PredictorPredictorPredictorPredictorPredictorPredictorModelBuilding 721CHAPTER 19MODEL BUILDINGSECTIONS 1 MULTIPLE CHOICE QUESTIONSIn the following multiple-choice questions, please circle the correct answer.1. The model 21322110xxxxy+ is referred to as:a. first order model with two predictor variables with no interactionb. first order model with two predictor variables with interactionc. second order model with three predictor variables with no interactiond. second order model with three predictor variables with interactionANSWER: b2. The model ppxxxy 2210 is referred to as a polynomial modelwith:a. one predictor variableb. p predictor variablesc. (p + 1) predictor variablesd. x predictor variablesANSWER: a3. For the following regression equation212135820ˆxxxxy , which combination of1x and2x, respectively, results in the largest average value of y?a. 3 and 5722 Chapter Nineteenb. 5 and 3c. 6 and 3d. 3 and 6ANSWER: c4. Which of the following statements is false regarding the graph of the third – orderpolynomial model 2 30 1 2 3y x x xb b b b e= + + + +?a. When 3b is negative, y decreases over the range of xb. When 3b is positive, y increases over the range of xc. The number of real – life applications of this model is quite large. Statisticspractitioners often encounter problems involving more than one curvature reversald. The coefficients, 1b and 2b determine the position of the curvature changes, whilethe coefficient 0b determines the point at which the curve interacts the y – axisANSWER: c5. For the following regression equation2121641050ˆxxxxy , a unit increase in 2x,while holding 1x constant at a value of 3, decreases the value of y on average by:a. 56b. 22c. 50d. An amount that depends on the value of 2xANSWER: b6. Suppose that the sample regression line of the first order model is21328ˆxxy . If weexamine the relationship between y and 1x for four different values of2x, we observe thatthe:a. effect of x1 on y remains the same no matter what the value of x2b. effect of x1 on y remains the same no matter what the value of x1c. only difference in the four equations produced is the coefficient of x2d. not enough information is given to answer this questionANSWER: a7. Suppose that the sample regression equation of a second-order model is given by245.015.050.2ˆxxy . Then, the value 4.60 is the:a. predicted value of y for any positive value of xb. predicted value of y when x = 2c. estimated change in y when x increases by 1 unit d. intercept where the response surface strikes the x-axisANSWER: b8. For the following regression equation21215152075ˆxxxxy , a unit increase in 2x, while holding 1x constant at 1, changes the value of y on average by:a. - 5b. +5ModelBuilding 723c. 10d. –10ANSWER: d9. For the following regression equation21214512100ˆxxxxy , a unit increase in 1x, while holding 2x constant at a value of 2, decreases the value of y on average by:a. 92b. 85c. 20d. an amount that depends on the value of 1xANSWER: c10. For the following regression equation214310ˆxxy , a unit increase in 2x increasesthe value of y on average by:a. 4b. 7c. 17d. an amount that depends on the value of 1xANSWER: a11. In first order model with two predictors 1x and 2x, an interaction term may be usedwhen the:a. relationship between the dependent variable and the independent variables is linearb. effect of 1x on the dependent variable is influenced by 2xc. effect of 2x on the dependent variable is influenced by 1xd. both (b) and (c)ANSWER: d12. The model 2210xxy+ is referred to as:a. simple linear regression modelb. first order model with one predictor variablec. second order model with one predictor variabled. third order model with two predictor variablesANSWER: c13. The model22110xxy+ is used whenever the statistician believes that, onaverage, y is linearly related to:a.1x and the predictor variables do not interactb.2x and the predictor variables do not interactc. either (a) or (b)d. both (a) and (b)724 Chapter NineteenANSWER: d14. For the following regression equation212145615ˆxxxxy , a unit increase in 1xincreases the value of y on average by:a. 5b. 30c. 26d. an amount that depends on the value of 2xANSWER: d15. When we plot x versus y, the graph of the model 2210xxy+ is shaped like a:a. straight line going upwardsb. straight line going downwardsc. circled. parabolaANSWER: d16. Suppose that the sample regression equation of a model is 21213410ˆxxxxy . Ifwe examine the relationship between 1x and y for three different values of 2x, weobserve that the:a. three equations produced differ only in the interceptb. coefficient of 2x remains unchangedc. coefficient of 1x variesd. three equations produced differ not only in the intercept term but the coefficient of1x, also variesANSWER: d17. The model 22110xxy+is referred to as:a. first order model with one predictor variableb. first order model with two predictor variablesc. second order model with one predictor variabled. second order model with two predictor variablesANSWER: b18. Which of the following is not an advantage of multiple regression as compared withanalysis of variance?a. Multiple regression can be used to estimate the relationship between the dependentvariable and independent variables.b. Multiple regression handles qualitative variables better than analysis of variance.c. Multiple regression handles problems with more than two independent variableseasier than analysis of variance.d. All of the above are advantages of multiple regression as compared with analysis ofvariance.ModelBuilding 725ANSWER: b19. Suppose that the sample regression equation of a second-order model is given by245.015.050.2ˆxxy . Then, the value 2.50 is the:a. intercept where the response surface strikes the y-axisb. intercept where the response surface strikes the x-axisc. predicted value of yd. predicted value of y when x = 1ANSWER: a20. Which of the following statements is false regarding the graph of the second – orderpolynomial model 20 1 2y x xb b b e= + + +?a. When we plot x versus y, the graph is shaped like a