Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

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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 p…

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Textbook Question

Chapter 12.12, Problem 12.121LM

Consider fitting the multiple regression model

E ( y ) = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 + β 5 x 5

A matrix of correlations for all pairs of independent variables is given below. Do you detect a multicollinearity problem? Explain.

Chapter 12.12, Problem 12.121LM, Consider fitting the multiple regression model E(y)=0+1x1+2x2+3x3+4x4+5x5 A matrix of correlations

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Chapter 12.12, Problem 12.120LM

Chapter 12.12, Problem 12.122ACB

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We have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.

The least-squares regression equation is y = 753.6x + 12,900 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a 55000- linear relation between the two variables with a correlation coefficient of 0.8274. Complete parts (a) through (d). 20000+ 15 20 25 30 35 40 45 50 55 60 Bachelor's % (a) Predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree. (Round to the nearest dollar as needed.) (b) In a particular region, 28.8 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,925. Is this income higher than what you would expect? Why? This is than expected because the expected income is $ (Round to the nearest dollar as needed.) (c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal. Do not…

The least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. In a particular region, 28.3 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,389. Is this income higher than what you would expect? Why?

Chapter 12 Solutions

Statistics for Business and Economics (13th Edition)

Ch. 12.3 - Write a first-order model relating E(y) to a. two...Ch. 12.3 - Minitab was used to fit the model E(y) = (0 + 1x1...Ch. 12.3 - Suppose you fit the multiple regression model y =0...Ch. 12.3 - Suppose you fit the first-order multiple...Ch. 12.3 - Prob. 12.5LM Ch. 12.3 - Prob. 12.6LM Ch. 12.3 - Prob. 12.7LM Ch. 12.3 - If the analysis of variance F-test leads to the...Ch. 12.3 - Ambiance of 5-star hotels. Although invisible and...Ch. 12.3 - Forecasting movie revenues with Twitter. Refer to...

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Consider fitting the multiple regression model E ( y ) = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 + β 5 x 5 A matrix of correlations for all pairs of independent variables is given below. Do you detect a multicollinearity problem? Explain.

Solution Summary: The author explains that the matrix shows the correlation for all pairs of independent variables. If left|rright|ge 0.8 there is extreme multicollinearity in the model.

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Chapter 12 Solutions