Deck 7: Linear Regression

Question 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. Based on the above data, 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

Answer 1

23.75

Question 2

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. The least squares regression line for predicting the amount of exercise from % fat is _________.

A) X' = - 1.931 Y + 66.363
B) X' = - 0.476 Y + 33.272
C) X' = 1.931 Y + 66.363
D) X' = - 1.905 Y + 62.325

Answer 2

X' = - 1.931 Y + 66.363

Question 3

S ( Y - Y' ) equals _________.

A) 0
B) 1
C) cannot be determined from information given
D) who cares

Answer 3

0

Question 4

The regression equation most often used in psychology minimizes _________.

A) Σ( Y - Y' )
B) Σ( Y - Y' ) ²
C) Σ( Y - X ) ²
D)
E) none of these

Question 5

If the relationship between X and Y is perfect:

A) r = b_Y
B) r ?0? b_Y
C) prediction is approximate
D) a and c
E) all of the above

Question 6

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. Should you accept the performers bet? Explain.

A) yes
B) need more information
C) no
D) yes, if he measures my height in centimeters

Question 7

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. Assuming a linear relationship holds, the least squares regression line for predicting % fat from the amount of exercise an individual gets is _________.

A) Y' = 0.476 X + 33.272
B) Y' = 1.931 X + 66.363
C) Y' = - 0.476 X + 33.272
D) Y' = - 0.432 X + 32.856

Question 8

If r = 0.4582, s Y = 3.4383, and s X = 5.2165, the value of b Y = _________.

A) 0.695
B) 0.458
C) 0.302
D) 1 - 0.458
E) none of these

Question 9

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. 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

Question 10

If = 0.0 the relationship between the variables is _________.

A) perfect
B) imperfect
C) curvilinear
D) unknown

Question 11

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

Question 12

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

Question 13

For regression purposes,

A) X is assigned to the variable being predicted.
B) Y is assigned to the variable being predicted.
C) It doesn't matter whether X or Y is assigned to the variable being predicted.
D) none of these

Question 14

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

Question 15

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

Question 16

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)
C) 0
D)

Question 17

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 '

Question 18

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. 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

Question 19

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. 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 these

Question 20

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

Question 21

If = 57.2, = 84.6, and b Y = 0.37, the value of a Y = _________.

A) 141.80
B) -25.90
C) 63.44
D) 27.40

Question 22

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 _YIX is the standard error of estimate for predicting Y given X .
D) All of these statements are true.
E) R ² is the multiple coefficient of nondetermination.

Question 23

In a particular relationship N = 80. How many points would you expect on the average to find within 1 of the regression line?

A) 40
B) 80
C) 54
D) 0

Question 24

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)

Question 25

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) are both slopes of straight lines and will equal each other when the variability of the X and Y distributions are equal

Question 26

If b Y 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

Question 27

S ( Y - Y' ) 2 represents _________.

A) the standard deviation
B) the variance
C) the standard error of estimate
D) the total error of prediction

Question 28

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

Question 29

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

A) 16.35
B) 24.69
C) 22.00
D) 17.75

Question 30

If s Y = s X = 1 and the value of b Y = 0.6, what will the value of r be?

A) 0.36
B) 0.60
C) 1.00
D) 0.00

Question 31

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' = 5 X
C) Y' = 5 X + 10
D) cannot be determined from information given.

Question 32

In the regression equation Y' = X , the Y -intercept is _________.

A)
B)
C) 0
D) 1

Question 33

If the value for a Y is negative, the relationship between X and Y is _________.

A) positive
B) negative
C) inverse
D) cannot be determined from information given

Question 34

When using more than one predictor variable, _________ tells us the proportion of variance accounted for b y the predictor variables.

A) r
B) ΣS _X
C) ΣS _Y
D) R ²

Question 35

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

Question 36

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

Question 37

The least-squares regression line minimizes _________.

A) s
B)
C) S ( Y - ) 2
D) S ( Y - Y' ) 2
E) b and d

Question 38

If N = 8, ΣX = 160, ΣX ² = 4656, ΣY = 79, Σ Y ² = 1309, and ΣXY = 2430, what is the value of b Y ?

A) 0.9217
B) - 1.8010
C) 0.5838
D) 0.7922

Question 39

If the value of = 4.00 for relationship A and = 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

Question 40

If b Y = 0, the regression line is _________.

A) horizontal
B) vertical
C) undefined
D) at a 45 ° angle to the X axis

Question 41

Multiple regression uses more than one predictor variable.

Question 42

The regression coefficient for predicting Y given X is symbolized by _______

A) b _Y
B) a _Y
C) b _X
D) a _X

Question 43

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

Question 44

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

Question 45

There is ________ between the s _{Y ½ X} and r .

A) a direct relationship
B) an inverse relationship
C) no relationship
D) animosity

Question 46

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

Question 47

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

Question 48

The regression constant for predicting Y given X is symbolized by _________.

A) b _Y
B) a _Y
C) b _X
D) a _X

Question 49

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) all of these

Question 50

The symbol for the standard error of estimate when predicting Y given X is _________.

A) r _{X ½ Y}
B) s_{X ½ Y}
C) r _{Y ½ X}
D) s _{Y ½ X}

Question 51

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

Question 52

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

Question 53

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

Question 54

The total error in prediction equals S ( Y - Y').

Question 55

If s X = s Y then r = b Y .

Question 56

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

Question 57

When doing regression, it is customary to assign X to the predicted variable .

Question 58

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

Question 59

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

Question 60

An imperfect relationship generally yields exact prediction.

Question 61

Using a second predictor variable always increases the accuracy of prediction.

Question 62

If the standard error of estimate for relationship 1 equals 5.26 and for relationship 2 it equals 8.01 then we can reasonably infer that relationship 2 is less perfect than relationship 1.

Question 63

In general one is less confident in predictions of Y when the value of X used for the prediction is outside the range of the original data used to construct the regression line.

Question 64

The regression line will always go through the point .

Question 65

The value a Y is the X axis intercept for minimizing errors in Y .

Question 66

Define Homoscedasticity.

Question 67

For regression purposes, it is customary to assign Y to the predicted variable.

Question 68

In regression analysis we are only concerned with perfect as opposed to imperfect relationships.

Question 69

If X and Y are plotted as standard ( z ) scores, then r equals the slope of the resulting regression line.

Question 70

If we minimize Σ( Y - Y' ) ² , we will minimize the total error of prediction.

Question 71

If the relationship between two variables is perfect the standard error of estimate equals 0.

Question 72

For regression purposes, it is customary to assign X to the variable we are predicting from.

Question 73

For regression purposes, it is customary to assign Y to the variable we are predicting from.

Question 74

It is impossible to have a negative value for the standard error of estimate.

Question 75

Define multiple coefficient of determination.

Question 76

If s Y = s X , then r = b Y .

Question 77

Define least-squares regression line.

Question 78

If the regression line is parallel to the X axis then the slope of the regression line equals 0.

Question 79

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 .

Question 80

Generally, one can use the same regression equation for predicting Y given X as for X given Y .