Deck 16: Introduction to Regression

Question 1

​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)​ = 0.25X + 4
B)​ = 4X - 9
C)​ = 0.50X +3
D)​ = 2X - 3

Answer 1

​ = 2X - 3

Question 2

The following X and Y scores produce SS_X = 2 and SP = 8.What is the regression equation for predicting Y? $$\begin{array} { l l } \mathrm { X } & \mathrm { Y } \\\hline 1 & 2 \\2 & 3 \\3 & 10 \\\hline\end{array}$$

A)?Y = 0.25X + 4.5
B)?Y = 0.25X - 4.5
C)?Y = 4X + 3
D)?Y = 4X - 3

Answer 2

?Y = 4X - 3

Question 3

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

A)(X - Y)²​
B)​(Y -Ȳ )
C)​(Y - )²
D)​r²(Y - )²

Answer 3

​(Y - )²

Question 4

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, 3
D)​4, 5

Question 5

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 6

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 7

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

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

Question 8

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 9

One use of a regression equation is to increase the accuracy of predicting Y scores.What determines the proportion of the variability in the Y scores that is predicted by the regression equation?​

A)​r²
B)​1 - r²
C)​r
D)​1 - r

Question 10

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,what is the Y-intercept value for the regression equation?​

A)​-2
B)​-22
C)​4
D)​-4

Question 11

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 12

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 13

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

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

Question 14

For the regression equation,= -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 zero.
D)​The correlation will be relatively large and positive.

Question 15

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 16

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)​4.0
B)​2.0
C)​0.25
D)​0.50

Question 17

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)​r = 0.99

Question 18

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 19

​If there is a positive correlation between X and Y then in the regression equation,Y = bX + a,____.

A)​b > 0
B)​b < 0
C)​a > 0
D)​a < 0

Question 20

For the regression equation,= -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 21

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 22

For a 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)​18
D)​19

Question 23

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 24

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 25

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)​It cannot be determined from the information given.

Question 26

For a 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 27

The distance between the Y value in the data and the Y value predicted from the regression equation is known 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 28

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 29

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 30

What 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 31

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 32

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 33

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

A)​2
B)​3
C)​22
D)​23

Question 34

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 35

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

A)​2
B)​3
C)​22
D)​23

Question 36

A linear regression equation is 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 37

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 38

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 39

​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.

Question 40

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 variability is contributed by adding the second variable as a predictor compared to using X₁ alone?​

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

Question 41

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

Question 42

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

Question 43

The best-fitting line is the one that has the smallest total squared error,so the resulting line is commonly called the least-squared-error solution.

Question 44

The statistical technique for finding the best-fitting straight line for a set of data is called regression,and the resulting straight line is called the regression line.

Question 45

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

Question 46

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

Question 47

A regression equation has a slope of b = 3,if M_X = 3 and M_Y = 10.The Y-intercept for the equation is 1.

Question 48

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

Question 49

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

Question 50

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 51

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

Question 52

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

Question 53

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

Question 54

The slope determines how much the Y variable changes when X is increased by one point.​

Question 55

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 56

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

Question 57

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 58

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 6/4 = 3 points.

Question 59

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

Question 60

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 61

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 62

A sample of n = 15 pairs of X and Y scores produces a Pearson correlation of r = 0.45 with SS_Y = 90.
a. If the regression equation was found for these scores, how much of the Y variability would be predicted by the regression equation (SS_regression) and how much would not be predicted (SS_residual)?
b. Does the regression equation predict a significant portion of the variability for the Y scores? (Equivalently, is the Pearson correlation significant?)

Question 63

A partial correlation measures the relationship that exists between two variables while a third variable is controlled or held constant.

Question 64

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

Question 65

For the data below: ​
a. Compute the Pearson correlation.
b. Find the regression equation for predicting Y from X.
c. Calculate the predicted Y for each X value, find each residual (Y - ), square each residual, and add the squared values to obtain SS_residual

Question 66

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 67

Multiple regression involves finding a regression equation with more than one predictor variable.

Question 68

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 than is X₂.

Question 69

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 70

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

Question 71

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 increases the variability that is predicted by the regression equation for the Y scores by 36% - 25% = 11%.

Question 72

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 73

Find the regression equation for the following set of data.​

Question 74

Suppose that a sample of n = 12 pairs of X and Y scores has SS_Y = 90 and a Pearson correlation of r = +0.40.
a. What proportion of the variance for the Y scores is predicted by the regression equation?
b. Does the regression equation predict a significant portion of the variance? Test with α = .05.

Question 75

A multiple regression equation has R² = 0.25 and SS_Y = 90 for a sample of n = 30 people.
a. Test the significance of the regression equation using α = .01.
b. Compute the standard error of estimate for the equation.