Deck 17: Understanding Regression Analysis

Question 1

A researcher measures the extent to which time spent watching educational preschool television programming predicts success in school.Which factor is the criterion variable in this example?

A)educational preschool television
B)type of television programming
C)success in school
D)time spent in school

Answer 1

success in school

Question 2

Using an analysis of regression,the variability in Y that is predicted by X is measured by the

A)regression variation
B)residual variation
C)correlation coefficient
D)coefficient of determination

Answer 2

regression variation

Question 3

Both sources of variation in an analysis of regression measure the variability in

A)X and Y
B)X only
C)Y only

Answer 3

Y only

Question 4

Linear regression describes the extent to which _______ predicts ________.

A)X;Y
B)the predictor variable;the criterion variable
C)the known variable;the to-be-predicted variable
D)all of the above

Question 5

The method of least squares is used to determine the ________ straight line to a set of data points.

A)best-fitting
B)straightest
C)most linear
D)approximate

Question 6

A researcher reports the following equation for a best-fitting straight line to a set of data points: .Which value is the slope?

A)
B)0.48
C)12.03
D)The slope is not given in this equation.

Question 7

Which of the following is used to determine the significance of predictions made by a best fitting linear equation?

A)correlational analysis
B)analysis of variance
C)analysis of regression
D)method of least squares

Question 8

A researcher reports the following equation for a best-fitting straight line to a set of data points: .Which value is the y-intercept?

A)
B)
C)ñ1.01
D)3.24

Question 9

Using an analysis of regression,the variability in Y that is associated with error is measured by the

A)regression variation
B)residual variation
C)correlation coefficient
D)coefficient of determination

Question 10

If = -16.32 and = 40.00 for a set of data points,then what is the value of the slope for the best-fitting linear equation?

A)-0.41
B)-2.45
C)positive
D)There is not enough information;you would also need to know the value of .

Question 11

A researcher measures the extent to which years of marriage predict perceptions of forgiveness.Which factor is the criterion variable in this example?

A)years of marriage
B)perceptions of forgiveness
C)both years of marriage and perceptions of forgiveness
D)none of the above

Question 12

Which of the following is not needed to compute the y-intercept using the method of least squares?

A)
B)
C)
D)the slope

Question 13

The regression equation measures

A)how far the sample mean deviates from the population mean
B)how far each data point deviates from the line that most closely fits the data
C)how significant mean differences are between groups
D)how often scores regress from deviations in the data

Question 14

A researcher measures the extent to which the speed at which people eat (in minutes)predicts calorie intake (in kilocalories).Which factor is the predictor variable in this example?

A)the speed at which people eat
B)calorie intake
C)minutes and kilocalories
D)all of the above

Question 15

The more that the variability in ____ is associated with regression variation,the more likely it is that X predicts Y.

A)XY
B)X
C)Y
D)all of the above

Question 16

Which of the following statements is true regarding the sources of variation present in an analysis of regression?

A)Regression variation measures variability in X,whereas residual variation measures variability in Y.
B)The closer that data points fall to the regression line,the more the variance in Y will be attributed to regression variation.
C)There are three sources of variation in an analysis of regression: regression variance,residual variance,and error variance.
D)When most of the variability in Y is associated with residual variation,then X predicts Y.

Question 17

If b = -0.57, = 2.75,and = 5.25 for a set of data points,then what is the value of the y-intercept for the best-fitting linear equation?

A)0.24
B)11.68
C)-0.24
D)5.74

Question 18

A researcher reports the following regression equation for two variables,X and Y: .If X = 2.30,then what is the value of ?

A)10.23
B)11.73
C)13.23

Question 19

Which of the following is not needed to compute the slope using the method of least squares?

A)
B)
C)

Question 20

Which of the following is used to determine the linear equation that ìbest fitsî a set of data points?

A)correlational analysis
B)analysis of variance
C)analysis of regression
D)method of least squares

Question 21

If the coefficient of determination is 0.25 and the sum of squares residual is 180,then what is the value of ?

A)60
B)180
C)240
D)800

Question 22

In a sample of 22 participants,suppose we conduct an analysis of regression with one predictor variable.If = 4.07,then what is the decision for this test at a .05 level of significance?

A)X significantly predicts Y.
B)X does not significantly predict Y.
C)There is not enough information to answer this question.

Question 23

The degrees of freedom associated with regression variation are equal to

A)the number of predictor variables
B)the number of predictor variables minus one
C)n ñ 1
D)n ñ 2

Question 24

A researcher computes a perfect negative correlation,in which each data point falls exactly on the regression line.In this example,the value of the standard error of estimate will be

A)less than 0
B)greater than 0
C)equal to 0
D)There is not enough information to answer this question.

Question 25

An estimate of the standard deviation or distance that data points fall from the regression line is measured by the

A)sum of squares
B)standard error of estimate
C)criterion variable
D)predictor variable

Question 26

Multiple regression is a statistical method that includes ____ predictor variable(s)in the equation of the regression line.

A)zero
B)one
C)two
D)two or more

Question 27

The predictions made using multiple regression are often more ________ than the predictions made using linear regression with one predictor variable.

A)informative
B)convoluted
C)confounded
D)realistic

Question 28

The degrees of freedom associated with residual variation are equal to

A)the number of predictor variables
B)the number of predictor variables minus one
C)n ñ 1
D)n ñ 2

Question 29

If the coefficient of determination is 0.30 and the sum of squares regression for an analysis of regression is 210,then what is the value of ?

A)210
B)300
C)490
D)700

Question 30

Which of the following equations is appropriate for a linear regression with three predictor variables?

A)
B)
C)
D)

Question 31

One key advantage for including multiple predictor variables in the equation of a regression line is that it allows you to

A)detect mean differences between groups for each criterion variable
B)detect the extent to which two or more predictor variables interact
C)show cause-and-effect because many predictor variables are added
D)all of the above

Question 32

If the coefficient of determination is 0.32 and = 150,then what is the sum of squares residual for an analysis of regression?

A)48
B)102
C)150
D)There is not enough information to answer this question.

Question 33

The standard error of estimate is used as a measure of the ________ in predictions using the equation of a regression line.

A)linearity
B)appropriateness
C)accuracy
D)certainty

Question 34

What is the computation for the standard error of estimate?

A)the square root of the mean square regression
B)the square root of the mean square residual
C)the mean square regression,squared
D)the mean square residual,squared

Question 35

If the coefficient of determination is 0.12 and = 225,then what is the sum of squares regression for an analysis of regression?

A)27
B)198
C)225
D)There is not enough information to answer this question.

Question 36

A researcher computes the following analysis of regression table.Based on the data given,what is the value of the standard error of estimate? (Note: Complete the table first. )

A)2.24
B)5.00
C)5.74
D)8.49

Question 37

A statistical method that includes two or more predictor variables in the equation of a regression line to predict changes in a criterion variable is called

A)analysis of variance
B)standard error of estimate
C)residual regression
D)multiple regression

Question 38

A researcher computes the following analysis of regression table.Based on the data given,what is the decision for this test at a .05 level of significance? (Note: Complete the table first. )

A)X significantly predicts Y.
B)X does not significantly predict Y.
C)There is not enough information to answer this question.

Question 39

In a sample of 28 participants,suppose we conduct an analysis of regression with one predictor variable.If = 4.28,then what is the decision for this test at a .05 level of significance?

A)X significantly predicts Y.
B)X does not significantly predict Y.
C)There is not enough information to answer this question.

Question 40

A researcher computes an analysis of regression in which = 0.82.What is the value of in this example?

A)0.67
B)0.82
C)0.91
D)There is not enough information to answer this question.

Question 41

In addition to evaluating the significance of a multiple regression equation,we also should consider:

A)the significance of the residual variability
B)the complexity of the correlation coefficient
C)the relative contribution of each factor
D)the significant of each individual data point

Question 42

When most of the variability in Y is attributed to regression variation,it is more likely that X predicts Y.

Question 43

Which of the following is a step to evaluate the significance for the relative contribution of each factor:

A)Find r² for the "other" predictor variable
B)Complete the F table and make a decision
C)Identify SS accounted for by the predictor variable of interest
D)All of the above

Question 44

For a multiple regression analysis with 2 and 12 degrees of freedom,MS regression is 135 and MS residual is 15.What is the decision for this test?

A)reject the null hypothesis;the predictive variability of two predictor factors are significant
B)retain the null hypothesis;the predictive variability of two predictor factors are not significant
C)reject the null hypothesis;the predictive variability of one predictor factor is significant
D)retain the null hypothesis;the predictive variability of one predictor factor is significant

Question 45

We do not need to know the value of the slope to compute the value of the y-intercept of a regression line.

Question 46

The regression line is not always the best fitting straight line to a set of data points.

Question 47

The predictor variable is a known value that is used to predict the value of another variable.

Question 48

The equation for the standardized regression equation is,

A)
B)
C)
D)

Question 49

In an analysis of regression there are three sources of variation: regression,residual,and error.

Question 50

The numerator of the formula for the slope (b)of a regression line is equal to the sum of products.

Question 51

Linear regression is used to measure the extent to which a criterion variable causes changes in a predictor variable.

Question 52

The scores or data points for a regression analysis are typically reported in,

A)a scatter plot
B)a bar chart
C)a pie chart
D)all of the above

Question 53

The "left-over" or remaining variation attributed to error in an analysis of regression is called residual variation.

Question 54

To summarize any type of regression analysis using APA format,we report each of the following except the,

A)test statistic
B)degrees of freedom
C)p value
D)critical values

Question 55

The slope (b)is a measure of the change in Y relative to the change in X.

Question 56

The value of b₁ and b₂ are referred to as,

A)unstandardized beta coefficients
B)standardized beta coefficients
C)regression variation
D)residual variation

Question 57

The equation for a straight line is Y = bX + a.

Question 58

To standardize the beta coefficients,we first,

A)analyze the significance of each data point
B)analyze the residual variation
C)convert the original data to standardized z scores
D)compute the standard error of estimate

Question 59

If F = 2.04 for the relative contribution of one factor,then what is this value when converted to a t statistic?

A)2.04
B)1.43
C)4.16
D)The conversion is not possible.

Question 60

For a multiple regression,we typically report which value that is not often reported for a one factor linear regression analysis?

A)effect size
B) $\beta$ coefficient
C)test statistic
D)p value

Question 61

To compute the standard error of estimate,we take the square root of the mean square residual.

Question 62

We can evaluate the relative contribution of each predictor variable by evaluating the significance of the added contribution of each factor.

Question 63

Including two or more predictor variables into a single equation of a regression line can be more informative than an analysis using only one predictor variable.

Question 64

For linear regression with one predictor variable, $\beta$ will equal r.

Question 65

The null hypothesis for a test of the relative contribution of two predictor variables is that adding one factor improves the prediction of variance in Y beyond that already predicted by the second factor.

Question 66

Multiple regression can be used to measure predictive variability for any number of predictor variables.

Question 67

To standardize the coefficients,we first convert the original data to standardized z scores.

Question 68

A researcher computes an analysis of regression with 1 and 18 degrees of freedom.If F = 4.05,then the decision will be that X is a significant predictor of variation in Y.

Question 69

A researcher computes an analysis of regression with 1 and 25 degrees of freedom.If F = 5.34,then the decision will be that X is a significant predictor of variation in Y.

Question 70

With multiple regression,we can use the method of least squares to find the regression equation and test for significance just as we did using simple linear regression.

Question 71

We can evaluate the significance of the relative contribution of each factor by first determining the differences between group means.

Question 72

If the mean square residual equals 0.93,then the standard error of estimate equals 0.87.

Question 73

To summarize the results of multiple regression,we typically add the standardized $\beta$ coefficient for each factor that significantly contributes to a prediction.

Question 74

The degrees of freedom residual is equal to the number of criterion variables.

Question 75

If the coefficient of determination is 0.09 and the sum of squares regression is 88,then the total variation in Y must be = 108.

Question 76

The data points for pairs of scores are often summarized in a bar chart.

Question 77

The larger the standard error of estimate,the more accurately known values of X will predict values of Y.

Question 78

The standardized beta coefficient, $\beta$ ,reflects the distinctive contribution of each criterion variable.

Question 79

For a simple linear regression with one predictor variable,we report the test statistic,degrees of freedom,and p value for the regression analysis.

Question 80

The standard error of estimate provides an estimate of the standard distance that data points fall from the regression line.