Question 1

If our regression equation is Ŷ = 0.75 × age 0.50 × experience - 0.10 × grade point average - 2.0, and if our first subject had scores of 16, 4, and 3.0 on those three variables, respectively, then that subject's predicted score would be
A) 11.7
B) 10
C) 16
D) -3

Accepted Answer

Substituting the given values in the equation, we get:

Ŷ = 0.75 × 16 0.50 × 4 - 0.10 × 3.0 - 2.0
Ŷ = 12 2 - 0.3 - 2.0
Ŷ = 11.7

Therefore, the predicted score for the first subject is 11.7.

Question 2

The multiple correlation of several variables with a dependent variable is
A) less than the largest individual correlation.
B) equal to the correlation of the dependent variable to the values predicted by the regression equation.
C) noticeably less than the correlation of the dependent variable to the values predicted by the regression equation.
D) It could take on any value.

Accepted Answer

The multiple correlation is equal to the correlation of the dependent variable to the values predicted by the regression equation. This is because the regression equation takes into account the combined effects of all the independent variables on the dependent variable, resulting in a more accurate prediction than any individual correlation.

Question 3

In simple correlation a squared correlation coefficient tells us the percentage of variability in Y associated with variability in X . In multiple regression, the squared multiple correlation coefficient
A) has the same kind of meaning.
B) has no meaning.
C) overestimates the degree of variance accounted for.
D) underestimates the degree of variance accounted for.

Accepted Answer

The squared multiple correlation coefficient in multiple regression has the same meaning as the squared correlation coefficient in simple correlation, indicating the percentage of variance in the dependent variable that is accounted for by the independent variables.

Question 4

If one independent variable has a larger coefficient than another, this means
A) that the variable with the larger coefficient is a more important predictor.
B) that the variable with the larger coefficient is a more statistically significant predictor.
C) that the variable with the larger coefficient contributes more to predicting the variability in the criterion.
D) We can't say anything about relative importance or significance from what is given here.

Accepted Answer

The size of a coefficient in a regression model does not necessarily indicate the variable's importance or statistical significance. It merely shows how much the dependent variable is expected to increase or decrease with a one-unit increase in the independent variable, assuming other variables are held constant. Importance and significance depend on the context, scale of variables, and statistical tests, not just on the coefficient size.

Question 5

If you have a number of scores that are outliers you should
A) throw them out.
B) run the analysis with and without them, to see what difference they make.
C) try to identify what is causing those scores to be outliers.
D) both b and c

Accepted Answer

It is not always appropriate to simply throw out outliers, as they may provide important information. Running the analysis with and without them can help determine their impact on the results. Additionally, trying to identify what is causing those scores to be outliers can provide insight into potential issues with data collection or measurement. Therefore, both options B and C are appropriate.

Question 6

If two variables taken together account for 65% of the variability in Y , and a third variable has a simple squared correlation with Y of .10, then adding that variable to the equation will allow us to account for
A) 65% of the variability in Y .
B) 75% of the variability in Y .
C) 10% of the variability in Y .
D) at least 65% of the variability in Y .

Accepted Answer

Adding a third variable with a simple squared correlation of .10 with Y to the equation does not guarantee that the total explained variability will increase to 75% due to potential overlap in the explained variance between variables. However, it does ensure that the explained variability will be at least 65%, as the addition of a variable cannot decrease the already explained variability.

Question 7

If we want to compare the contribution of several predictors to the prediction of a dependent variable, we can get at least a rough idea by comparing
A) the regression coefficients.
B) the standardized regression coefficients.
C) the variances of the several variables.
D) the simple Pearson correlations of each variable with the dependent variable.

Accepted Answer

The best choice is to compare the standardized regression coefficients. This is because the standardized coefficients represent the magnitude of the effect of each predictor on the dependent variable, while controlling for the effects of other predictors in the model. This allows for a fair and direct comparison of the contribution of each predictor to the prediction of the dependent variable. Comparing regression coefficients alone could be misleading as they are dependent on the scale of the variables, and comparing variances of several variables or simple Pearson correlations of each variable with the dependent variable does not account for the contributions of other predictors in the model.

Question 8

If we find all of the residuals when predicting our obtained values of Y from the regression equation, the sum of squared residuals would be expected to be _______ the sum of the squared residuals for a new set of data.
A) less than
B) greater than
C) the same as
D) We can't tell.

Accepted Answer

The answer of If we find all of the residuals...

Question 9

In the previous question, a student who scored 0 on both X ₁ and X ₂ would be expected to have a dependent variable score of A) 0. B) 3.5. C) 12. D) the mean of Y .

Accepted Answer

Based on the regression equation, Y = 2X + 12, if X is 0, then Y would be 12. Therefore, the student would be expected to have a dependent variable score of 12.

Question 10

If we have three predictors and they are all individually correlated with the dependent variable, we know that
A) each of them will play a significant role in the regression equation.
B) each of them must be correlated with each other.
C) each regression coefficient will be significantly different from zero.
D) none of the above

Accepted Answer

The presence of individual correlations between predictors and the dependent variable does not guarantee that each predictor will play a significant role in the regression equation, that they must be correlated with each other, or that each regression coefficient will be significantly different from zero. These outcomes depend on the shared variance among predictors and their unique contributions to explaining the dependent variable.

Question 11

In multiple regression an outlier is one that
A) is reasonably close to the regression surface.
B) is far from the regression surface.
C) is extreme on at least one variable.
D) will necessarily influence the final result in an important way.

Accepted Answer

An outlier in multiple regression is defined as an observation that is far from the regression surface, meaning it deviates significantly from the overall pattern of the data. Outliers can have a large impact on the regression coefficients and can result in misleading results.

Question 12

Before running a multiple regression, it is smart to look at the distribution of each variable. We do this because
A) we want to see that the distributions are not very badly skewed.
B) we want to look for extreme scores.
C) we want to pick up obvious coding errors.
D) all of the above

Accepted Answer

It is best to check for all of the above before running a multiple regression. Skewed distributions can affect the assumptions of normality and equal variance needed for multiple regression. Extreme scores can also affect the results of the regression. Checking for coding errors is important to ensure accurate results.

Question 13

The difference between multiple regression and simple regression is that
A) multiple regression can have more than one dependent variable.
B) multiple regression can have more than one independent variable.
C) multiple regression does not produce a correlation coefficient.
D) both b and c

Accepted Answer

The difference between multiple regression and simple regression is that multiple regression can have more than one independent variable, while simple regression only has one. Multiple regression can still only have one dependent variable. The statement that multiple regression does not produce a correlation coefficient is not entirely accurate; while it does not produce a single correlation coefficient like simple regression, it can produce multiple coefficients of determination (R-squared values) for each independent variable in the model. Option D is partially correct but not the best answer because the statement about correlation coefficient is inaccurate.

Question 14

When we speak of the correlations among the independent variables, we are speaking of
A) homoscedasticity.
B) multicollinearity.
C) independence.
D) multiple correlation.

Accepted Answer

Correlations among independent variables are indicators of multicollinearity, which is a statistical issue where independent variables are highly correlated with each other, leading to unstable and unreliable regression coefficients.

Question 15

If two variables are each correlated significantly with the dependent variable, then the multiple correlation will be
A) the sum of the two correlations.
B) the sum of the two correlations squared.
C) no less than the larger of the two individual correlations.
D) It could take on any value.

Accepted Answer

When two variables are each significantly correlated with a dependent variable, the multiple correlation coefficient (which measures the strength of the relationship between the dependent variable and more than one independent variable) will be at least as large as the correlation of the dependent variable with the more strongly correlated independent variable. This is because the multiple correlation coefficient considers the combined explanatory power of both variables, which cannot be less than the explanatory power of the more strongly correlated variable alone.

Question 16

Assume that we generated a prediction just by adding together the number of stressful events you report experiencing over the last month, the number of close friends you have, and your score on a measure assessing how much control you feel you have over events in your life (i.e., prediction = stress + friends + control). The regression coefficient for stressful events would be
A) 1.0
B) 4.0
C) 0.0
D) There is no way to know.

Accepted Answer

The regression coefficient for stressful events would indicate the amount of change in the prediction for every unit change in the number of stressful events reported. Since the prediction is just the sum of these three variables, the coefficient for stressful events would be 1.0 - meaning that for every additional stressful event reported, the prediction would increase by one.

Question 17

Given the following regression equation ( Ŷ = 3.5 X ₁ + 2 X ₂ + 12), the coefficient for X ₁ would mean that A) two people who differ by one point on X ₁ would differ by 3.5 points on Ŷ . B) two people who differ by one point on X ₁ would differ by 3.5 points on Ŷ , assuming that they did not differ on X ₂. C) X ₁ causes a 3.5 unit change in the dependent variable. D) X ₁ is more important than X ₂.

Accepted Answer

The coefficient of 3.5 for $X_1$ in the regression equation indicates the expected change in the dependent variable ($\hat{Y}$) for a one-unit change in $X_1$, assuming all other variables in the model are held constant. This means that if two individuals differ by one unit on $X_1$, their predicted values on $\hat{Y}$ would differ by 3.5 units, assuming no difference in $X_2$.

Question 18

In multiple regression the intercept is usually denoted as A) a B) b₁ C) b₀ D) 0

Accepted Answer

The intercept in multiple regression is denoted as b0. Option C represents the correct notation for it.

Question 19

Suppose that in the previous question another subject had a predicted score of 10.3, and actually obtained a score of 12.4. For this subject the residual score would be
A) 2.1
B) -0.7
C) 12.4
D) 0.0

Accepted Answer

The residual score is calculated as the actual score minus the predicted score, which in this case is 12.4 - 10.3 = 2.1.

Question 20

In the previous question the intercept would be
A) 1.0
B) 0.0
C) 3.0
D) There would be no way to know.

Accepted Answer

The answer of In the previous question the intercept would...

Quiz 11: Multiple Regression

If our regression equation is Ŷ = 0.75 × age 0.50 × experience - 0.10 × grade point average - 2.0, and if our first subject had scores of 16, 4, and 3.0 on those three variables, respectively, then that subject's predicted score would be

The multiple correlation of several variables with a dependent variable is

In simple correlation a squared correlation coefficient tells us the percentage of variability in Y associated with variability in X . In multiple regression, the squared multiple correlation coefficient

If one independent variable has a larger coefficient than another, this means

If you have a number of scores that are outliers you should

If two variables taken together account for 65% of the variability in Y , and a third variable has a simple squared correlation with Y of .10, then adding that variable to the equation will allow us to account for

If we want to compare the contribution of several predictors to the prediction of a dependent variable, we can get at least a rough idea by comparing

If we find all of the residuals when predicting our obtained values of Y from the regression equation, the sum of squared residuals would be expected to be _______ the sum of the squared residuals for a new set of data.

In the previous question, a student who scored 0 on both X ₁ and X ₂ would be expected to have a dependent variable score of

If we have three predictors and they are all individually correlated with the dependent variable, we know that

In multiple regression an outlier is one that

Before running a multiple regression, it is smart to look at the distribution of each variable. We do this because

The difference between multiple regression and simple regression is that

When we speak of the correlations among the independent variables, we are speaking of

If two variables are each correlated significantly with the dependent variable, then the multiple correlation will be

Given the following regression equation ( Ŷ = 3.5 X ₁ + 2 X ₂ + 12) , the coefficient for X ₁ would mean that

In multiple regression the intercept is usually denoted as

Suppose that in the previous question another subject had a predicted score of 10.3, and actually obtained a score of 12.4. For this subject the residual score would be

In the previous question the intercept would be