Question 1

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

Accepted Answer

The additional variance predicted by adding X2 is calculated by the difference in R² values: R² with both variables - R² with X1 alone. R² with X1 alone is r² = 0.40² = 0.16. The additional variance is 0.25 - 0.16 = 0.09, which is 9 points.

Question 2

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

Accepted Answer

In a linear regression analysis, the degrees of freedom for the F-ratio are calculated as df1 = k - 1 and df2 = n - k, where k is the number of predictors (including the intercept) and n is the sample size. For a simple linear regression with one predictor and one intercept, k = 2. Therefore, df1 = 2 - 1 = 1, and df2 = 13 - 2 = 11, making the correct df values for the F-ratio 1, 11.

Question 3

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

Accepted Answer

The degrees of freedom for the residuals in linear regression is calculated as n - 2, where n is the number of data points. For n = 20, the degrees of freedom is 20 - 2 = 18.

Question 4

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)

Accepted Answer

In multiple regression with two predictors, the degrees of freedom for the residuals is n - 3, so the standard error of estimate is calculated using SS_residual/(n - 3).

Question 5

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)

Accepted Answer

The standard error of estimate for a linear regression equation is calculated as the square root of the sum of the squared residuals divided by the degrees of freedom, which is (n-2) for simple linear regression. Therefore, the correct formula is the square root of SSS(residuals)/(n-2). This corresponds to choice A.

Question 6

The following X and Y scores produce SS_X = 2 and SP = 8..What is regression equation for predicting Y? $\begin{array}{rr} \mathrm{X} & \mathrm{Y} \ \hline 1 & 2 \ 2 & 3 \ 3 & 10 \end{array}$ A) $ Y=0.25 X+4.5 $ B) $ Y=0.25 \mathrm{X}-4.5 $ C) $ Y=4 X+3 $ D) $ Y=4 X-3 $

Accepted Answer

The slope (b) is calculated as SP/SSx = 8/2 = 4. The intercept (a) is calculated using the formula a = Ȳ - bX̄. With the given data, the mean of X is 2 and the mean of Y is 5, so a = 5 - 4*2 = -3. Therefore, the regression equation is Y = 4X - 3.

Question 7

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)

Accepted Answer

The standard error of estimate for either linear regression or multiple regression is computed as the square root of the mean square error (MSE) or residual mean square, which is represented in option A as "the square root of MS_residual". This formula essentially captures the average distance that the observed values fall from the regression line.

Question 8

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

Accepted Answer

The answer of A multiple regression equation with two predictor...

Question 9

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

Accepted Answer

The degrees of freedom for the F-ratio in a linear regression analysis are determined by the number of predictors and the sample size. For a simple linear regression (one predictor), the numerator df is 1 (for the predictor), and the denominator df is n - 2, where n is the sample size. With n = 20, the denominator df is 20 - 2 = 18.

Question 10

.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

Accepted Answer

In multiple regression, the degrees of freedom for the regression (predicted portion) is equal to the number of predictor variables. Here, there are two predictor variables, so the degrees of freedom is 2.

Question 11

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

Accepted Answer

The answer of For linear regression calculated for a sample...

Question 12

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

Accepted Answer

The degrees of freedom for the unpredicted portion of the Y-score variance, MSresidual, is equal to n - k - 1, where n is the sample size and k is the number of predictor variables. In this case, n = 25 and k = 2, so the degrees of freedom for MSresidual is 25 - 2 - 1 = 22.

Question 13

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.

Accepted Answer

The given correlations do not provide enough information to determine the shared variance between X1, X2, and Y, nor the unique contributions of each predictor in a multiple regression context. Additional information, such as the correlation between X1 and X2, is needed to calculate the explained variance in Y.

Question 14

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

Accepted Answer

The degrees of freedom for the standard error of estimate in linear regression is calculated as n - 2, where n is the number of data pairs. Here, n = 20, so df = 20 - 2 = 18.

Question 15

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%

Accepted Answer

The coefficient of determination (R-squared) represents the proportion of the variability in the dependent variable (Y) that is explained by the regression equation. In this case, the R-squared value would be 0.10 (given in the equation), which means 10% of the variability in Y can be predicted by the two predictor variables in the equation. Therefore, the answer is B, 10%.

Question 16

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%

Accepted Answer

The square of the correlation coefficient (r) equals the proportion of variance in Y that can be predicted by X. Therefore, 0.80^2 = 0.64 or 64% of the variance for the Y scores is predicted by the relationship with X.

Question 17

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%

Accepted Answer

The coefficient of determination (r^2) tells us the proportion of variance in Y that is accounted for by X₁. The formula for r^2 is r^2 = (correlation)^2 = 0.70^2 = 0.49 or 49%. Therefore, choice C is the correct answer.

Question 18

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

Accepted Answer

The degrees of freedom for an F-ratio in multiple regression are determined by the number of predictors and the sample size. With 2 predictors (X1 and X2) and a sample size of n = 20, the degrees of freedom for the numerator (number of predictors) is 2, and for the denominator (n - number of predictors - 1), it is 20 - 2 - 1 = 17.

Question 19

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

Accepted Answer

The answer of A researcher who is evaluating the significance...

Question 20

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

Accepted Answer

The numerator degrees of freedom (df1) for the F-ratio in a two-predictor regression model is 2 (number of predictor variables). The denominator degrees of freedom (df2) is the total sample size minus the number of predictor variables minus 1. Therefore, 2 + 24 + 1 = 27 individuals were needed to produce the sample data used to find the regression equation.

Quiz 16: Introduction to Regression

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 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?

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?

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

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

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

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

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?

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?

.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?

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?

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?

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?

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 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 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?

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 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 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 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?

Quiz 16: Introduction to Regression

The Pearson correlation between X1 and Y is r = 0.40 and SSY = 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 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?

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, MSresidual?

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

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

The following X and Y scores produce SSX = 2 and SP = 8..What is regression equation for predicting Y? XY1223310\begin{array}{rr}\mathrm{X} & \mathrm{Y} \\\hline 1 & 2 \\2 & 3 \\3 & 10\end{array}X123​Y2310​​

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

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?

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?

.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, MSregression?

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, MSregression?

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, MSresidual?

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?