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# Understanding Statistics in the Behavioral Sciences 9th Edition Pagano Test Bank

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## 9780495596523

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# Free Nursing Test Questions:

Chapter 7—Linear Regression

MULTIPLE CHOICE

1. The primary reason we use a scatter plot in linear regression is ____.
 a. to determine if the relationship is linear or curvilinear b. to determine the direction of the relationship c. to compute the magnitude of the relationship d. to determine the slope of the least squares regression line

ANS:  A                    PTS:   1

1. When the relation between X and Y is imperfect, the prediction of Y given X is ____.
 a. perfect b. always equal to Y c. impossible to determine d. approximate

ANS:  D                    PTS:   1

1. The regression equation most often used in psychology minimizes ____.
 a. S (Y – Y’) b. S (Y – Y’)2 c. S (Y – X)2 d. e. none of the above

ANS:  B                    PTS:   1

1. The regression of Y on X ____.
 a. predicts X given Y b. predicts X’ given X c. predicts Y given X d. predicts Y given Y’

ANS:  C                    PTS:   1

1. The regression of X on Y ____.
 a. predicts Y given X b. predicts Y given X c. predicts X given Y d. is generally the same as the regression of Y on X e. c and d

ANS:  C                    PTS:   1

1. If the correlation between two sets of scores is 0 and one had to predict the value of Y for any given value of X, the best prediction of Y would be ____.
 a. bY b. c. 0 d.

ANS:  B                    PTS:   1

1. During the past 5 years there has been an inflationary trend. Listed below is the average cost of a gallon of milk for each year.

 1981 1982 1983 1984 1985 \$1.10 \$1.23 \$1.30 \$1.50 \$1.65

Assuming a linear relationship exists, and that the relationship continues unchanged through 1986, what would you predict for the average cost of a gallon of milk in 1986?

 a. \$1.77 b. \$1.72 c. \$1.70 d. \$1.83

ANS:  A                    PTS:   1

Exhibit 7-1

A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded.

 Individual 1 2 3 4 5 Exercise (min) 10 18 26 33 44 % Fat 30 25 18 17 14

1. Refer to Exhibit 7-1. Assuming a linear relationship holds, the least squares regression line for predicting % fat from the amount of exercise an individual gets is ____.
 a. Y’ =   0.476X + 33.272 b. Y’ =   1.931X + 66.363 c. Y’ = -0.476X + 33.272 d. Y’ = -0.432X + 32.856

ANS:  C                    PTS:   1

1. Refer to Exhibit 7-1. If an individual exercises 20 minutes daily, his predicted % body fat would be ____.
 a. 21.63 b. 27.74 c. 27.88 d. 23.75

ANS:  D                    PTS:   1

1. Refer to Exhibit 7-1. The least squares regression line for predicting the amount of exercise from % fat is ____.
 a. X’ = -1.931Y + 66.363 b. X’ = -0.476Y + 33.272 c. X’ =   1.931Y + 66.363 d. X’ = -1.905Y + 62.325

ANS:  A                    PTS:   1

1. Refer to Exhibit 7-1. If an individual has 22% fat, his predicted amount of daily exercise is ____.
 a. 22.8 b. 23.88 c. 24.76 d. 20.22

ANS:  B                    PTS:   1

1. Refer to Exhibit 7-1. The value for the standard error of estimate in predicting % fat from daily exercise is ____.
 a. 3.35 b. 4.32 c. 2.14 d. 1.66 e. none of the above

ANS:  C                    PTS:   1

1. The assumption of homoscedasticity is that ____.
 a. the range of the Y scores is the same as the X scores b. the X and Y distributions have the same mean values c. the variability of Y doesn’t change over the X scores d. the variability of the X and Y distributions is the same

ANS:  C                    PTS:   1

1. You go to a carnival and a sideshow performer wants to bet you \$100 that he can guess your exact weight just from knowing your height. It turns out that there is the following relationship between height and weight.

 Height (in) 60 62 63 66.5 73.5 84 Weight (lbs) 99 107 111 125 153 195

Should you accept the performer’s bet? Explain.

 a. yes b. need more information c. no d. yes, if he measures my height in centimeters

ANS:  C                    PTS:   1

1. If r = 0.4582, sY = 3.4383, and sX = 5.2165, the value of bY = ____.
 a. 0.695 b. 0.458 c. 0.302 d. 1 – 0.458 e. none of the above

ANS:  C                    PTS:   1

1. In multiple regression, if the second predictor variable correlates highly with the predicted variable, than it is quite likely that ____.
 a. R2 = 1.00 b. R2 > r2 c. R2 = r2 d. R2 < r2

ANS:  B                    PTS:   1

1. If the relationship between X and Y is perfect:
 a. r = b b. the equation for Y‘ equals the equation for X‘ c. prediction is approximate d. a and b e. all of the above

ANS:  D                    PTS:   1

1. When predicting Y, adding a second predictor variable to the first predictor variable X, will ____.
 a. always increase prediction accuracy b. increase prediction accuracy depending on the relationship between the second predictor variable and X c. Increase prediction accuracy depending on the relationship between the second predictor variable and Y d. b and c

ANS:  D                    PTS:   1

1. The higher the standard error of estimate is,
 a. the more accurate the prediction is likely to be b. the less accurate is the prediction is likely to be c. the less confidence we have in the accuracy of the prediction d. the more confidence we have in the accuracy of the prediction e. a and d f. b and c

ANS:  F                    PTS:   1

1. If sY|X = 0.0 the relationship between the variables is ____.
 a. perfect b. imperfect c. curvilinear d. unknown

ANS:  A                    PTS:   1                    MSC:  WWW

1. S (YY’) equals ____.
 a. 0 b. 1 c. cannot be determined from information given d. who cares

ANS:  A                    PTS:   1

1. S (YY’)2 represents ____.
 a. the standard deviation b. the variance c. the standard error of estimate d. the total error of prediction

ANS:  D                    PTS:   1                    MSC:  WWW

1. In a particular relationship N = 80. How many points would you expect on the average to find within ±1sY|X of the regression line?
 a. 40 b. 80 c. 54 d. 0

ANS:  C                    PTS:   1

1. What would you predict for the value of Y for the point where the value of X is ?
 a. cannot be determined from information given b. 0 c. 1 d.

ANS:  D                    PTS:   1

1. If the value of sY|X = 4.00 for relationship A and sY|X = 5.25 for relationship B, in which relationship would you have the most confidence in a particular prediction?
 a. A b. B c. it makes no difference d. cannot be determined from information given

ANS:  A                    PTS:   1                    MSC:  WWW

1. If bY is negative, higher values of X are associated with ____.
 a. lower values of X’ b. higher values of Y c. higher values of (Y – Y’) d. lower values of Y

ANS:  D                    PTS:   1

1. Which of the following statement(s) is (are) an important consideration(s) in applying linear regression techniques?
 a. the relationship should be linear b. both variables must be measured in the same units c. predictions for Y should be within the range of the X variable in the sample d. a and c

ANS:  D                    PTS:   1                    MSC:  WWW

1. In the regression equation Y’ = X, the Y-intercept is ____.
 a. b. c. 0 d. 1

ANS:  C                    PTS:   1

1. If the value for aY is negative, the relationship between X and Y is ____.
 a. positive b. negative c. inverse d. cannot be determined from information given

ANS:  D                    PTS:   1                    MSC:  WWW

1. If bY = 0, the regression line is ____.
 a. horizontal b. vertical c. undefined d. at a 45° angle to the X axis

ANS:  A                    PTS:   1

1. The least-squares regression line minimizes ____.
 a. s b. sY|X c. S (Y – )2 d. S (Y – Y’)2 e. b and d

ANS:  E                    PTS:   1

1. The points (0,5) and (5,10) fall on the regression line for a perfect positive linear relationship. What is the regression equation for this relationship?
 a. Y’ = X + 5 b. Y’ = 5X c. Y’ = 5X + 10 d. cannot be determined from information given.

ANS:  A                    PTS:   1

1. For the following points what would you predict to be the value of Y’ when X = 19? Assume a linear relationship.

 X 6 12 30 40 Y 10 14 20 27

 a. 16.35 b. 24.69 c. 22 d. 17.75

ANS:  A                    PTS:   1                    MSC:  WWW

1. If N = 8, S X = 160, S X2 = 4656, S Y = 79, S Y2 = 1309, and S XY = 2430, what is the value of bY?
 a. 0.9217 b. -1.801 c. 0.5838 d. 0.7922

ANS:  C                    PTS:   1

1. If X and Y are transformed into z scores, and the slope of the regression line of the z scores is -0.80, what is the value of the correlation coefficient?
 a. -0.8 b. 0.8 c. 0.4 d. -0.4

ANS:  A                    PTS:   1                    MSC:  WWW

1. If the regression equation for a set of data is Y’ = 2.650X + 11.250 then the value of Y’ for X = 33 is ____.
 a. 87.45 b. 371.25 c. 98.7 d. 76.2

ANS:  C                    PTS:   1                    MSC:  WWW

1. If  = 57.2,  = 84.6, and bY = 0.37, the value of aY = ____.
 a. 141.8 b. -25.9 c. 63.44 d. 27.4

ANS:  C                    PTS:   1

1. If the regression line for predicting X given Y were X’ = 103Y + 26.2, what would the value of X’ be if Y = 0.2?
 a. 129.2 b. 25.8 c. 5.2 d. 46.8

ANS:  D                    PTS:   1

1. If sY = sX = 1 and the value of bY = 0.6, what will the value of r be?
 a. 0.36 b. 0.6 c. 1 d. 0

ANS:  B                    PTS:   1

1. When using more than one predictor variable, ____ tells us the proportion of variance accounted for by the predictor variables.
 a. r b. SSX c. SSY d. R2

ANS:  D                    PTS:   1                    MSC:  WWW

1. Which of the following statements is(are) false?
 a. bY is the slope of the line for minimizing errors in predicting Y. b. aY is the Y axis intercept for minimizing errors in predicting Y. c. sY½X is the standard error of estimate for predicting Y given X. d. All of the above statements are true. e. R2 is the multiple coefficient of nondetermination.

ANS:  E                    PTS:   1                    MSC:  WWW

1. The regression coefficient bY and the correlation coefficient r ____.
 a. necessarily increase in magnitude as the strength of relationship increases b. are both slopes of straight lines c. are not related d. will equal each other when the variability of the X and Y distributions are equal e. b and d

ANS:  E                    PTS:   1

1. When predicting Y given X, ____.
 a. the prediction is valid only within the range of X b. the variability of the Y values over the range of the X values should be the same c. the representativeness of the sample used to derive the regression line is an important consideration d. a, b, and c e. a and c

ANS:  D                    PTS:   1

1. When predicting Y from two variables relative to using only one variable, ____.
 a. prediction accuracy always increases b. prediction accuracy is dependent on the relationship between the second variable and the Y variable c. increase in prediction accuracy depends on the correlation between the two predictor variables d. b and c

ANS:  D                    PTS:   1

1. There is ____ between the sY|X and r.
 a. a direct relationship b. an inverse relationship c. no relationship d. animosity

ANS:  B                    PTS:   1

1. The regression coefficient for predicting Y given X is symbolized by ____
 a. bY b. aY c. bX d. aX

ANS:  A                    PTS:   1

1. The regression coefficient for predicting X given Y is symbolized by ____.
 a. bY b. aY c. bX d. aX

ANS:  C                    PTS:   1

1. The regression constant for predicting Y given X is symbolized by ____.
 a. bY b. aY c. bX d. aX

ANS:  B                    PTS:   1

1. The regression constant for predicting X given Y is symbolized by ____.
 a. bY b. aY c. bX d. aX

ANS:  D                    PTS:   1

1. The symbol for the standard error of estimate when predicting Y given X is ____.
 a. rX|Y b. sX|Y c. rY|X d. sY|X

ANS:  D                    PTS:   1

TRUE/FALSE

1. The total error in prediction equals S (YY’).

ANS:  F                    PTS:   1                    MSC:  WWW

1. In general, the regression line for predicting X given Y is the same as the regression line for predicting Y given X.

ANS:  F                    PTS:   1

1. An imperfect relationship generally yields exact prediction.

ANS:  F                    PTS:   1

1. When the relationship is perfect, the regression of Y on X is the same as the regression of X on Y.

ANS:  T                    PTS:   1                    MSC:  WWW

1. Properly speaking, we should limit our predictions to the range of the base data.

ANS:  T                    PTS:   1

1. The least squares regression line insures the maximum number of direct hits.

ANS:  F                    PTS:   1                    MSC:  WWW

1. To do linear regression, there must be paired scores on two variables.

ANS:  T                    PTS:   1

1. If the standard deviations of the X and Y distributions are equal, then r = bY.

ANS:  T                    PTS:   1

1. If sX = sY then bX = bY.

ANS:  T                    PTS:   1                    MSC:  WWW

1. The higher the r value, the lower the standard error of estimate.

ANS:  T                    PTS:   1                    MSC:  WWW

1. Multiple regression uses more than one predictor variable.

ANS:  T                    PTS:   1

1. Multiple regression always results in greater prediction accuracy than simple regression.

ANS:  F                    PTS:   1

1. If the correlation between two variables is 1.00, the standard error of estimate equals 0.

ANS:  T                    PTS:   1

1. Pearson r is the slope of the least squares regression line when the scores are plotted as z scores.

ANS:  T                    PTS:   1

1. When there are two predictor variables, R2 is the simple sum of r2 for the relationship of the first predictor variable and Y and r2 for the relationship of the second predictor variable and Y.

ANS:  F                    PTS:   1

DEFINITIONS

1. Define Homoscedasticity.

ANS:

PTS:   1

1. Define least-squares regression line.

ANS:

PTS:   1                    MSC:  WWW

1. Define multiple coefficient of determination.

ANS:

PTS:   1

1. Define multiple correlation.

ANS:

PTS:   1

1. Define regression.

ANS:

PTS:   1

1. Define regression constant.

ANS:

PTS:   1

1. Define regression line.

ANS:

PTS:   1

1. Define regression of X on Y.

ANS:

PTS:   1                    MSC:  WWW

1. Define regression of Y on X.

ANS:

PTS:   1

1. Define standard error of estimate.

ANS:

PTS:   1

1. Why is it important to know the standard error of estimate for a set of paired scores?

ANS:

PTS:   1

1. Why does the least squares regression line minimize S (YY’)2, rather than S (YY’)?

ANS:

PTS:   1                    MSC:  WWW

1. Is it true that, generally, the regression lines for predicting Y given X and X given Y, are not the same? Explain.

ANS:

PTS:   1

1. The least squares regression line is the prediction line that results in the most direct “hits.” Is this true? Explain.

ANS:

PTS:   1

1. In what situation would the regression line for predicting Y given X be the same as the line predicting X given Y? Explain.

ANS:

PTS:   1

1. In multiple regression, will use of a second predictor variable always increase the accuracy of prediction? Explain.

ANS:

PTS:   1                    MSC:  WWW

1. If there is no relationship between the X and Y variables and we desire to predict Y given X using a least-squares criterion, it is best to predict  for every Y score. Is this correct? If so, explain why. (Hint: one of the properties of the mean might be helpful here)

ANS:

PTS:   1                    MSC:  WWW

1. A friend that thinks a lot about statistics asserts that, “the closer the points in the scatter plot are to the least-squares regression line, the higher the correlation.” Is your friend correct? Discuss.

ANS: