Model Building 721 CHAPTER 19 MODEL BUILDING SECTIONS 1 MULTIPLE CHOICE QUESTIONS In the following multiple choice questions please circle the correct answer 1 The model y 0 1 x1 2 x 2 3 x1 x 2 is referred to as a first order model with two predictor variables with no interaction b first order model with two predictor variables with interaction c second order model with three predictor variables with no interaction d second order model with three predictor variables with interaction ANSWER b 2 2 p The model y 0 1 x 2 x p x is referred to as a polynomial model with a one predictor variable b p predictor variables c p 1 predictor variables d x predictor variables ANSWER a 3 For the following regression equation y 20 8 x1 5 x 2 3x1 x 2 which combination of x1 and x 2 respectively results in the largest average value of y a 3 and 5 722 Chapter Nineteen b 5 and 3 c 6 and 3 d 3 and 6 ANSWER c 4 Which of the following statements is false regarding the graph of the third order polynomial model y b0 b1 x b2 x 2 b3 x 3 e a When b3 is negative y decreases over the range of x b When b3 is positive y increases over the range of x c The number of real life applications of this model is quite large Statistics practitioners often encounter problems involving more than one curvature reversal d The coefficients b1 and b2 determine the position of the curvature changes while the coefficient b0 determines the point at which the curve interacts the y axis ANSWER c 5 For the following regression equation y 50 10 x1 4 x 2 6 x1 x 2 a unit increase in x 2 while holding x1 constant at a value of 3 decreases the value of y on average by a 56 b 22 c 50 d An amount that depends on the value of x 2 ANSWER b 6 Suppose that the sample regression line of the first order model is y 8 2 x1 3 x 2 If we examine the relationship between y and x1 for four different values of x2 we observe that the a effect of x 1 on y remains the same no matter what the value of x 2 b effect of x 1 on y remains the same no matter what the value of x 1 c only difference in the four equations produced is the coefficient of x 2 d not enough information is given to answer this question ANSWER a 7 Suppose that the sample regression equation of a second order model is given by y 2 50 0 15 x 0 45 x 2 Then the value 4 60 is the a predicted value of y for any positive value of x b predicted value of y when x 2 c estimated change in y when x increases by 1 unit d intercept where the response surface strikes the x axis ANSWER b 8 For the following regression equation y 75 20 x1 15 x 2 5 x1 x 2 a unit increase in x 2 while holding x1 constant at 1 changes the value of y on average by a 5 b 5 Model Building 723 c 10 d 10 ANSWER d 9 For the following regression equation y 100 12 x1 5 x 2 4 x1 x 2 a unit increase in x1 while holding x 2 constant at a value of 2 decreases the value of y on average by a 92 b 85 c 20 d an amount that depends on the value of x1 ANSWER c 10 For the following regression equation y 10 3 x1 4 x 2 a unit increase in x 2 increases the value of y on average by a 4 b 7 c 17 d an amount that depends on the value of x1 ANSWER a 11 In first order model with two predictors x1 and x 2 an interaction term may be used when the a relationship between the dependent variable and the independent variables is linear b effect of x1 on the dependent variable is influenced by x 2 c effect of x 2 on the dependent variable is influenced by x1 d both b and c ANSWER d 12 13 2 The model y 0 1 x 2 x is referred to as a simple linear regression model b first order model with one predictor variable c second order model with one predictor variable d third order model with two predictor variables ANSWER c The model y 0 1 x1 2 x 2 is used whenever the statistician believes that on average y is linearly related to a x1 and the predictor variables do not interact b x 2 and the predictor variables do not interact c either a or b d both a and b 724 Chapter Nineteen ANSWER d 14 15 For the following regression equation y 15 6 x1 5 x 2 4 x1 x 2 a unit increase in x1 increases the value of y on average by a 5 b 30 c 26 d an amount that depends on the value of x 2 ANSWER d 2 When we plot x versus y the graph of the model y 0 1 x 2 x is shaped like a a straight line going upwards b straight line going downwards c circle d parabola ANSWER d 16 Suppose that the sample regression equation of a model is y 10 4 x1 3x 2 x1 x 2 If we examine the relationship between x1 and y for three different values of x 2 we observe that the a three equations produced differ only in the intercept b coefficient of x 2 remains unchanged c coefficient of x1 varies d three equations produced differ not only in the intercept term but the coefficient of x1 also varies ANSWER d 17 The model y 0 1 x1 2 x 2 is referred to as a first order model with one predictor variable b first order model with two predictor variables c second order model with one predictor variable d second order model with two predictor variables ANSWER b 18 Which of the following is not an advantage of multiple regression as compared with analysis of variance a Multiple regression can be used to estimate the relationship between the dependent variable and independent variables b Multiple regression handles qualitative variables better than analysis of variance c Multiple regression handles problems with more than two independent variables easier than analysis of variance d All of the above are advantages of multiple regression as compared with analysis of variance Model Building 725 ANSWER b 19 Suppose that the sample regression equation of a second order model is given by y 2 50 0 15 x 0 45 x 2 Then the value 2 50 is the a intercept where the response surface strikes the y axis b intercept where the response surface strikes the x axis c predicted value of y d predicted value of …