Multiple Regression BPS chapter 28 © 2006 W.H. Freeman and Company

Parallel regression lines What is always true about two parallel regression lines? a) The slopes are approximately the same. b) The intercepts are approximately the same. c) Both the slopes and the intercepts are approximately the same. d) None of the above.

Parallel regression lines (answer) What is true about two parallel regression lines? a) The slopes are approximately the same. b) The intercepts are approximately the same. c) Both the slopes and the intercepts are approximately the same. d) None of the above.

Indicator variable When do we use an indicator variable in a regression equation? a) When we have a quantitative variable with two possible answers, 0 and 1. b) When we have a categorical variable with two possible answers, one we assign the code “0” and the other we assign the code “1”.

Indicator variable (answer) When do we use an indicator variable in a regression equation? a) When we have a quantitative variable with two possible answers, 0 and 1. b) When we have a categorical variable with two possible answers, one we assign the code “0” and the other we assign the code “1”.

Regression vocabulary The formula “observed y – predicted y” is the a) Correlation b) Regression c) R 2 d) Residual e) Measure of Normality

Regression vocabulary (answer) The formula “observed y – predicted y” is the a) Correlation b) Regression c) R 2 d) Residual e) Measure of Normality

Parameters The parameters for multiple regression are:  X and Y.  The  ’s.  The  and .  The correlation and standard deviation.  The  ’s and .

Parameters (answer) The parameters for multiple regression are:  X and Y.  The  ’s.  The  and .  The correlation and standard deviation.  The  ’s and .

ANOVA If we reject the null hypothesis for the ANOVA F-test, what does that tell us about our multiple regression model? a) All of our  parameters are 0. b) All of our  parameters are not 0. c) One of our  parameters is 0. d) One of our  parameters is not 0. e) At least one of our  parameters is not 0.

ANOVA (answer) If we reject the null hypothesis for the ANOVA F-test, what does that tell us about our multiple regression model? a) All of our  parameters are 0. b) All of our  parameters are not 0. c) One of our  parameters is 0. d) One of our  parameters is not 0. e) At least one of our  parameters is not 0.

Significance How do you know which coefficients are significant? a) Perform a t-test for each coefficient, and any with small P-values are significant. b) Perform a t-test for each coefficient, and any with large P-values are significant. c) Perform an F-test for all coefficients, and if the P-value is small, all coefficients are significant. d) Perform an F-test for all coefficients, and if the P-value is large, all coefficients are significant.

Significance (answer) How do you know which coefficients are significant? a) Perform a t-test for each coefficient, and any with small P- values are significant. b) Perform a t-test for each coefficient, and any with large P-values are significant. c) Perform an F-test for all coefficients, and if the P-value is small, all coefficients are significant. d) Perform an F-test for all coefficients, and if the P-value is large, all coefficients are significant.

Interaction Which of the following is FALSE if you have interaction between two explanatory variables, x 1 and x 2 ? a) The individual regression lines for each explanatory variable will be parallel. b) The interaction term can be expressed as x 1 x 2 in the model. c) The relationship between the mean response and one explanatory variable changes when we change the value of the other explanatory variable. d) The interaction term changes the slope of the full model from the slope of either of the simple (one x-variable) regression models.

Interaction (answer) Which of the following is FALSE if you have interaction between two explanatory variables, x 1 and x 2 ? a) The individual regression lines for each explanatory variable will be parallel. b) The interaction term can be expressed as x 1 x 2 in the model. c) The relationship between the mean response and one explanatory variable changes when we change the value of the other explanatory variable. d) The interaction term changes the slope of the full model from the slope of either of the simple (one x-variable) regression models.

Multiple regression models True or false: When considering which model is the best one for your setting, you should assume you have parallel regression lines (no interaction) in your model before considering a model with an interaction term. a) True b) False

Multiple regression models (answer) True or false: When considering which model is the best one for your setting, you should assume you have parallel regression lines (no interaction) in your model before considering a model with an interaction term. a) True b) False

Multiple regression True or false: The relationship between y and any explanatory variable can change greatly depending on which other explanatory variables are present in the model. a) True b) False

Multiple regression (answer) True or false: The relationship between y and any explanatory variable can change greatly depending on which other explanatory variables are present in the model. a) True b) False

Residual plots What does it mean if you see a quadratic pattern in your residual plot? a) All the regression assumptions were met. b) There are many outliers. c) The Normality assumption was not met. d) An x 2 term may need to be added to the model.

Residual plots (answer) What does it mean if you see a quadratic pattern in your residual plot? a) All the regression assumptions were met. b) There are many outliers. c) The Normality assumption was not met. d) An x 2 term may need to be added to the model.

Multiple regression models Which of the following is NOT an important indication of a good model? a) The ANOVA F-test rejected the null hypothesis. b) R 2 is close to 100%. c) The  0 coefficient is significant. d) The  i coefficients in the model (not counting  0 ) are significant. e) The residual plot shows a random scattering of points.

Multiple regression models (answer) Which of the following is NOT an important indication of a good model? a) The ANOVA F-test rejected the null hypothesis. b) R 2 is close to 100%. c) The  0 coefficient is significant. d) The  i coefficients in the model (not counting  0 ) are significant. e) The residual plot shows a random scattering of points.