Description
Understanding Statistics in the Behavioral Sciences 9th Edition Pagano Test Bank
ISBN:
0495596523
ISBN-13:
9780495596523
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Below you will find some free nursing test bank questions from this test bank:
Chapter 7—Linear Regression
MULTIPLE CHOICE
- 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
- 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
- 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
- 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
- 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
- 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
- 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 |
- 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
- 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
- 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
- Refer to Exhibit 7-1. If an individual has 22% fat, his predicted amount of daily exercise is ____.
a. | 22.80 |
b. | 23.88 |
c. | 24.76 |
d. | 20.22 |
ANS: B PTS: 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
- 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
- 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) | 60.0 | 62.0 | 63.0 | 66.5 | 73.5 | 84.0 |
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
- 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
- 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
- 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
- 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
- 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
- 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
- S (Y – Y’) equals ____.
a. | 0 |
b. | 1 |
c. | cannot be determined from information given |
d. | who cares |
ANS: A PTS: 1
- S (Y – Y’)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
- 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
- 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
- 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
- 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
- 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
- In the regression equation Y’ = X, the Y-intercept is ____.
a. | |
b. | |
c. | 0 |
d. | 1 |
ANS: C PTS: 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
- 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
- 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
- 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
- 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. | 22.00 |
d. | 17.75 |
ANS: A PTS: 1 MSC: WWW
- 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. | -1.8010 |
c. | 0.5838 |
d. | 0.7922 |
ANS: C PTS: 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. | -0.80 |
b. | 0.80 |
c. | 0.40 |
d. | -0.40 |
ANS: A PTS: 1 MSC: WWW
- 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. | 98.70 |
d. | 76.20 |
ANS: C PTS: 1 MSC: WWW
- If = 57.2, = 84.6, and bY = 0.37, the value of aY = ____.
a. | 141.80 |
b. | -25.90 |
c. | 63.44 |
d. | 27.40 |
ANS: C PTS: 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
- If sY = sX = 1 and the value of bY = 0.6, what will the value of r be?
a. | 0.36 |
b. | 0.60 |
c. | 1.00 |
d. | 0.00 |
ANS: B PTS: 1
- When using more than one predictor variable, ____ tells us the proportion of variance accounted for the predictor variables.
a. | r |
b. | SSX |
c. | SSY |
d. | R2 |
ANS: D PTS: 1 MSC: WWW
- 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
- 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
- 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
- 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
- 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
- The regression coefficient for predicting Y given X is symbolized ____
a. | bY |
b. | aY |
c. | bX |
d. | aX |
ANS: A PTS: 1
- The regression coefficient for predicting X given Y is symbolized ____.
a. | bY |
b. | aY |
c. | bX |
d. | aX |
ANS: C PTS: 1
- The regression constant for predicting Y given X is symbolized ____.
a. | bY |
b. | aY |
c. | bX |
d. | aX |
ANS: B PTS: 1
- The regression constant for predicting X given Y is symbolized ____.
a. | bY |
b. | aY |
c. | bX |
d. | aX |
ANS: D PTS: 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
- The total error in prediction equals S (Y – Y’).
ANS: F PTS: 1 MSC: WWW
- 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
- An imperfect relationship generally yields exact prediction.
ANS: F PTS: 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
- Properly speaking, we should limit our predictions to the range of the base data.
ANS: T PTS: 1
- The least squares regression line insures the maximum number of direct hits.
ANS: F PTS: 1 MSC: WWW
- To do linear regression, there must be paired scores on two variables.
ANS: T PTS: 1
- If the standard deviations of the X and Y distributions are equal, then r = bY.
ANS: T PTS: 1
- If sX = sY then bX = bY.
ANS: T PTS: 1 MSC: WWW
- The higher the r value, the lower the standard error of estimate.
ANS: T PTS: 1 MSC: WWW
- Multiple regression uses more than one predictor variable.
ANS: T PTS: 1
- Multiple regression always results in greater prediction accuracy than simple regression.
ANS: F PTS: 1
- If the correlation between two variables is 1.00, the standard error of estimate equals 0.
ANS: T PTS: 1
- Pearson r is the slope of the least squares regression line when the scores are plotted as z scores.
ANS: T PTS: 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
- Define Homoscedasticity.
ANS:
Answer not provided.
PTS: 1
- Define least-squares regression line.
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- Define multiple coefficient of determination.
ANS:
Answer not provided.
PTS: 1
- Define multiple correlation.
ANS:
Answer not provided.
PTS: 1
- Define regression.
ANS:
Answer not provided.
PTS: 1
- Define regression constant.
ANS:
Answer not provided.
PTS: 1
- Define regression line.
ANS:
Answer not provided.
PTS: 1
- Define regression of X on Y.
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- Define regression of Y on X.
ANS:
Answer not provided.
PTS: 1
- Define standard error of estimate.
ANS:
Answer not provided.
PTS: 1
SHORT ANSWER
- Why is it important to know the standard error of estimate for a set of paired scores?
ANS:
Answer not provided.
PTS: 1
- Why does the least squares regression line minimize S (Y – Y’)2, rather than S (Y – Y’)?
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- Is it true that, generally, the regression lines for predicting Y given X and X given Y, are not the same? Explain.
ANS:
Answer not provided.
PTS: 1
- The least squares regression line is the prediction line that results in the most direct “hits.” Is this true? Explain.
ANS:
Answer not provided.
PTS: 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:
Answer not provided.
PTS: 1
- In multiple regression, will use of a second predictor variable always increase the accuracy of prediction? Explain.
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- 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:
Answer not provided.
PTS: 1 MSC: WWW
- 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:
Answer not provided.
PTS: 1