Howell 9e_TBChapter 10

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Chapter 10—Regression MULTIPLE CHOICE QUESTIONS 10.1 + When I want to make a prediction but don’t have the value of X on which to base that prediction, my best estimate is a) the value that I calculate with a regression equation. b) the smallest value of Y. c) *the mean of Y . d) There is no good prediction. 10.2 When we make a prediction using a regression equation, our prediction is _______ on X . a) dependent b) conditional c) correlated d) *both a and b 10.3 + If the correlation between X and Y is negative, the slope of the regression equation must be a) *negative. b) positive. c) non-significant. d) It could be either a or b. 10.4 + When we have considerable spread of the points about the regression line, the slope of that line will be _______ the slope of a similar line when there is less scatter. a) less than b) more than c) *the same as d) more extreme than 10.5 + The equation for a straight line is an equation of the form a) Y = bX a b) Y = bX c) Y = bX 2 + a d) * Y = bX + a 10.6 In the equation for a straight line used in the text, the intercept is represented by a) * a b) b c) X d) Y

Test Bank 10.7 In the equation for a straight line used in the text, the slope is represented by a) a b) * b c) X d) Y 10.8 When the slope of the regression line is positive, the line goes from a) upper left to lower right. b) *lower left to upper right. c) the line is flat. d) It depends on the intercept. 10.9 If we have a regression line predicting the amount of improvement in your performance as a function of the amount of tutoring you receive, an intercept of 12 would mean that a) you need to have 12 hours of tutoring to get an A. b) if you don’t have any tutoring, the best you can do is a grade of 12. c) *even without tutoring you will improve. d) tutoring helps. 10.10 + Suppose that you sell ice cream from a cart on the street. After you pay the ice cream supplier, the regression line that predicts your ice cream profits from the number of hours you work has a slope of 15. But the man who owns the cart charges you $5 per hour in rent. How much money will you earn per hour? a) $15 b) *$10 c) $5 d) nothing 10.11 + In the previous problem your best estimate of the intercept relating the total earning from the hours worked is a) -10. b) *0. c) 10. d) We have no idea. 10.12 The notation is used instead of Y a) to indicate that the answer is only approximate. b) to indicate that we have an equation for a straight line. c) *to indicate that the result is a prediction. d) because this is a mathematical equation. 10.13 The “best fitting line” is that regression line that a) minimizes the errors of prediction. b) minimizes each squared error of prediction. c) *minimizes the sum of squared errors of prediction. d) hits the most points as it goes through the scatterplot. 283

Chapter 10 10.14 The notation ( Y - ˆ Y ) represents a) our best prediction. b) the regression line. c) the predicted value. d) *error in prediction. 10.15 In calculating the regression coefficients we square the errors of prediction because a) statisticians square everything. b) *the sum of the errors would always be 0 for a great many lines we could draw. c) squaring makes the errors more striking. d) little errors are more important than big errors. 10.16 The symbols a and b are frequently referred to as a) *regression coefficients. b) constants. c) slopes. d) regression correlations. 10.17 In the equation = 12.6 X + 5 a) a difference of one unit in X will lead to a 5 point difference in the prediction. b) will decrease as X increases. c) the correlation is certain to be significant. d) *a difference of one unit in X will lead to a 12.6 point difference in the prediction. 10.18 + When we standardize paired data we a) divide everything by the standard deviation of X . b) convert X to a T score. c) *convert both X and Y to z scores. d) subtract the mean from each value of X and Y . 10.19 When we have standardized data, the slope will be denoted as a) b b) *  c) 1.0 d) r 10.20 + When we think in terms of standardized data, the slope represents a) the change in X for a one unit change in Y . b) *the number of standard deviations will differ for a one standard deviation difference in X . c) the height of the regression line. d) 0. 284

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Test Bank 10.21 If data with only one predictor variable were standardized, the slope would equal a) * r b) b c) a d) 10.22 + If you want to plot the regression line, after having found the regression equation, you need to calculate for _______ value(s) of X . a) all possible b) one c) *a minimum of two d) at least five 10.23 The regression line always passes through the point a) 0, 0 b) * , c) , 0 d) a, b 10.24 The notation Y - ˆ Y is referred to as a) error. b) deviation. c) residual. d) *all of the above 10.25 If we do not know X , our measure of error in predicting Y is a) *the standard deviation of Y. b) the standard deviation of X. c) the standard error of estimate. d) the standardized residual. 10.26 If we do know X , our measure of error is a) the standard deviation of Y. b) the standard deviation of X. c) *the standard error of estimate. d) the standardized residual. 10.27 + The standard error of estimate is given by a) b) c) d) *none of the above 285

Chapter 10 10.28 The standard error of estimate is denoted by a) b) * c) d) none of the above 10.29 We can think of the standard error of estimate as a) *the standard deviation of the errors that we make when using the regression equation. b) the standard deviation of Y. c) the variance of the errors that we would make when using the regression equation. d) the variance of X . 10.30 When we use a regression equation to make a prediction, the errors that we make are often referred to as a) *residuals. b) predictions. c) . d) standard errors. 10.31 + If the correlation between a body image measure and an eating disorders measure is .50, we can conclude that a) body image has very little to do with eating disorders. b) 50% of the variability in the eating disorders scales is associated with variability in body image. c) *one quarter of the variability in the eating disorders scores is associated with variability in body image. d) overweight people eat too much. 10.32 The notation SS stands for a) simply sensational. b) statistical significance. c) squared sums. d) *sum of squares. 10.33 If we want to specify the percentage of the overall variability in life expectancy attributable to variability in smoking behavior, the statistic we want to look at is a) r b) * r 2 c) b d)  10.34 + An important thing about r 2 is that it represents a measure of a) causal relationships. b) *accountable variability. 286

Test Bank c) the correlation. d) statistical significance. 10.35 + Which of the following does NOT belong with the rest? a) variance attributable to b) variance associated with c) variance predictable from d) *variance caused by 10.36 + If the correlation between X and Y is significant, that tells us a) *that the slope is significant. b) that the intercept is significant. c) that X causes Y. d) nothing about the regression equation. 10.37 A significant slope means that a) the slope is positive. b) there is a significant relationship between X and Y in the population. c) the slope is not equal to 0 in the population. d) *both b and c 10.38 If the slope is significant we know that a) the intercept is not significant. b) the intercept is significant. c) there is a strong relationship between the two variables. d) *none of the above 10.39 If you drop a pencil randomly on a scatterplot, what aspect are you changing as you move the pencil vertically on the page without rotating it? a) the slope. b) *the intercept. c) the correlation. d) the residual. 10.40 If you drop a pencil randomly on a scatterplot, what aspect are you changing as you rotate the pencil about the point where it crosses the Y axis? a) *the slope. b) the intercept. c) the correlation. d) the residual. 10.41 In a scatterplot, an outlier is one that a) is far to the left of the display. b) is in the center of the display. c) *is far from the regression line. d) is the largest value of Y . 287

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Chapter 10 10.42 + An example in the text hypothesized that 4% of the variability in life expectancy was accounted for by variability in smoking behavior. The values of r and r 2 , respectively, are equal to a) *.20 and .04. b) .04 and .16. c) .04 and .20. d) More information is needed. 10.43 A regression analysis of hours spent exercising and ounces of weight loss had a slope of 3. We would predict that a) *for every 1 hour of exercise, a person would lose 3 ounces of weight. b) for every ounce lost, a person has to exercise for 7 hours. c) every hour of exercise would have no effect on weight. d) The slope cannot be used to make predictions, you need the intercept. 10.44 When one refers to the degree that variable A changes as variable B changes they are referring to a) variance. b) *regression. c) covariance. d) habituation. 10.45 A regression line is a) a line of covariance. b) a correlation matrix. c) *the best fit straight line. d) the equal to a correlation line. 10.46 The intercept of a regression line is a) *the value of when X=0. b) always greater than 0. c) significant when the correlation is significant. d) never informative. TRUE/FALSE QUESTIONS 10.47 [FALSE] Regression is only appropriate for predicting a criterion variable from one predictor variable. 10.48 [TRUE] Regression can be used to examine both linear and curvilinear relationships. 10.49 [FALSE] If the correlation between smoking and lung cancer is .50, smoking accounts for 50% of the variability in lung cancer. 288

Test Bank 10.50 [TRUE] If the association between warm parenting practices and self-esteem is .50, then 75% of the variability in self-esteem is independent of warm parenting practices. 10.51 [FALSE] Regression is typically used to test cause-effect relationships. 10.52 [TRUE] The regression equation can be used to estimate the value of the criterion variable based on knowing the value of the predictor variable. 10.53 [TRUE] In a regression using standardized data, to predict health symptoms from stress, the beta = .5. This means that for every 1 point increase in stress there is half a point increase in symptoms. 10.54 [TRUE] When there is only one predictor variable in a regression, beta (regression coefficient) = r (correlation coefficient). 10.55 [FALSE] Using a regression equation to predict a value will always lead to highly accurate predictions. 10.56 [TRUE] Residual refers to the error of prediction. OPEN-ENDED QUESTIONS 10.57 Given this regression equation, = .75 X + 5, estimate Y for the following values of X. a) X = 0 b) X = 1 c) X = -3 d) X = 75 10.58 Given the following values, calculate the regression equation. Age of car (years) Mileage 1.00 40.00 1.00 25.00 2.00 37.00 2.00 35.00 3.00 36.00 3.00 35.00 4.00 32.00 5.00 30.00 6.00 25.00 10.00 20.00 10.59 Calculate the residuals for the previous data. Explain how you did it. 10.60 Calculate SS error for the previous data. Explain how you did it. 289

Chapter 10 10.61 Given this regression equation, = .3 X + 25, estimate the values of X given the following values of Y. a) Y = 0 b) Y = 25 c) Y = -30 10.62 Write a sentence interpreting the regression data in the following table. 30.377 4.599 6.605 .000 5.116 1.287 .448 3.975 .000 (Constant) Maternal report of toddler anger Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Dependent variable: Child Behavior Problem Score 10.63 Answer the following questions based on the regression data in the previous table. a) What percent of variability in behavior problems is accounted for by anger? b) What percent of variability in behavior problems independent of anger? 10.64 Given the data in the previous table: a) What is the slope of the regression line? b) What does the value of the slope mean here? c) Is the slope significantly different from 0? 10.65 Given the following data, do you believe the regression equation would be a reliable way to predict values of Y. Explain your answer. 10.66 Briefly describe the difference between the standardized beta coefficient and the unstandardized b 290

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Howell 9e_TBChapter 10

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