/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 59 What does a linear correlation c... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 59

What does a linear correlation coefficient tell about the relationship between two variables? Within what range can a correlation coefficient assume a value?

Short Answer

Expert verified
The correlation coefficient, \( r \), quantifies the degree and direction of the linear relationship between two variables. Positive values indicate a direct relationship, negative values indicate an inverse relationship, and zero indicates no linear relationship. The correlation coefficient value can only fall within the range of -1 to 1.

Step by step solution

01

Understanding Correlation Coefficient

A correlation coefficient, denoted as \( r \), is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. A calculated number greater than 1.0 or less than -1.0 means that there was an error in the correlation measurement.
02

Interpretation of Correlation Coefficient Values

A correlation coefficient of 1 indicates a perfect positive correlation between the two variables - as one variable increases, the other one does too. A correlation coefficient of -1 indicates a perfect negative correlation between the variables - as one variable increases, the other one decreases. A correlation of 0 indicates no linear relationship between the variables.
03

Possible Value Range of Correlation Coefficient

The correlation coefficient can assume a value within the range of -1 to 1. The fact that its value is contained within this range makes it a useful, standardized measure of correlation.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Explain the meaning of independent and dependent variables for a regression model.

The following table containing data on the aerobic exercise levels (running distance in miles) and blood sugar levels for 12 different days for a diabetic is reproduced from Exercise \(13.27 .\) $$ \begin{array}{l|rrrrrrrrrrr} \hline \text { Distance (miles) } & 2 & 2 & 2.5 & 2.5 & 3 & 3 & 3.5 & 3.5 & 4 & 4 & 4.5 & 4.5 \\ \hline \text { Blood sugar }(\mathrm{mg} / \mathrm{dL}) & 136 & 146 & 131 & 125 & 120 & 116 & 104 & 95 & 85 & 94 & 83 & 75 \\ \hline \end{array} $$ a. Find the standard deviation of errors. b. Compute the coefficient of determination. What percentage of the variation in blood sugar level is explained by the least squares regression of blood sugar level on the distance run? What percentage of this variation is not explained?

A population data set produced the following information. $$ N=250, \quad \Sigma x=9880, \quad \Sigma y=1456, \quad \Sigma x y=85,080, \quad \Sigma x^{2}=485,870 $$ Find the population regression line.

A researcher took a sample of 10 years and found the following relationship between \(x\) and \(y\), where \(x\) is the number of major natural calamities (such as tornadoes, hurricanes, earthquakes, floods, etc.) that occurred during a year and \(y\) represents the average annual total profits (in millions of dollars) of a sample of insurance companies in the United States. $$ \hat{y}=342.6-2.10 x $$ a. A randomly selected year had 24 major calamities. What are the expected average profits of U.S. insurance companies for that year? b. Suppose the number of major calamities was the same for each of 3 years. Do you expect the average profits for all U.S. insurance companies to be the same for each of these 3 years? Explain. c. Is the relationship between \(x\) and \(y\) exact or nonexact?

A population data set produced the following information. $$ \begin{aligned} &N=460, \quad \Sigma x=3920, \quad \Sigma y=2650, \quad \Sigma x y=26,570 \\ &\Sigma x^{2}=48,530, \text { and } \Sigma y^{2}=39,347 \end{aligned} $$ Find the linear correlation coefficient \(\rho\).
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

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.