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Exam 17: Multiple Regression

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Question 51

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The adjusted coefficient of determination is adjusted for the:

A) number of independent variables and the sample size.
B) number of dependent variables and the sample size.
C) coefficient of correlation and the significance level.
D) number of regression parameters including the y -intercept.

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Question 52

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When an additional explanatory variable is introduced into a multiple regression model, the coefficient of determination will never decrease.

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Question 53

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Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below. SUMMARY OUTPUT ANOVA {Real Estate Builder Narrative} Suppose the builder wants to test whether the coefficient on education is significantly different from 0. What is the value of the relevant t -statistic?

If all the points for a multiple regression model with two independent variables were right on the regression plane, then the coefficient of determination would equal:

A(n)____________________ value of the F -test statistic indicates that the multiple regression model is valid.

In a multiple regression model, the value of the coefficient of determination has to fall between

From the coefficient of determination, we cannot detect the strength of the relationship between the dependent variable y and any individual independent variable.

The total variation in y in a regression model will never exceed the regression sum of squares (SSR).

Some of the requirements for the error variable in a multiple regression model are that the standard deviation is a(n)____________________ and the errors are ____________________.

Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below. SUMMARY OUTPUT ANOVA {Real Estate Builder Narrative} What percentage of the variability in house size is explained by this model?

A high value of the coefficient of determination significantly above 0 in multiple regression, accompanied by insignificant t -statistics on all parameter estimates, very often indicates a high correlation between independent variables in the model.

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

A small value of F indicates that most of the variation in y is explained by the regression equation and that the model is useful.

Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below. SUMMARY OUTPUT ANOVA   {Real Estate Builder Narrative} One individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet. What is the residual (in hundreds of square feet)for this data point?

A high correlation between two independent variables is an indication of ____________________.

When an explanatory variable is dropped from a multiple regression model, the adjusted coefficient of determination can increase.

In a multiple regression analysis involving k independent variables and n data points, the number of degrees of freedom associated with the sum of squares for error is:

The coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

Multiple regression has four requirements for the error variable. One is that the probability distribution of the error variable is ____________________.

Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below. SUMMARY OUTPUT ANOVA   {Real Estate Builder Narrative} What is the predicted house size for an individual earning an annual income of $40,000, having a family size of 4, and having 13 years of education?