a. Explanation Given info: A sample of 50 observations is considered with one response variable ( y ), and six independent variables. The model of the firm is E ( y ) = β 0 + β 1 x i . where x i is the i th independent variable. The coefficients and standard errors are given. Calculation: The formula to find the test statistic is, t = β ^ i s β ^ i The best one-variable predictor of y is obtained by selecting the largest absolute t for the independent variables. To obtain the best one-variable predictor of y the absolute test statistic t value should be calculated. For variable x 1 , The value of t is obtained by substituting 1.6 as β ^ 1 , and 0.42 as s β ^ 1 in the test statistic formula, t = β ^ 1 s β ^ 1 = 1.6 0.42 = 3.81 Similarly, Independent variable t = β ^ i s β ^ i x 1 t = 3 b. To determine To Explain: The variables x 2 included in the model at this stage or not. c. To determine To Describe: The next phase that a stepwise procedure would execute.

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.

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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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Chapter 12.10, Problem 12.111LM

To determine

To Explain: Which independent variable is declared the best one-variable predictor of y.

To determine

To Explain: The variables x2 included in the model at this stage or not.

To determine

To Describe: The next phase that a stepwise procedure would execute.

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Chapter 12.9, Problem 12.110ACA

Chapter 12.10, Problem 12.112ACB

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The measure of standard error can also be applied to the parameter estimates resulting from linear regressions. For example, consider the following linear regression equation that describes the relationship between education and wage: WAGEi=β0+β1EDUCi+εi where WAGEi is the hourly wage of person i (i.e., any specific person) and EDUCi is the number of years of education for that same person. The residual εi encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero. Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates: WAGEi=−11.5+6.1 EDUCi If the standard error of the estimate of β1 is 1.32, then the true value of β1 lies between(4.78, 4.12, 3.46, 5.44) and (6.76, 7.42, 8.74) . As the number of observations in a data set grows, you would expect this range to (DECREASE , INCREASE) in size.

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Chapter 12 Solutions

Statistics for Business and Economics (13th Edition)

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Which independent variable is declared the best one-variable predictor of y .

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To Explain: Which independent variable is declared the best one-variable predictor of y.

To Explain: The variables x2 included in the model at this stage or not.

To Describe: The next phase that a stepwise procedure would execute.

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