10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

Concept explainers

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 B.3, Problem 70E

Home Sale Prices. Refer to Exercise B.67 regarding the relationship between the sale price of a home and the predictor variables size in square feet and type of roof (tile or non-tile). In that exercise, we considered the regression of price on size and roof, the indicator variable for type of roof. Use the technology of your choice to obtain output similar to that in Outputs B.52–B.56 on pages B–9G–B-92.

a. Obtain a plot of price versus size with different plot symbols for homes having a tile roof and for homes having a non-tile roof. Based on this plot, does it appear that roof is a useful predictor variable? Explain your answer.
b. Obtain the regression analysis of price on size and roof. Conduct the t-tests for the individual utility of the two predictor variables at the 5% level of significance. Interpret your results.
c. Based on the output in part (b), obtain the individual regression equations relating price to size for homes having tile roofs and for homes having non-tile roofs.
d. Obtain plots of residuals versus fitted values, residuals versus size, residuals versus roof and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
e. Provide a scatterplot of price versus size with the individual regression lines for homes with the roofs and homes with non-tile roofs. Based on this plot and your residual analysis from part (d), do you feel that this model fits the data well? Explain your answer.
f. To check for possible interaction between the two predictor variables, perform the regression analysis of price on size, roof and roof-size. Is there an interaction between size and roof that is, is the cross-product term roof-size a useful predictor variable in the regression equation that also contains size and roof? Use α = 0.05.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter B.3, Problem 69E

Chapter B.3, Problem 71E

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Chapter B Solutions

Introductory Statistics (10th Edition)

Ch. B.1 - Regarding the regression of a response variable,...Ch. B.1 - Fill in the blanks. a. The assumption that all...Ch. B.1 - Answer true or false to each of the following...Ch. B.1 - Prob. 4E Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - Prob. 6E Ch. B.1 - Prob. 7E Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...

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Solution Summary: The author explains that roof is a useful predictor variable based on the price versus size plot.

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