1. A relationship between height (in inches) and arm length (in inches) was found to have acorrelation coefficient of r = 0.985. Describe the relationship between the variables.2. The scatterplot shows a relationship between the TVs purchased and price. Which bestdescribes the relationship between the variables? (Circle the letter of choice.)A. Strong, positive, linear correlationBest BuyB. Weak, positive, linear correlation150012501000C. Strong, negative, linear correlation750500D. Weak, negative, linear correlation2501020 30 40Number of TVs3. The table provides information on hours studied and corresponding test scores.Hours1233.54455.5StudiedTest658073828187908892Scorea. Using your calculator, calculate the correlation coefficient.b. Use part a to describe the relationship between the variables.Prices per TV 3. CONTINUED:c. Using your calculator, determine the regression equation.d. What is the rate of change AND interpret it in terms of the context of the problem.e. What is the y-intercept AND interpret it in terms of the context of the problem.f. Predict a student’s test score if they were to study for 2.5 hours.g. In part f, was this interpolation or extrapolation. Explain your answer.h. Predict a student’s test score if they were to study for 8 hours.i. In part h, was this interpolation or extrapolation. Explain your answer.

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Answered: 1. A relationship between height (in…

1. A relationship between height (in inches) and arm length (in inches) was found to have a correlation coefficient of r = 0.985. Describe the relationship between the variables.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

1. A relationship between height (in inches) and arm length (in inches) was found to have a
correlation coefficient of r = 0.985. Describe the relationship between the variables.
2. The scatterplot shows a relationship between the TVs purchased and price. Which best
describes the relationship between the variables? (Circle the letter of choice.)
A. Strong, positive, linear correlation
Best Buy
B. Weak, positive, linear correlation
1500
1250
1000
C. Strong, negative, linear correlation
750
500
D. Weak, negative, linear correlation
250
10
20 30 40
Number of TVs
3. The table provides information on hours studied and corresponding test scores.
Hours
1
2
3
3.5
4
4
5
5.5
Studied
Test
65
80
73
82
81
87
90
88
92
Score
a. Using your calculator, calculate the correlation coefficient.
b. Use part a to describe the relationship between the variables.
Prices per TV

3. CONTINUED:
c. Using your calculator, determine the regression equation.
d. What is the rate of change AND interpret it in terms of the context of the problem.
e. What is the y-intercept AND interpret it in terms of the context of the problem.
f. Predict a student’s test score if they were to study for 2.5 hours.
g. In part f, was this interpolation or extrapolation. Explain your answer.
h. Predict a student’s test score if they were to study for 8 hours.
i. In part h, was this interpolation or extrapolation. Explain your answer.

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