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If a stepwise regression procedure is used to enter, one at a time, three variables into a regression model, the resulting regression equation may differ from the regression equation that occurs when all three variables are entered at one step.

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Which of the following statements is true?


A) Thevalue will tend to be smaller than the adjustedvalue when insignificant independent variables are included in the model.
B) The y -intercept will usually be negative in a multiple regression model when the regression slope coefficients are positive.
C) If the confidence interval estimate for the regression slope coefficient, based on the sample information, crosses over zero, then the true population regression slope coefficient could be zero.
D) The x-intercept will usually be positive in a multiple regression model when the regression slope coefficients are negative.
E) None of these.

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Which of the following statements is correct?


A) The number of dummy variables that must be added to a regression model is one less than the number of categories for a qualitative independent variable.
B) A dummy variable is incorporated into a regression model if the dependent variable is qualitative.
C) Including a dummy variable into a regression model will simplify the regression results and help people to interpret the meaning of the regression parameters.
D) The number of dummy variables that must be added to a regression model is one more than the number of categories for a qualitative independent variable.
E) All of these.

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Discuss some of the signals for the presence of multicollinearity.

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There are several clues to the presence of multicollinearity: a. An independent variable known to be an important predictor ends up having a partial regression coefficient that is not significant. b. A partial regression coefficient exhibits the wrong sign. c. When an independent variable is added or deleted, the partial regression coefficients for the other variables change dramatically. A more practical way to identify multicollinearity is through the examination of a correlation matrix, which is a matrix that shows the correlation of each variable with each of the other variables. A high correlation between two independent variables is an indication of multicollinearity.

In a multiple regression analysis involving 24 data points, the mean squares for error, MSE, is 2, and the sum of squares for error, SSE, is 36. The number of the predictor variables must be:


A) 7
B) 6
C) 5
D) 4
E) 3

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In a multiple regression model, the coefficient of determination (sometimes called multiple In a multiple regression model, the coefficient of determination (sometimes called multiple ) can be simply computed by squaring the largest correlation coefficient between the dependent variable, and any independent variable. ) can be simply computed by squaring the largest correlation coefficient between the dependent variable, and any independent variable.

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Which of the following statements regarding multicollinearity is not true?


A) It exists in virtually all multiple regression models.
B) It is also called collinearity and intercorrelation.
C) It is a condition that exists when the independent variables are highly correlated with the dependent variable.
D) It does not affect the F-test of the analysis of variance.
E) All of these.

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C

A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted multiple coefficient of determination. Then, the adjusted multiple coefficient of determination is:


A) 0.385
B) 0.877
C) 0.591
D) 0.736
E) 0.819

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In regression analysis, a p-value provides the probability (judged by the t-value associated with an estimated regression coefficient) of In regression analysis, a p-value provides the probability (judged by the t-value associated with an estimated regression coefficient) of being true, given the claim : The true regression coefficient equals 0. being true, given the claim In regression analysis, a p-value provides the probability (judged by the t-value associated with an estimated regression coefficient) of being true, given the claim : The true regression coefficient equals 0. : The true regression coefficient equals 0.

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In testing the validity of a multiple regression model, a large value of the F-test statistic indicates that:


A) most of the variation in the independent variables is explained by the variation in y
B) most of the variation in y is explained by the regression equation
C) most of the variation in y is unexplained by the regression equation
D) the model provides a poor fit
E) most of the variation in y is explained by the regression equation and the model provides a poor fit

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Stepwise regression is a statistical technique that is always implemented when developing a regression model to fit a nonlinear relationship between the dependent and potential independent variables.

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In a multiple regression model, which of the following statements is false?


A) The coefficient of determination will be equal to the square of the largest correlation value between the dependent variable and the independent variables.
B) The mean of the residuals is equal to the variance of all combinations of levels of the independent variables.
C) Adding more independent variables that have a low correlation with the dependent variable will decrease the value of the coefficient of multiple determination.
D) All of these.
E) None of these.

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An engineer was investigating the relationship between the thrust of an experimental rocket (y), the percent composition of a secret chemical in the fuel (x1) and the internal temperature of a chamber of the rocket (x2). The engineer starts by fitting a quadratic model, but he believes that the full quadratic model is too complex and can be reduced by only including the linear terms and the interaction term. The engineer obtained a random sample of 66 measurements and computed the SSE for both the complete model and the reduced model. The values were 1477.8 and 1678.8, respectively. Perform the appropriate test of hypothesis to determine whether the reduced model is adequate for the engineer's use. Use An engineer was investigating the relationship between the thrust of an experimental rocket (y), the percent composition of a secret chemical in the fuel (x<sub>1</sub>) and the internal temperature of a chamber of the rocket (x<sub>2</sub>). The engineer starts by fitting a quadratic model, but he believes that the full quadratic model is too complex and can be reduced by only including the linear terms and the interaction term. The engineer obtained a random sample of 66 measurements and computed the SSE for both the complete model and the reduced model. The values were 1477.8 and 1678.8, respectively. Perform the appropriate test of hypothesis to determine whether the reduced model is adequate for the engineer's use. Use = 0.05. Test statistic: F = ______________ What is the critical value of F? ______________ Conclude: ______________ . There ______________ evidence to indicate that at least one of the two quadratic variables is contributing significant information for predicting y. = 0.05. Test statistic: F = ______________ What is the critical value of F? ______________ Conclude: ______________ An engineer was investigating the relationship between the thrust of an experimental rocket (y), the percent composition of a secret chemical in the fuel (x<sub>1</sub>) and the internal temperature of a chamber of the rocket (x<sub>2</sub>). The engineer starts by fitting a quadratic model, but he believes that the full quadratic model is too complex and can be reduced by only including the linear terms and the interaction term. The engineer obtained a random sample of 66 measurements and computed the SSE for both the complete model and the reduced model. The values were 1477.8 and 1678.8, respectively. Perform the appropriate test of hypothesis to determine whether the reduced model is adequate for the engineer's use. Use = 0.05. Test statistic: F = ______________ What is the critical value of F? ______________ Conclude: ______________ . There ______________ evidence to indicate that at least one of the two quadratic variables is contributing significant information for predicting y. . There ______________ evidence to indicate that at least one of the two quadratic variables is contributing significant information for predicting y.

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4.08; 3.15...

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The adjusted value of The adjusted value of is mainly used to compare two or more regression models that have the same number of independent predictors to determine which one fits the data better. is mainly used to compare two or more regression models that have the same number of independent predictors to determine which one fits the data better.

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The stepwise regression analysis is best used as a preliminary tool for identifying which of a large number of variables should be considered in the model.

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In a multiple regression analysis, if the model provides a poor fit, this indicates:


A) that the sum of squares for error (SSE) will be large
B) that the standard error of estimate will be large
C) that the multiplewill be close to zero
D) all of these
E) none of these

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If multicollinearity exists among the independent variables included in a multiple regression model, then:


A) regression coefficients will be difficult to interpret
B) standard errors of the regression coefficients for the correlated independent variables will increase
C) multiple coefficient of determination will assume a value close to zero
D) regression coefficients will be difficult to interpret and standard errors of the regression coefficients for the correlated independent variables will increase
E) none of these

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A coefficient of multiple correlation is a measure of how well an estimated regression plane (or hyperplane) fits the sample data on which it is based.

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False

If we want to relate a random variable y to two-independent variables If we want to relate a random variable y to two-independent variables and , a regression hyperplane is the three-dimensional equivalent of a regression line that minimizes the sum of the squared vertical deviations between the sample points suspended in y vs. vs. space and their associated multiple regression estimates, all of which lie on this hyperplane. and If we want to relate a random variable y to two-independent variables and , a regression hyperplane is the three-dimensional equivalent of a regression line that minimizes the sum of the squared vertical deviations between the sample points suspended in y vs. vs. space and their associated multiple regression estimates, all of which lie on this hyperplane. , a regression hyperplane is the three-dimensional equivalent of a regression line that minimizes the sum of the squared vertical deviations between the sample points suspended in y vs. If we want to relate a random variable y to two-independent variables and , a regression hyperplane is the three-dimensional equivalent of a regression line that minimizes the sum of the squared vertical deviations between the sample points suspended in y vs. vs. space and their associated multiple regression estimates, all of which lie on this hyperplane. vs. If we want to relate a random variable y to two-independent variables and , a regression hyperplane is the three-dimensional equivalent of a regression line that minimizes the sum of the squared vertical deviations between the sample points suspended in y vs. vs. space and their associated multiple regression estimates, all of which lie on this hyperplane. space and their associated multiple regression estimates, all of which lie on this hyperplane.

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Qualitative predictor variables are entered into a regression model through dummy variables.

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