Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q. 65 (page 721)

65. Explain what it means when a correlation has anr2 of 0.72.

Short Answer

Expert verified

A correlation has an r2of 0.72, it means that the 72% of the dependent variable can be justified by the independent variable utilizing the regression line.

Step by step solution

01

Given information

A correlation has an r2of 0.72. Correlation is a statistical estimation that represents how two variables are linearly connected.

02

Explanation

The ratio of explained variation to total variation in the model is known as the coefficient of determination. The coefficient of determination, abbreviated as r2, is a metric for determining the regression line's quality of fit. It's the correlation coefficient squared.

Here, it is delivered that r2=0.72, which indicates that the 72%of variation in the dependent variable can be clarified by the independent variable utilizing the regression line.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For a given line of best fit, you computed that r=0.6501using n=12data points and the critical value is 0.576. Can the line be used for prediction? Why or why not?

Using the data to determine the linear-regression line equation with the outliers removed. Is there a linear correlation for the data set with outliers removed? Justify your answer.

If the level of significance is 0.05 and the p-value is 0.04, what conclusion can you draw?

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level).

a. Using “stories” as the independent variable and “height” as the dependent variable, make a scatter plot of the data.

b. Does it appear from inspection that there is a relationship between the variables?

c. Calculate the least squares line. Put the equation in the form of: \(\hat{y}=a+bx\)

Table 12.20 shows the life expectancy for an individual born in the United States in certain years.

a. Decide which variable should be the independent variable and which should be the dependent variable.

b. Draw a scatter plot of the ordered pairs.

c. Calculate the least squares line. Put the equation in the form of: \(\hat{y}=a+bx\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free