of over 90. Knowing the identity of these outliers is key to understanding their impact. Often, they might represent movies with exceptional characteristics or factors not captured by the simple budget versus audience score metric.