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CH 7 - Linear Regression 1. _____ is a statistical procedure used to develop an equation showing how two variables are related. a. Regression analysis b. Data mining c. Time series analysis d. Factor analysis 2. A regression analysis involving one independent variable and one dependent variable is referred to as a a. factor analysis. b. time series analysis. c. simple linear d. data mining. regression. 3. The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are a. . b. y and x. c. a and b. d. a and B.

4. In a simple linear regression model, y = ß0 + ß1x + ε B1 represents the a. intercept. b. slope of the true regression line. c. mean value of x. d. error term. 5. In the simple linear regression model, the ____________ accounts for the variability in the dependent variable that cannot be explained by the linear relationship between the variables. a. constant term b. error term c. model parameter d. residual 6. In a linear regression model, the variable that is being predicted or explained is known as _____________. It is denoted by y and is often referred to as the response variable. a. dependent variable b. independent variable c. residual variable d. regression variable 7. The graph of the simple linear regression equation is a(n) a. ellipse. b. hyperbola. c. parabola. d. straight line.

8. In the graph of the simple linear regression equation, the parameter line. a. slope b. xintercept c. yd. end-point intercept Copyright Cengage Learning. Powered by Cognero.

represents the ___________ of the regression

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CH 7 - Linear Regression

9. In the graph of the simple linear regression equation, the parameter a. slope b. xintercept c. yd. end-point intercept

is the ___________ of the regression line.

10. In a linear regression model, the variable (or variables) used for predicting or explaining values of the response variable are known as the ________________. It(they) is(are) denoted by x. a. dependent variable b. independent variable c. residual variable d. regression variable 11. In a simple linear regression analysis the quantity that gives the amount by which the dependent variable changes for a unit change in the independent variable is called the a. coefficient of determination. b. slope of the regression line. c. correlation coefficient. d. standard error. 12. A ___________ is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables. a. contingency table b. scatter chart c. Gantt chart d. pie chart 13. A procedure for using sample data to find the estimated regression equation is a. point estimation. b. interval estimation. c. the least squares d. extrapolation. method. 14. When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is a. positive. b. zero. c. negative. d. infinite.

15. The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the a. constant term. b. error term. c. residual. d. model parameter. 16. The _______________ is the range of values of the independent variables in the data used to estimate the regression model. a. confidence interval b. codomain c. experimental region d. validation set Copyright Cengage Learning. Powered by Cognero.

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CH 7 - Linear Regression

17. Prediction of the value of the dependent variable outside the experimental region is called a. interpolation. b. forecasting. c. averaging. d. extrapolation.

18. Prediction of the mean value of the dependent variable y for values of the independent variables x1, x2, . . . , xq that are outside the experimental range is called a. dummy variable. b. overfitting. c. extrapolation. d. interacton. 19. The ____________________ is a measure of the error that results from using the estimated regression equation to preduct the values of the dependent variable in the sample a. sum of squares due to regression b. error (SSR) term c. sum of squares due to error (SSE) d. residual 20. The least squares regression line minimizes the sum of the a. differences between actual and predicted y values. b. absolute deviations between actual and predicted y values. c. absolute deviations between actual and predicted x d. squared differences between actual and predicted y values. values 21. What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89? a. 31.89 b. 19.32 c. 18.43 d. 15.32 22. The ___________ is a measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation. a. residual b. coefficient of determination c. dummy variable d. interaction variable 23. The coefficient of determination a. takes values between –1 to +1. c. is equal to negative one for the poorest fit.

b. is equal to zero for a perfect fit. d. is used to evaluate the goodness of fit.

24. What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03? a. 2.32 b. 0.43 c. 0.19 d. 0.89

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CH 7 - Linear Regression 25. Regression analysis involving one dependent variable and more than one independent variable is known as a. simple regression. b. linear regression. c. multiple regression. d. none of these. 26. The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as a. inductive inference. b. deductive inference. c. statistical inference. d. Bayesian inference. 27. The process of making conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is known as a. postulation. b. hypothesis testing. c. statistical inference. d. empirical research. 28. __________________ refers to the use of sample data to calculate a range of values that is believed to include the value of the population parameter. a. Interval estimation b. Hypothesis testing c. Statistical d. Point estimation inference 29. A normally distributed error term with mean of zero would a. have values that are symmetric about the variance. b. allow more accurate modeling. c. yield biased regression estimates. d. be a hyperbolic curve. 30. The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn from the scatter chart given below?

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CH 7 - Linear Regression a. The residuals have a increasing variance as the dependent variable increases. b. The model captures the relationship between the variables accurately. c. The regression model follows the standard normal probability distribution. d. The residual distribution is consistently scattered about zero. 31. The scatter chart below displays the residuals verses the dependent variable, t. Which of the following conclusions can be drawn based upon this scatter chart?

a. model is time-invariant. b. model captures the relationship between the variables accurately. c. residuals are not independent. d. residuals are normally distributed. 32. The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart?

a. The residuals have a constant variance. b. The model fails to capture the relationship between the variables accurately. c. The model over predicts the value of the dependent variable for small values and large values of the Copyright Cengage Learning. Powered by Cognero.

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CH 7 - Linear Regression independent variable. d. The residuals are normally distributed. 33. The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart?

a. The residuals have a constant variance. b. The model captures the relationship between the variables accurately. c. The model underpredicts the value of the dependent variable for intermediate values of the independent variable. d. The residual distribution is not normally distributed. 34. The _____________ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating. a. residual b. tolerance factor c. confidence level d. accuracy level 35. ______________ refers to the degree of correlation among independent variables in a regression model. a. Multicollinearity b. Tolerance c. Rank d. Confidence level 36. The degree of correlation among independent variables in a regression model is called a. multicollinearity. b. interaction. c. the coefficient of determination. d. the sum of squared errors (SSE).

37. ________________ is used to test the hypothesis that the values of the regression parameters B0, B1, B2, ... Bq are all zero. a. An F test b. A t test c. The least squares d. Extrapolation Copyright Cengage Learning. Powered by Cognero.

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CH 7 - Linear Regression method 38. A variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called a. a residual. b. the coefficient of determination. c. a dummy variable. d. interaction. 39. A variable used to model the effect of categorical independent variables in a regression model is known as a a. dependent variable. b. response. c. dummy variable. d. predictor variable. 40. Which of the following regression models is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable in the model? a. a multiple regression b. quadratic regression model model c. a simple regression model d. a least squares regression model 41. The prespecified value of the independent variable at which its relationship with the dependent variable changes in a piecewise linear regression model is referred to as the a. milestone. b. knot. c. tipping point. d. watchpoint. 42. _____________ refers to the scenario in which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable. a. Interaction b. Multicollinearity c. Autocorrelatio d. Covariance n 43. Fitting a model too closely to sample data, resulting in a model that does not accurately reflect the population is termed as a. approximation b. hypothesizing. . c. overfitting. d. postulating. 44. Assessing the regression model on data other than the sample data that was used to generate the model is known as a. approximation. b. cross-validation. c. graphical d. postulation. validation. 45. __________ is the data set used to build the candidate models. a. Range b. Codomain c. Validation set d. Training set Copyright Cengage Learning. Powered by Cognero.

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46. _____________ refers to the data set used to compare model forecasts and ultimately pick a model for predicting values of the dependent variable. a. Codomain b. Training set c. Validation set d. Range 47. Listed below is da t aonpr ofita ndma r ke tc a pi t a l i z a t i onf oras a mpl eof15di ffe r e ntfir msi nU. S. Pr ofit s( $ Mar ke tCapi t al i z at i on( $ mi l l i ons )y mi l l i ons )x 296. 2 1 , 936. 9 –25 1, 17 1. 8 4, 085 55 , 135. 8 6, 558 97 , 417. 2 12, 525 95, 198 . 9 3, 394 53 , 579. 7 442. 8 12 , 466. 3 633. 1 8 , 894. 3 3, 528 65 , 872. 4 2, 698 25 , 661. 3 1, 200. 6 5 19, 854. 7 11. 987 195 , 643. 8 641. 8 10 , 447. 8 5, 043 66 , 695. 5 5, 206 53 , 558. 4 a .De v e l opas c a t t e rc ha r tf ort hea bo v eda t a .Wha tdoe st hi sc ha r ti ndi c a t ea boutt her e l a t i ons hi pbe t we e nma r ke t c a pi t a l i z a t i ona ndpr ofit ? b .Us et heda t at od e v e l opa ne s t i ma t e dr e gr e s s i one qua t i ont ha tc oul dbeus e dt oe s t i ma t eafir m’ spr ofitba s e doni t s ma r ke tc a pi t a l i z a t i on.Wha ti st hee s t i ma t e dr e gr e s s i onmode l ? c .Wh a ti st hepr e di c t e dpr ofitf ort hema r ke tc a pi t a l i z a t i onof70, 721. 3( mi l l i on) ? 48. Ar e s e a r c hc e nt e ri si nt e r e s t e di ni n v e s t i g a t i nga bouthe i ghta nda geofc hi l dr e nwhoa r ebe t we e n5t o9y e a r sol d . I nor de rt odot hi s ,as a mpl eof15c hi l dr e ni ss e l e c t e da ndt heda t ai sgi v e nbe l o w. Ag e( i ny e ar s ) He i ght( i nc he s ) 7 47. 3 8 48. 8 5 41. 3 8 50. 4 8 51 7 47. 1 7 46. 9 7 48 9 51. 2 8 51. 2 5 40. 3 8 48. 9 6 45. 2 Copyright Cengage Learning. Powered by Cognero.

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CH 7 - Linear Regression 5 8

41. 9 49. 6

a .De v e l opas c a t t e rc ha r twi t ha g ea st hei nde pe nde ntv a r i a bl e .Wha tdoe st hes c a t t e rc ha r ti ndi c a t ea boutt her e l a t i ons hi p be t we e nt hehe i ghta nda g eofc hi l dr e n? b .Us et heda t at ode ve l opa ne s t i ma t e dr e gr e s s i one qu a t i ont ha tc oul dbeus e dt oe s t i ma t et hehe i ghtba s e dont hea g e . Wha ti st hee s t i ma t e dr e gr e s s i onmode l ? c .Ho wmuc hoft hev a r i a t i oni nt hes a mpl ev a l ue sofhe i ghtdoe st hemode le s t i ma t e di npa r t( b)e xpl a i n? 49. Listed below is a c ompa ny ’ ss a l e si nt hepe r i od2000t o2011a l on gwi t ht hena t i ona li nc omeoft hec ount r y , whe r et he bus i ne s si ss e tup. Nat i onalI nc ome( i n Company' ss al e s( i n Ye ar mi l l i onsofdol l ar s )x t hous andsofdol l ar s )y 2000 305 470 2001 316 485 2002 358 499 2003 350 515 2004 375 532 2005 392 532 2006 400 556 2007 398 576 2008 430 583 2009 456 587 2010 578 601 2011 498 605 a .De v e l opas c a t t e rc ha r tf ort hea bo v eda t a . Wh a tdoe st hi sc ha r ti ndi c a t ea boutt her e l a t i ons hi pbe t we e nt he Na t i on a lI nc omea ndt heCompa n y' ss a l e si nt hepe r i od2000t o2011? b .Us et heda t at ode ve l opa ne s t i ma t e dr e gr e s s i one qu a t i ont ha tc oul dbeus e dt oe s t i ma t et hec ompa n y’ ss a l e s ba s e dont hena t i ona li nc ome .Wha ti st hee s t i ma t e dr e gr e s s i onmode l ? 50. Listed below is a c ompa ny ’ ss a l e si nt hepe r i od2000t o2011a l on gwi t ht hena t i ona li nc omeoft hec ount r y , whe r et he bus i ne s si ss e tup. Nat i onalI nc ome( i n Company' ss al e s( i n Ye ar mi l l i onsofdol l ar s )x t hous andsofdol l ar s )y 2000 305 470 2001 316 485 2002 358 499 2003 350 515 2004 375 532 2005 392 532 2006 400 556 2007 398 576 2008 430 583 2009 456 587 2010 578 601 2011 498 605 Copyright Cengage Learning. Powered by Cognero.

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CH 7 - Linear Regression se qua lt oz e r oa ta0. 05l e v e lofs i gni fic a nc e .Wha ta r et he Te s twhe t he re a c hoft her e gr e s s i onpa r a me t e r sβ0a ndβ1i c or r e c ti n t e r pr e t a t i onsoft hee s t i ma t e dr e gr e s s i onpa r a me t e r s ? 51. Theda t al i s t e dbe l o wi st hea v e r a gep e r s ona li nc omea ndpe r s ona lc ons umpt i one xpe ndi t ur e sba s e dont hes ur v e y c onduc t e di nt hey e a r1995t o2009i nU. S. Pe r s onali nc ome Pe r s onalc ons umpt i on ( $) e xpe ndi t ur e s( $) 23, 310 18, 714 24, 444 19, 569 25, 657 20, 414 27, 260 21, 434 28, 336 22, 738 30, 317 24, 227 31, 162 25, 074 31, 448 25, 865 32, 282 26, 848 33, 872 28, 228 35, 423 29, 818 37, 723 31, 210 39, 418 32, 551 40, 156 33, 273 39, 113 32, 853 a .De v e l opas c a t t e rc ha r tf ort hea bo v eda t a . Wh a tdoe st hi sc ha r ti ndi c a t ea boutt her e l a t i ons hi pbe t we e na v e r a g e pe r s ona li nc omea ndpe r s ona lc ons umpt i one xpe ndi t ur e ? b .De v e l opa ne s t i ma t e dr e gr e s s i one qua t i ons ho wi n gho wpe r s ona lc ons umpt i one xpe ndi t ur ei sr e l a t e dpe r s ona l i nc ome . c .Wh a tpr opor t i onofv a r i a t i oni nt hes a mpl ev a l ue sofpr opor t i onofpe r s ona lc ons umpt i one xpe ndi t ur edoe st hi s mode le xpl a i n? POINTS: 1 DIFFICULTY: Moderate REFERENCES: THE SIMPLE LINEAR REGRESSION MODEL, LEAST SQUARES METHOD, ASSESSING THE FIT OF THE SIMPLE LINEAR REGRESSION MODEL, Pages 304 and 308 NATIONAL STANDARDS: United States - BUSPROG: Analytic skills - and DISC: Descriptive Statistics KEYWORDS: Bloom’s: Application 52. Theda t al i s t e dbe l o wi st hea v e r a gep e r s ona li nc omea ndpe r s ona lc ons umpt i one xpe ndi t ur e sba s e dont hes ur v e y c onduc t e di nt hey e a r1995t o2009i nU. S. Pe r s onali nc ome Pe r s onalc ons umpt i on ( $) e xpe ndi t ur e s( $) 23, 310 18, 714 24, 444 19, 569 25, 657 20, 414 27, 260 21, 434 28, 336 22, 738 30, 317 24, 227 31, 162 25, 074 Copyright Cengage Learning. Powered by Cognero.

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CH 7 - Linear Regression 31, 448 32, 282 33, 872 35, 423 37, 723 39, 418 40, 156 39, 113

25, 865 26, 848 28, 228 29, 818 31, 210 32, 551 33, 273 32, 853

? s e dont hi si nt e r v a l ,wha t a .Wha ti st he95pe r c e ntc onfide nc ei nt e r v a lf ort her e gr e s s i onpa r a me t e r βBa 1 se qua lt oz e r o? c onc l us i onc a ny ouma kea boutt heh ypot he s e st ha tt her e gr e s s i onpa r a me t e rβ 1i ? s e dont hi si nt e r v a l ,wha t d. Wha ti st he95pe r c e ntc onfide nc ei nt e r va lf ort her e gr e s s i onpa r a me t e r βBa 0 se qua lt oz e r o? c onc l us i onc a ny ouma kea boutt heh ypot he s e st ha tt her e gr e s s i onpa r a me t e rβ 0i 53. As ur ve yi sc onduc t e dt ode t e r mi newhe t he rt hea g eofc a ri nflue nc e st hea nnua lma i nt e na nc ec os t .As a mpl eof10 c a r si ss e l e c t e da ndt heda t ai ss ho wnbe l o w.

Ageofc ar( mont hs )x 3 5 6 7 9 10 11 13 14 15

AnnualMai nt e nanc e Cos t( $)y 120 115 135 290 275 300 350 475 500 550

a .De v e l opas c a t t e rc ha r tf ort he s eda t awi t ha g eofc a r sa st hei nde pe nde ntva r i a bl e .Wha tdoe st hes c a t t e rc ha r t i nd i c a t ea boutt her e l a t i ons hi pbe t we e na geofac a ra ndt hea nnua lma i nt e na nc ec os t ? b .Us et heda t at ode ve l opa ne s t i ma t e dr e gr e s s i one qu a t i ont ha tc oul dbeus e dt opr e di c tt hea nnua lma i nt e na nc e c os tgi v e nt hea g eoft hec a r .Wha ti st hee s t i ma t e dr e gr e s s i onmode l ? ANSWER: c .Thes c a t t e rc ha r twi t ha g eofc a r sa st hei nd e pe nde ntv a r i a bl ef ol l o ws .

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CH 7 - Linear Regression

Thi ss c a t t e rc ha r ti ndi c a t e st he r ei sapos i t i v el i ne a rr e l a t i on s hi pbe t we e na geofac a r a ndt hea nnua lma i nt e na nc ec os t . d. Thef ol l o wi n gEx c e lout putpr o vi de st hee s t i ma t e dr e gr e s s i one qua t i ont ha tc oul dbe us e dt oe s t i ma t et hea nnua lma i nt e na nc eba s e dont hea geofac a r .

Thee s t i ma t e ds i mpl el i ne a rr e gr e s s i one qua t i oni s

.

The estimated simple linear regression equation can also be found by adding a trendline to the scatter chart as shown on page 304 of the text book. POINTS: DIFFICULTY: REFERENCES: NATIONAL STANDARDS: KEYWORDS:

1 Moderate THE SIMPLE LINEAR REGRESSION MODEL, LEAST SQUARES METHOD, Page 304 United States - BUSPROG: Analytic skills - and DISC: Descriptive Statistics Bloom’s: Application

54. As ur ve yi sc onduc t e dt ode t e r mi newhe t he rt hea g eofc a ri nflue nc e st hea nnua lma i nt e na nc...