Deck 8: Linear Regression

Question 1

In regression,we sometimes talk about using X to predict Y.In such situations,Y is then called

A)
B)the predictor variable.
C)the criterion variable.
D)the intercept.

Answer 1

the criterion variable.

Question 2

A regression line is used to obtain

A)the Y at each X.
B)the X at each Y.
C)the at any X.
D)the X at any .

Answer 2

the at any X.

Question 3

What is the slope of the following regression equation?

A)3.92
B)-3.92
C)2.69
D)2.69X

Answer 3

2.69

Question 4

The linear regression line indicates

A)whether a relationship exists.
B)the strength of a relationship.
C)the direction of a relationship.
D)the best-fitting straight line in a linear relationship.

Question 5

The slope of a line is a number indicating the

A)slant of the line and the Y-intercept.
B)slant of the line and the direction in which it slants.
C)slant of the line and the X-intercept.
D)length of the regression line to be drawn.

Question 6

Linear regression is important because

A)it is used to predict unknown Y scores based on X scores from a correlated variable.
B)it is used to predict unknown Y scores based on X scores,even if the X variable is not correlated with the Y variable.
C)it is a statistic that summarizes the relationship between the X and Y variables.
D)it indicates how close our predictions of Y values are to the actual Y values.

Question 7

The best-fitting line through a scatterplot is known as the ______ line.

A)scatterplot
B)correlation
C)variance
D)regression

Question 8

Which of the following formulas represents the Y intercept of the regression line?

A)
B)
C)
D)

Question 9

Which of the following is not true of the linear regression equation?

A)It is the equation from which the correlation coefficient is calculated.
B)It defines the straight line that summarizes a relationship.
C)It describes two characteristics of the regression line: its slope and its Y-intercept.
D)It is the equation that produces the value of at each X.

Question 10

What is the Y-intercept of the following regression equation?

A)0.56X
B)0.56
C)2.41
D)X + 2.41

Question 11

In the regression equation,the slope summarizes ______ and the Y-intercept indicates ______.

A)predictor variables;what the value of the criterion variable is
B)the steepness and direction of the regression line;the value of when X = 0
C)the length of the regression line;the starting point of the regression line
D)the starting point from which the Y scores begin to change as the X scores increase;the direction and rate in which Ys change as X increases

Question 12

What is the Y-intercept of the following regression equation? = -4.30X - 1.72

A)-1.72
B)1.72
C)-4.30
D)-4.30X

Question 13

The regression line is the best-fitting line because

A)it best takes into account all the X and Y scores.
B)on average,the regression line passes through the center of the various Y standard deviations.
C)it is the straightest line that can be created through the Y scores.
D)on average,the regression line passes through the center of the various Y means.

Question 14

In looking at the regression equation,we know that the relationship is negative if the

A)Y-intercept value is negative.
B)slope value is negative.
C)slope value is zero.
D)Y-intercept value is zero.

Question 15

What is the slope of the following regression equation? = -8.27X + 3.09

A)8.27
B)-8.27
C)3.09
D)-3.09

Question 16

The Y-intercept is the value of when X equals

A)1.0
B)0.0
C)-1.0
D)2.0

Question 17

Which of the following is NOT representative of a strong relationship?

A)Y scores that are relatively close to their corresponding scores.
B)A correlation coefficient close to 1.
C)Y scores that are spread out.
D)Less prediction error and a smaller value of

Question 18

Which of the following formulas represents the slope of the regression line?

A)
B)
C)
D)

Question 19

is

A)the actual Y scores.
B)the predicted Y scores.
C)the standard deviation of Y.
D)the standard error of the estimate.

Question 20

If there is no relationship between two variables,the slope of the regression line will equal

A)1.0
B)0.5
C)0.0
D)-1.0

Question 21

For the following data,what is the predicted test score for a person with a stress level of 10?

A)0.76
B)20.93
C)-7.16
D)12.43

Question 22

One assumption of linear regression is

A)the Y scores at each X form an approximately normal distribution.
B)the X scores at each Y form an approximately normal distribution.
C)at each X,both the X and Y score samples should represent an approximately normal distribution.
D)at each X,approximately 68% of all Y scores should be between .

Question 23

For the following data,what is the standard error of the estimate?

A)3.71
B)5.72
C)32.72
D)1,070.49

Question 24

For the following data,what is the regression equation?

A) = 20.93X - 0.85
B) = -0.85 X + 20.93
C) = 20.93 X + 0.85
D) = 0.85 X + 20.93

Question 25

The sum of the deviations of the true Y scores from the predicted scores is always

A)zero.
B)a very large number.
C)equal to N times the mean of Y.
D)negative.

Question 26

Homoscedasticity occurs when

A)there is a nonlinear relationship between the X and Y scores.
B)the Y scores have a different degree of spread at different Xs.
C)the Y scores are spread out to the same degree at every X.
D)the Y' scores are spread out to the same degree at every X.

Question 27

A nutrition major at State University was studying the relationship between carbohydrates (X)and calories (Y).For example,a serving of a particular brand of wheat pasta yielded 42 carbohydrates and 210 calories.After collecting X and Y data on many kinds of foods,the student determined the slope of the regression line to be 4.0 and the Y intercept to be 3.0.If a new food is tested,and the number of carbohydrates (X)is 100,what would be the predicted calories ( )?

A)304
B)403
C)305
D)504

Question 28

If the correlation coefficient turns out to be a relatively high value,then the value of will be

A)relatively low.
B)relatively high.
C)unrelated to the value of r.
D)low if r is positive and high if r is negative.

Question 29

The standard error of the estimate is similar to the

A)sum of the actual Y scores around their predicted Y' scores.
B)standard deviation of actual Y scores around their predicted Y' scores.
C)degree to which any predicted Y' will deviate from its actual Y score.
D)standard deviation of actual Y scores around their actual X scores.

Question 30

The "error" in a single prediction is equal to the degree to which a participant's ______ score deviates from the ______.

A)actual;mean
B)predicted;mean
C)predicted;given X
D)actual;corresponding predicted score

Question 31

In a study of the relationship between amount of sugar consumed (X)and excitability (Y)in children,the regression equation was calculated to be .The amount of sugar consumed ranged from 1 to 4 ounces.Which of the following graphs correctly displays the regression line?

A)Graph A
B)Graph B
C)Graph C
D)Graph D

Question 32

To predict a score from a given X score using the regression equation,we would

A)first multiply X by the slope and then add the Y-intercept.
B)first multiply X by the Y-intercept and then add the slope.
C)first add the Y-intercept to X and then multiply by the slope.
D)first add the slope to X and then multiply by the Y-intercept.

Question 33

When heteroscedasticity exists,the problem with r is that it

A)does not accurately describe the predicted Y values.
B)is very large.
C)does not accurately describe the strength of the relationship for all Xs.
D)will equal 0.

Question 34

In the following study,researchers wanted to determine if a relationship existed between the minutes of light therapy a patient receives and the patient's reported score on a seasonal affective disorder (SAD)test.What is the regression equation for the data below?

A) = -3.08X + 1.64
B) = 9.5 X + 12.5
C) = 2.69 X - 0.49
D) = 1.64 X - 3.08

Question 35

Heteroscedasticity occurs when

A)there is a nonlinear relationship between the X and Y scores.
B)the scores are spread out to the same degree at every X.
C)the Y scores are spread out to the same degree at every X.
D)the Y scores have a different degree of spread at different Xs.

Question 36

Computing the standard error of the estimate ( )by subtracting each from the corresponding Y,squaring the difference,summing the results,dividing by N,and then taking the square root (the defining formula)is difficult and time-consuming.Fortunately,the same value can be computed by multiplying the standard deviation of Y (i.e. , )by

A)100
B)
C)
D)0.5

Question 37

When r = 1.0,then equals

A)r
B)0
C)1.0
D)

Question 38

In the following study,researchers wanted to determine if a relationship existed between the minutes of light therapy a patient receives and the patient's reported score on a seasonal affective disorder (SAD)test.What is the standard error of the estimate?

A)2.31
B)4.86
C)5.34
D)1.52

Question 39

When there is no relationship between two variables,the value of every is equal to

A)the value of every X.
B)the value of every Y.
C)the value of the Y-intercept.
D)zero.

Question 40

When r = 0.0,the value of is equal to

A)
B)0
C)1.0
D)

Question 41

The coefficient of alienation is interpreted as the

A)amount of variance determined in all the Y scores.
B)alienation of variance in all the Y scores.
C)degree to which the scores are efficient.
D)proportion of variance not accounted for.

Question 42

When we square the correlation coefficient to produce ,the result is equal to the

A)proportion of variance not accounted for.
B)proportion of variance accounted for.
C)standard error of the estimate.
D)coefficient of alienation.

Question 43

We calculate the proportion of variance accounted for because it is the statistical basis for evaluating

A)the usefulness of a relationship.
B)the strength of the correlation coefficient.
C)the linearity of the two scores.
D)the average deviation among the Y scores.

Question 44

The coefficient of determination is interpreted as the

A)amount of variance determined in all the Y scores.
B)determined amount of variance in all the Y scores.
C)degree to which the scores are efficient.
D)proportion of variance accounted for.

Question 45

For the following data,what is the proportion of variance accounted for?

A)-0.76
B)0.58
C)0.76
D)-0.58

Question 46

When we use a relationship to predict scores,our error is

A)the mean of Y.
B)the mean of X.
C) .
D) .

Question 47

In general,the greater the proportion of variance accounted for,

A)the more error there is in the data.
B)the less accurately we can predict behavior.
C)the more accurately we can predict behavior.
D)the less important the relationship to our ability to make predictions.

Question 48

A recent study of burnout among therapists shows a positive correlation of 0.53 between the number of clients a therapist is treating and the therapist's feelings of burnout.What proportion of the variance in feelings of burnout is accounted for by this relationship?

A)0.73
B)0.47
C)0.28
D)0.53

Question 49

Compared to a strong relationship,a weak relationship between two variables results in

A)greater prediction error and a larger value of .
B)greater prediction error and a smaller value of .
C)less prediction error and a larger value of .
D)less prediction error and a smaller value of .

Question 50

In the following study,researchers wanted to determine if a relationship existed between the minutes of light therapy a patient receives and the patient's reported score on a seasonal affective disorder (SAD)test.What is the proportion of variance not accounted for?

A)0.77
B)2.31
C)0.23
D)4.86

Question 51

The coefficient of determination is equal to

A) .
B) .
C) .
D)

Question 52

When we divide the error remaining after we use the relationship to predict Y scores ( )by the total error when we use the mean to predict the Y scores ( )and then subtract the result from 1,the final result is the

A)proportion of variance not accounted for.
B)proportion of variance accounted for.
C)standard error of the estimate.
D)coefficient of alienation.