Multiple Regression BPS 7e Chapter 29 © 2015 W. H. Freeman and Company

Variables ______________ are commonly used to indicate sex (0 male, 1 female), condition of patient (0 good, 1 poor), status of order (0 undelivered, 1 delivered), and many other characteristics for individuals. Indicator (dummy) variables Continuous variables Interaction terms None of the above

Variables (answer) ______________ are commonly used to indicate sex (0 male, 1 female), condition of patient (0 good, 1 poor), status of order (0 undelivered, 1 delivered), and many other characteristics for individuals. Indicator (dummy) variables Continuous variables Interaction terms None of the above.

Square of Correlation Coefficient For simple linear regression models, the square of the correlation coefficient r2 between y and x measures the proportion of variation in the ___________ variable that is explained by using the _________ variable. explanatory; response response; indicator (dummy) response; explanatory indicator (dummy); explanatory

Square of Correlation Coefficient For simple linear regression models, the square of the correlation coefficient r2 between y and x measures the proportion of variation in the ___________ variable that is explained by using the _________ variable. explanatory; response response; indicator (dummy) response; explanatory indicator (dummy); explanatory

Inference Here is a multiple regression model predicting shoe size from height (inches) and weight (lbs): What is the slope for height? −13.2086 0.290390 0.020321 0.0220

Inference (answer) Here is a multiple regression model predicting shoe size from height (inches) and weight (lbs): What is the slope for height? −13.2086 0.290390 0.020321 0.0220

Inference Here is a multiple regression model predicting shoe size from height (inches) and weight (lbs): How do we interpret the R2? 71% of variability in shoe size is accounted for by the regression model. 71% of variability in shoe size is not accounted for by the regression model. 71% of variability in shoe size is accounted for by weight variable. 71% of variability in shoe size is accounted for by height variable.

Inference (answer) Here is a multiple regression model predicting shoe size from height (inches) and weight (lbs): How do we interpret the R2? 71% of variability in shoe size is accounted for by the regression model. 71% of variability in shoe size is not accounted for by the regression model. 71% of variability in shoe size is accounted for by weight variable. 71% of variability in shoe size is accounted for by height variable.

Inference Here is a multiple regression model predicting shoe size from height (inches) and weight (lbs): What is the expected shoe size for an average person with a height of 6’ (72”) and weight of 150 lbs? 7.3 (~7.5) 10.7 (~11) 8.5 12

Inference (answer) Here is a multiple regression model predicting shoe size from height (inches) and weight (lbs): What is the expected shoe size for an average person with a height of 6’ (72”) and weight of 150 lbs? 7.3 (~7.5) 10.7 (~11) 8.5 12

Inference The regression below predicts the average miles per gallon (MPG) for 82 cars using their engine horsepower (HP) and weight (WT, in 100’s of pounds). What are the hypotheses for the test of the coefficient of horsepower? H0: βHP ≠ 0; Ha: βHP = 0 H0: βHP = 0; Ha: βHP ≠ 0 H0: βHP = βWT; Ha: βHP ≠ βWT

Inference (answer) The regression below predicts the average miles per gallon (MPG) for 82 cars using their engine horsepower (HP) and weight (WT, in 100’s of pounds). What are the hypotheses for the test of the coefficient of horsepower? H0: βHP ≠ 0; Ha: βHP = 0 H0: βHP = 0; Ha: βHP ≠ 0 H0: βHP = βWT; Ha: βHP ≠ βWT

Inference The regression below predicts the average miles per gallon (MPG) for 82 cars using their engine horsepower (HP) and weight (WT, in 100’s of pounds). Should you retain or reject the null hypothesis, H0: βHP = 0 (using alpha p < 0.05)? reject retain inconclusive (incomplete information)

Inference (answer) The regression below predicts the average miles per gallon (MPG) for 82 cars using their engine horsepower (HP) and weight (WT, in 100’s of pounds). Should you retain or reject the null hypothesis, H0: βHP = 0 (using alpha p < 0.05)? reject retain inconclusive (incomplete information)

Inference The regression below predicts the average miles per gallon (MPG) for 82 cars using their engine horsepower (HP) and weight (WT, in 100’s of pounds). Which explanatory variable is statistically significant to predict MPG (at p < 0.05)? Only weight is statistically significant to explain MPG. Both weight and height matter significantly to explain MPG. Only height is statistically significant to explain MPG. Neither explanatory variable is statistically significant to explain MPG.

Inference (answer) The regression below predicts the average miles per gallon (MPG) for 82 cars using their engine horsepower (HP) and weight (WT, in 100’s of pounds). Which explanatory variable is statistically significant to predict MPG (at p < 0.05)? Only weight is statistically significant to explain MPG. Both weight and height matter significantly to explain MPG. Only height is statistically significant to explain MPG. Neither explanatory variable is statistically significant to explain MPG.

Multiple Regression In multiple regression, the following equation captures the: regression confidence interval. regression standard error. sum of squared residuals. None of the above

Multiple Regression (answer) In multiple regression, the following equation captures the: regression confidence interval. regression standard error. sum of squared residuals. None of the above

Multiple Regression: Inference To test the null hypothesis that one of the β’s in a specific regression model is zero, we compute the: t statistic. F statistic. R2 (R-squared). model sum of squares.

Multiple Regression: Inference (answer) To test the null hypothesis that one of the β’s in a specific regression model is zero, we compute the: t statistic. F statistic. R2 (R-squared). model sum of squares.

Individual t Tests In order to test the null hypothesis that one of the β’s in a specific regression model is zero, we compute the t statistic: (Note: SE = Standard Error) t = b2 / SEb. t = b / SEb. t = b / SEb. t = b / SEb. √ √

Individual t Tests (answer) In order to test the null hypothesis that one of the β’s in a specific regression model is zero, we compute the t statistic: (Note: SE = Standard Error) t = b2 / SEb. t = b / SEb. t = b / SEb. t = b / SEb. √ √

Interaction Terms True or False: The product (i.e., interaction) term means that the relationship between the mean response and one explanatory variable x1 changes when we change the value of the other explanatory variable x2. True False

Interaction Terms (answer) True or False: The product (i.e., interaction) term means that the relationship between the mean response and one explanatory variable x1 changes when we change the value of the other explanatory variable x2. True False