3rd Edition

ISBN: 9780135190210

Author: Gould

Publisher: PEARSON CO

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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 p…

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Textbook Question

Chapter 4, Problem 78CRE

Granola Bars The following table shows the fat content (in grams) and calories for a sample of granola bars. (Source: calorielab. com)

Chapter 4, Problem 78CRE, Granola Bars The following table shows the fat content (in grams) and calories for a sample of , example 1

Chapter 4, Problem 78CRE, Granola Bars The following table shows the fat content (in grams) and calories for a sample of , example 2

a. Use technology to make a scatterplot of the data. Use fat as the independent variable x and calories as the dependent variable y . Does there seem to be a linear trend to the data?

b. Compute the correlation coefficient and the regression equation, using fat as the independent variable and calories as the dependent variable.

c. What is the slope of the regression equation? Interpret the slope in the context of this problem.

d. What is the y-intercept of the regression equation? Interpret the y-intercept in the context of this problem or explain why it would be inappropriate to do so.

e. Find and interpret the coefficient of determination.

f. Use the regression equation to predict the calories in a granola bar containing 7 grams of fat.

g. Would it be appropriate to use the regression equation to predict the calories in a granola bar containing 25 grams of fat? If so, predict the number of calories in such a bar. If not, explain why it would be inappropriate to do so.

h. Looking at the scatterplot there is a granola bar in the sample that has an extremely high number of calories given the moderate amount of fat it contains. Remove its data from the sample and recalculate the correlation coefficient and regression equation. How did removing this unusual point change the value of r and the regression equation?

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

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Chapter 4, Problem 77CRE

Chapter 4, Problem 79CRE

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Solution Summary: The author explains how to plot a scatterplot using fat as an independent variable and calories as the dependent variable.

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