Deck 16: Introduction to Regression

Question 1

For the linear equation Y = 2X + 4, if X increases by 1 point, how much will Y increase?

A)1 points
B)2 points
C)3 points
D)4 points

Answer 1

B

Question 2

Assuming that SS_Y is constant, which of the following correlations would have the largest SS_residual?

A)r = -0.10
B)r = +0.40
C)r = -0.70
D)There is no relationship between the correlation and SS_residual.

Answer 2

A

Question 3

A set of X and Y scores has a regression equation with a slope of b = 4.If the mean for the X values is M_X = 2 and the mean for the Y values is M_Y = 6, then what is the Y-intercept value for the regression equation?

A)-2
B)-22
C)4
D)-4

Answer 3

A

Question 4

The regression equation is determined by finding the minimum value for which of the following?

A) $\Sigma$ (X - Y)²
B) $\Sigma$ (Y - ?)
C) $\Sigma$ (Y - ?)²
D)r² $\Sigma$ (Y - ?)²

Question 5

For the regression equation Y = X - 2, if the mean for Y is M_Y = 6, what is the mean for X?

A)4
B)6
C)8
D)10

Question 6

For which of the following correlations would the data points be most widely scattered around the regression line?

A)r = 0.10
B)r = 0.50
C)r = -0.80
D)There is no relationship between the correlation and how close the data points are to the regression line.

Question 7

The distance between the Y value in the data and the Y value predicted from the regression equation is know as the residual.What is the value for the sum of the squared residuals?

A)SS_residual = r²(SS_X)
B)SS_residual = (1 - r²)(SS_X)
C)SS_residual = r²(SS_Y)
D)SS_residual = (1 - r²)(SS_Y)

Question 8

The standardized form of the regression equation is z_Y = (beta)z_X.In the equation, what is the value of beta?

A)Beta is equal to the correlation between X and Y.
B)Beta is equal to SP/ SS_X.
C)Beta is equal to r/(n - 1)
D)Beta is equal to r/n

Question 9

A set of X and Y scores has SS_X = 20, SS_Y = 10, and SP = 40.What is the slope for the regression equation?

A)40/10
B)40/20
C)10/40
D)20/40

Question 10

A set of n = 15 pairs of X and Y scores has SS_X = 10, SS_Y = 40, and SP = 30.What is the slope for the regression equation for predicting Y from X?

A)10/30
B)10/40
C)40/10
D)30/10

Question 11

In the general linear equation, Y = bX + a, what is the value of b called?

A)the slope
B)the Y?intercept
C)the X?intercept
D)the beta factor

Question 12

One use of regression equation is to increase the accuracy of predicting Y scores.How much of the variability in the Y scores is predictable from the regression equation?

A)r²
B)1 - r²
C)r
D)1 - r

Question 13

A linear regression equation has b = 3 and a = - 6.What is the predicted value of Y for X = 4?

A)Ŷ = 6
B)Ŷ = - 21
C)Ŷ = - 2
D)cannot be determined without additional information

Question 14

For the regression equation, Ŷ = -2X + 6, what can be determined about the correlation between X and Y?

A)The correlation definitely will be positive.
B)The correlation definitely will be negative.
C)The correlation will be relatively large and positive
D)The correlation will be relatively large and negative.

Question 15

If there is a positive correlation between X and Y then the regression equation, Y = bX + a will have _____.

A)b > 0
B)b < 0
C)a > 0
D)a < 0

Question 16

For the regression equation, Ŷ = -2X + 6, if the X value is above the mean (positive deviation), then what can be determined about the predicted Y value?

A)The predicted Y value will be above the mean for the Y scores.
B)The predicted Y value will be below the mean for the Y scores.
C)The predicted Y value will be equal to the mean for the Y scores.
D)It is impossible to determine where the predicted Y value will be.

Question 17

For the regression equation Y = 2X - 3, if the mean for X is M_X = 5, what is the mean for Y?

A)2
B)4
C)5
D)7

Question 18

For the linear equation Y = 2X - 3, which of the following points will not be on the line?

A)0, -3
B)2, 1
C)3, 0
D)4, 5

Question 19

For a linear regression equation, the sum of the squared residuals can be computed directly by finding the difference between each Y and its predicted Y, then squaring the difference and adding the squared values.An alternative procedure is to calculate

A)r²SS_Y
B)(1 - r²)SS_Y
C)(1 + r²)SS_Y
D)SS_Y/SS_X

Question 20

A set of X and Y scores has M_X = 4, SS_X = 10, M_Y = 5, SS_Y = 40, and SP = 20.What is the regression equation for predicting Y from X?

A)Ŷ = 0..25X + 4
B)Ŷ = 4X - 9
C)Ŷ = 0.50X +3
D)Ŷ = 2X - 3

Question 21

The Pearson correlation between X₁ and Y is r = 0.40 and SS_Y = 100.When a second variable, X₂, is added to the regression equation, we obtain R² = 0.25.How much additional variance is predicted by adding the second variable compared to using X₁ alone?

A)9 points
B)15 points
C)25 points
D)40 points

Question 22

A linear regression equation is computed for a sample of n = 13 pairs of X and Y scores.For the analysis of regression testing the significance of the equation what are the df values for the F-ratio?

A)df = 1, 11
B)df = 1, 12
C)df = 2, 10
D)df = 2, 11

Question 23

For linear regression calculated for a sample of n = 20 pairs of X and Y values, what is the value for degrees of freedom for the unpredicted portion of the Y-score variance, MS_residual?

A)1
B)2
C)18
D)19

Question 24

Which of the following is the standard error of estimate for a multiple regression equation with two predictor variables?

A)the square root of SS_residual/(n - 2)
B)the square root of SS_residual/(n - 3)
C)the square root of SS_regression/(n - 2)
D)the square root of SS_regression/(n - 3)

Question 25

Which of the following is the standard error of estimate for a linear regression equation?

A)the square root of SS_residual/(n - 2)
B)the square root of SS_residual/(n - 3)
C)the square root of SS_regression/(n - 2)
D)the square root of SS_regression/(n - 3)

Question 26

The following X and Y scores produce SS_X = 2 and SP = 8..What is regression equation for predicting Y?

Question 27

For either linear regression or multiple regression, the standard error of estimate can be computed as

A)the square root of MS_residual
B)MS_residual/(n - 2)
C)the square root of MS_regression
D)MS_regression/(n - 2)

Question 28

A multiple regression equation with two predictor variables is calculated for a set of scores.If the constant values in the equation are b₁ = 2, b₂ = -3, and a = 7, then what Y value would be predicted for an individual with X₁ = 2 and X₂ = 4?

A)1
B)-1
C)17
D)41

Question 29

An analysis of regression is used to test the significance of a linear regression equation based on a sample of n = 20 individuals.What are the df values for the F-ratio?

A)1, 18
B)1, 19
C)2, 18
D)2, 19

Question 30

.The multiple regression with two predictor variables is computed for a sample of n = 25 participants.what is the value for degrees of freedom for the predicted portion of the Y-score variance, MS_regression?

A)2
B)3
C)22
D)23

Question 31

For linear regression calculated for a sample of n = 20 pairs of X and Y values, what is the value for degrees of freedom for the predicted portion of the Y-score variance, MS_regression?

A)1
B)2
C)19
D)18

Question 32

The multiple regression with two predictor variables is computed for a sample of n = 25 participants.What is the value for degrees of freedom for the unpredicted portion of the Y-score variance, MS_residual?

A)2
B)3
C)22
D)23

Question 33

The Pearson correlation between X₁ and Y is r = 0.50 and the correlation between X₂ and Y is r = 0.20.How much variance for the Y scores is predicted by using both X₁ and X₂ as predictor variables in a multiple regression equation?

A)0.25 or 25%
B)0.29 or 29%
C)0.70 or 70%
D)Cannot be determined from the information given.

Question 34

For a linear regression equation calculated for a sample of n = 20 pairs of X and Y values, what would be the df value for the standard error of estimate?

A)1
B)2
C)18
D)19

Question 35

A multiple regression equation with two predictor variables produces R² = 0.10.What portion of the variability for the Y scores is predicted by the equation?

A)1%
B)10%
C)90%
D)99%

Question 36

A set of n = 25 pairs of scores (X and Y values) has a Pearson correlation of r = 0.80.How much of the variance for the Y scores is predicted by the relationship with X?

A)0.36 or 36%
B)0.20 or 20%
C)0.80 or 80%
D)0.64 or 64%

Question 37

The Pearson correlation between X₁ and Y is r = 0.70.When a second variable, X₂, is added to the regression equation, we obtain R² = 0.64.How much variance for the Y scores is predicted by using only X₁ as a predictor variable?

A)0.06 or 6%
B)0.15 or 15%
C)0.49 or 49%
D)0.70 or 70%

Question 38

A multiple regression equation is computed for a sample of n = 20 sets of X₁, X₂, and Y scores.If the significance of the regression equation is evaluated using an F-ratio, then the ratio would have degrees of freedom equal to

A)df = 1, 18
B)df = 1, 19
C)df = 2, 17
D)df = 2, 18

Question 39

A researcher who is evaluating the significance of a multiple regression equation with two predictor variables, obtains an F-ratio with df = 2, 18.How many individuals were needed to produce the sample data used to find the regression equation?

A)18
B)19
C)20
D)21

Question 40

A researcher who is evaluating the significance of a multiple regression equation with two predictor variables, obtains an F-ratio with df = 2, 24.How many individuals were needed to produce the sample data used to find the regression equation?

A)24
B)25
C)26
D)27

Question 41

For linear regression, if X = M_X, then the predicted Y value is M_Y.

Question 42

If the Pearson correlation between X and Y is negative, then the regression equation will have a negative slope.

Question 43

For a regression equation with a positive slope, if the X value is above the mean for the X scores, then the predicted Y value will be above the mean for the Y scores.

Question 44

The line defined by the Y = -3X + 6 slopes up to the right.

Question 45

It is possible for the regression equation to have none of the actual (observed) data points located on the regression line.

Question 46

If other factors are held constant, a larger numerical value for the Pearson correlation will result in a smaller standard error of estimate.

Question 47

If the correlation between X and Y is r = 0.00, then the regression equation, Ŷ = bX + a, will have b = 0.

Question 48

For linear regression, the value of SS_residual can be computed directly by Σ(Y - Ŷ)².

Question 49

The linear regression equation is structured so that when X = M_X, the predicted value of Y is equal to M_Y.

Question 50

If the Pearson correlation between X and Y is r = 0.60, then the regression equation predicts 36% of the variance in the Y scores.

Question 51

A set of n = 6 pairs of X and Y values has a Pearson correlation of r = 0.80 and SS_Y = 100.The standard error of estimate for the regression equation is √36/4 = 3 points.

Question 52

The line produced by the equation Y = 4X - 5 crosses the vertical axis at Y = 5.

Question 53

The F-ratio evaluating the significance of a linear regression equation based on n = 10 pairs of X and Y scores has df = 1, 8.

Question 54

If a set of X and Y scores has r > 0, then the regression equation, Ŷ = bX + a, will have a > 0.

Question 55

A set of X and Y scores has SS_X = 10, SS_Y = 36, and SP = 20.The regression equation for these scores will have a slope constant of 2.

Question 56

For a regression equation with a slope of b = 3, if M_X = 3 and M_Y = 10 then the Y-intercept for the equation is 1.

Question 57

It is possible for two sets of data have the same regression equation, but different correlations.

Question 58

The point defined by X = 2 and Y = -1 is located on the line defined by the equation
Y = 2X - 3.

Question 59

A set of X and Y scores has M_X = 4, M_Y = 10, SS_X = 10, and SP = 5.The regression equation for these scores is Y = 0.5X - 8.

Question 60

If other factors are held constant, if the Pearson correlation between X and Y is r = 0.80, then the regression equation will produce more accurate predictions than would be obtained if r = 0.60.

Question 61

For a linear regression equation computed for a sample of n = 30, the predicted portion of the Y-score variance (MS_regression) has df = 2.

Question 62

The value of SS_residual measures the total squared distance between the actual Y values and the Y values predicted by the regression equation.

Question 63

For a linear regression equation computed for a sample of n = 30, the unpredicted portion of the Y-score variance (MS_residual) has df = 28.

Question 64

If the correlation between X₁ and Y is r = 0.40 and the correlation between X₂ and Y is r = 0.30, then a multiple regression equation using both X₁ and X₂ as predictors will produce R² = 0.25.

Question 65

If a linear regression equation predicts more than 50% of the variance in the Y scores, then the correlation between X and Y must be greater than r = 0.70.

Question 66

In a multiple regression equation with two predictor variables, if b₁ is larger than b₂, then X₁ is a better predictor of the Y-score variance than is X₂.

Question 67

The proportion of SS_Y that is not predicted by the regression equation is equal to r².

Question 68

The Pearson correlation between X₁ and Y is r = 0.50.When a second variable, X₂, is added to the regression equation, we obtain R² = 0.60.Adding the second variable increased the predicted variance for the Y scores by 36% - 25% = 11%.

Question 69

A multiple regression equation with two predictor variables is computed for a sample of n = 35 participants.The standard error of estimate for the equation would have df = 33.

Question 70

For either linear regression or multiple regression, the standard error of estimate is equal to the square root of MS_residual.