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

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

ISBN:

## 0495596523

ISBN-13:

## 9780495596523

## Description

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

ISBN:

## 0495596523

ISBN-13:

## 9780495596523

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# Free Nursing Test Questions:

**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. | b_{Y} |

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,*s*= 3.4383, and_{Y}*s*= 5.2165, the value of_{X}*b*= ____._{Y}

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. | R^{2} = 1.00 |

b. | R^{2} > r^{2} |

c. | R^{2} = r^{2} |

d. | R^{2} < r^{2} |

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
*s*= 0.0 the relationship between the variables is ____._{Y|X}

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 ±1*s*of the regression line?_{Y|X}

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
*s*= 4.00 for relationship_{Y|X}*A*and*s*= 5.25 for relationship_{Y|X}*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
*b*is negative, higher values of_{Y}*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
*a*is negative, the relationship between_{Y}*X*and*Y*is ____.

a. | positive |

b. | negative |

c. | inverse |

d. | cannot be determined from information given |

ANS: D PTS: 1 MSC: WWW

- If
*b*= 0, the regression line is ____._{Y}

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. | s_{Y|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*X*^{2}= 4656, S*Y*= 79, S*Y*^{2}= 1309, and S*XY*= 2430, what is the value of*b*?_{Y}

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’*= 2.650*X*+ 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
*b*= 0.37, the value of_{Y}*a*= ____._{Y}

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’*= 103*Y*+ 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
*s*=_{Y}*s*= 1 and the value of_{X}*b*= 0.6, what will the value of_{Y}*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 by the predictor variables.

a. | r |

b. | SS_{X} |

c. | SS_{Y} |

d. | R^{2} |

ANS: D PTS: 1 MSC: WWW

- Which of the following statements is(are) false?

a. | b_{Y} is the slope of the line for minimizing errors in predicting Y. |

b. | a_{Y} is the Y axis intercept for minimizing errors in predicting Y. |

c. | s_{Y}_{½} is the standard error of estimate for predicting _{X}Y given X. |

d. | All of the above statements are true. |

e. | R^{2} is the multiple coefficient of nondetermination. |

ANS: E PTS: 1 MSC: WWW

- The regression coefficient
*b*_{Y}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
*s*and_{Y|X}*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 by ____

a. | b_{Y} |

b. | a_{Y} |

c. | b_{X} |

d. | a_{X} |

ANS: A PTS: 1

- The regression coefficient for predicting
*X*given*Y*is symbolized by ____.

a. | b_{Y} |

b. | a_{Y} |

c. | b_{X} |

d. | a_{X} |

ANS: C PTS: 1

- The regression constant for predicting
*Y*given*X*is symbolized by ____.

a. | b_{Y} |

b. | a_{Y} |

c. | b_{X} |

d. | a_{X} |

ANS: B PTS: 1

- The regression constant for predicting
*X*given*Y*is symbolized by ____.

a. | b_{Y} |

b. | a_{Y} |

c. | b_{X} |

d. | a_{X} |

ANS: D PTS: 1

- The symbol for the standard error of estimate when predicting
*Y*given*X*is ____.

a. | r_{X|Y} |

b. | s_{X|Y} |

c. | r_{Y|X} |

d. | s_{Y|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*=*b*._{Y}

ANS: T PTS: 1

- If
*s*=_{X}*s*then_{Y}*b*=_{X}*b*._{Y}

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,
*R*^{2}is the simple sum of*r*^{2}for the relationship of the first predictor variable and*Y*and*r*^{2}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

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