Question 1

We want to predict a person's happiness from the following variables: degree of optimism, success in school, and number of close friends. What type of statistical test can tell us whether these variables predict a person's happiness?

Accepted Answer

Multiple regression is the appropriate statistical test for predicting the value of a dependent variable (in this case, a person's happiness) based on the values of multiple independent variables (degree of optimism, success in school, and number of close friends).

Question 2

The text generally recommended against formal procedures for finding an optimal regression procedure because

Accepted Answer

The text suggests that formal procedures for finding an optimal regression procedure may pay too much attention to chance differences and result in overfitting the model to the specific sample data, rather than selecting a more generalizable model. It does not necessarily state that those procedures never work or that statistical software cannot handle them.

Question 3

Multicollinearity occurs when the predictor variables are highly correlated with one another.

Accepted Answer

Multicollinearity is the condition of high intercorrelation among two or more independent variables used in a multiple regression model. It is considered problematic because it can increase the variance of the coefficient estimates and make it difficult to determine the true contribution of each variable in predicting the outcome variable.

Question 4

The example in Chapter 11 of predicting weight from height and sex showed that

Accepted Answer

The example showed that adding sex as a predictor accounted for an important source of variability, suggesting that sex is a useful predictor in predicting weight from height.

Question 5

If we predict anxiety from stress and intrusive thoughts, and if the multiple regression is significant, that means that

Accepted Answer

A significant multiple regression model does not guarantee that each predictor within the model is significant. The overall model significance indicates that at least one of the predictors is contributing to the prediction of the outcome variable, but it does not specify which ones without looking at the individual predictors' p-values.

Question 6

Multiple regression analysis yielded the following regression equation:
Predicted Happiness = .36 × friends - .13 × s tress + 1.23
Which of the following is true?

Accepted Answer

According to the regression equation, the coefficient for Friends is positive (.36), which means that as Friends increase, Predicted Happiness also increases. The coefficient for Stress is negative (-.13), which means that as Stress increases, Predicted Happiness decreases. Therefore, the correct choice is A.

Question 7

If you drop a predictor from the regression equation

Accepted Answer

Dropping a predictor from the regression equation could either result in a decreased correlation or the same correlation as before. If the predictor was not significantly contributing to the regression equation, then dropping it may not change the correlation drastically. However, if the predictor was a strong contributor to the regression equation, dropping it could result in a decreased correlation. Therefore, both options B and C are possible outcomes.

Question 8

Multiple regression means there is more than one criterion variable.

Accepted Answer

Multiple regression involves one criterion (dependent) variable and two or more predictor (independent) variables.

Question 9

If the multiple correlation is high, we would expect to have _______ residuals than if the multiple correlation is low.

Accepted Answer

If the multiple correlation is high, it means that the independent variables are strong predictors of the dependent variable, and the regression line is able to explain a large portion of the variance in the data. Thus, the residuals (the difference between the actual and predicted values) are expected to be smaller.

Question 10

The example in the text predicting distress in cancer patients used distress at an earlier time as one of the predictors. This was done

Accepted Answer

Including earlier distress as a predictor allows the authors to control for initial differences in distress levels, enabling them to isolate and examine the effects of self-blame on distress over time.

Question 11

In an example in Chapter 10 we found that the relationship between how a student evaluated a course, and that student's expected grade was significant. In this chapter Grade was not a significant predictor. The difference is

Accepted Answer

The difference lies in the fact that grade did not predict significantly once other predictors were considered (B), and these other predictors were correlated with grade (C), making both B and C correct.

Question 12

Many of the procedures for finding an optimal regression equation (whatever that means) are known as

Accepted Answer

Stepwise procedures involve selecting variables for inclusion or exclusion in a regression model based on a mathematical algorithm. This approach is more efficient than trial and error or trialwise procedures, and less arbitrary than hunting procedures.

Question 13

The following regression equation was found for a sample of college students. predicted happiness = 32.8 GPA + 17.3 × pocket money + 7.4
Which of the following can be concluded?

Accepted Answer

The coefficients in a regression equation represent the change in the dependent variable (predicted happiness) for a one-unit change in the independent variable, holding other variables constant. Therefore, a one-unit increase in GPA increases predicted happiness by 32.8 units, assuming no pocket money. Choices A, B, and D cannot be concluded without additional information such as the actual correlation values or r-squared values.

Question 14

A multiple regression analysis was used to test the values of visual acuity, swing power, and cost of clubs for predicting golf scores. The regression analysis showed that visual acuity and swing power predicted significant amounts of the variability in golf scores, but cost of clubs did not. What can be concluded from these results?

Accepted Answer

Since the cost of clubs did not predict a significant amount of variability in golf scores, removing it from the model will not significantly reduce the model's R² value.

Question 15

The statistical tests on regression coefficients are usually

Accepted Answer

The statistical tests on regression coefficients are usually t tests because they are used to test if the coefficient is statistically significant. The t test determines if there is a significant difference between the observed coefficient and the hypothesized value of 0. Z tests and r tests are not typically used for this purpose. F tests are used to test the overall significance of a regression model.

Question 16

When testing null hypotheses about multiple regression we

Accepted Answer

When testing null hypotheses about multiple regression, we need to have a separate significance test for each predictor and for overall significance. This is because the contribution of each predictor variable needs to be evaluated individually as well as the overall contribution of all predictors. Therefore, option B is the best choice.

Question 17

If we know that a regression coefficient is statistically significant, we know that

Accepted Answer

If a regression coefficient is statistically significant, it means that we can reject the null hypothesis that the true coefficient is zero. Therefore, option B is the correct choice - we know that the coefficient is not 0.0. The other options (positive, not 1.0, and large) cannot be inferred solely from the fact that the coefficient is statistically significant.

Question 18

The Analysis of Variance section in computer results for multiple regression

Accepted Answer

The Analysis of Variance (ANOVA) section in computer results for multiple regression tests the overall significance of the regression. It does not compare the means, test the significance of each predictor, or compare the variances of the variables.

Question 19

A table in which each variable is correlated with every other variable is called

Accepted Answer

An intercorrelation matrix is a table that shows the correlation coefficients between every pair of variables in a dataset. It is also known as a correlation matrix or a covariance matrix. A multivariate table may not necessarily show correlations between variables, but rather may display frequencies, means, and other descriptive statistics for multiple variables. A contingency table displays the frequencies of two or more categorical variables, while a pattern matrix is commonly used in factor analysis to display the loadings of observed variables on underlying factors.

Question 20

If the overall analysis of variance is NOT significant

Accepted Answer

If the overall analysis of variance is not significant, it indicates that there is no significant relationship between the independent and dependent variables. Therefore, looking at the individual variables may not be useful in this case. It is better to focus on other aspects of the analysis or consider revising the research question or hypothesis.

Quiz 11: Multiple Regression