Question 1

Regression analysis procedures have as their primary purpose the development of an equation that can be used for predicting values on some DV for all members of a population.

Accepted Answer

Regression analysis is used to develop a mathematical equation that describes the relationship between a dependent variable (DV) and one or more independent variables, allowing for the prediction of the DV for individuals or cases.

Question 2

A secondary purpose is to use regression analysis as a means of explaining causal relationships among variables.

Accepted Answer

Regression analysis can indeed be used to explain the relationships among variables, including identifying potential causal relationships, by estimating the quantitative effect of one variable on another.

Question 3

In order to make predictions, three important facts about the regression line must be known. One of them is: The point at which the line crosses the X-axis.

Accepted Answer

The three important facts about the regression line for making predictions are the slope of the line, the intercept where the line crosses the Y-axis, and the fit of the line to the data (often measured by R-squared). The point where the line crosses the X-axis is not typically used for making predictions.

Question 4

The regression line is essentially an equation that expresses X as a function of Y.

Accepted Answer

The regression line typically expresses Y as a function of X, predicting the value of the dependent variable (Y) based on the independent variable (X).

Question 5

Residuals (errors of prediction) are essentially calculated as the difference between the actual value and the predicted value for the IV.

Accepted Answer

Residuals are calculated as the difference between the actual value and the predicted value for the dependent variable (DV), not the independent variable (IV).

Question 6

The reason that we obtain the best-fitting line as our regression equation is that we mathematically calculate the line with the smallest amount of total squared error.

Accepted Answer

The best-fitting line in regression analysis is determined by minimizing the sum of the squares of the vertical distances (errors) between the observed values and the values predicted by the line, which is known as the least squares criterion.

Question 7

Multiple regression is used to predict the value of a single DV from a weighted, linear combination of IVs.

Accepted Answer

Multiple regression is designed to predict the value of one dependent variable (DV) based on the linear combination of multiple independent variables (IVs), with each IV being assigned a weight that reflects its contribution to the prediction.

Question 8

The coefficient of determination in multiple regression is the proportion of DV variance that can be explained by at least one IV.

Accepted Answer

The coefficient of determination in multiple regression (often denoted as R^2) is the proportion of the variance in the dependent variable (DV) that can be explained by all the independent variables (IVs) together, not just by at least one IV.

Question 9

Multicollinearity is desirable in multiple regression.

Accepted Answer

Multicollinearity refers to a situation in which two or more explanatory variables in a multiple regression model are highly linearly related, making it difficult to isolate the individual effects of the variables on the dependent variable. This is generally undesirable as it increases the variance of the coefficient estimates and makes the model interpretation more challenging.

Question 10

Multicollinearity tends to increase the variances in regression coefficients, which ultimately results in a more stable prediction equation.

Accepted Answer

Multicollinearity increases the variances of the regression coefficients, making the model's predictions less reliable and the coefficients unstable, not more stable.

Question 11

Tolerance is a measure of collinearity among IVs, where possible values range from 0-1.

Accepted Answer

Tolerance is indeed a measure used in statistics to assess the degree of collinearity among independent variables (IVs) in regression analyses, where its values range from 0 to 1, with values closer to 0 indicating higher collinearity.

Question 12

The variance inflation factor (VIF) for a given predictor "indicates whether there exists a strong linear association between it and all remaining predictors" (Stevens, 2001).

Accepted Answer

The Variance Inflation Factor (VIF) measures how much the variance of an estimated regression coefficient increases if your predictors are correlated. If a predictor has a high VIF, it means it is highly correlated with other predictors, indicating multicollinearity in the model.

Question 13

In standard multiple regression, the IV that has the highest correlation with the DV is entered into the analysis first.

Accepted Answer

In standard multiple regression, variables are not entered based on their correlation with the dependent variable (DV); rather, all independent variables (IVs) are entered into the analysis simultaneously, unless a stepwise method is specifically chosen.

Question 14

Sequential multiple regression is also sometimes referred to as statistical multiple regression.

Accepted Answer

Sequential multiple regression is a specific type of multiple regression analysis where variables are entered into the regression equation one at a time in a specified order, often based on theoretical considerations or previous research. This is different from standard multiple regression, where all variables are entered into the equation simultaneously. The term "statistical multiple regression" is not commonly used to specifically refer to sequential multiple regression.

Question 15

Stepwise multiple regression is often used in studies that are explanatory in nature.

Accepted Answer

The answer of Stepwise multiple regression is often used in...

Question 16

Model validation, sometimes called model cross-validation, is an important issue in multiple regression.

Accepted Answer

Model validation, including techniques like cross-validation, is crucial in multiple regression to assess the predictive ability of the model and ensure it generalizes well to new, unseen data.

Question 17

Multiple regression can be very sensitive to extreme outliers.

Accepted Answer

Multiple regression analysis can be significantly affected by the presence of extreme outliers, as they can distort the estimated relationships between the dependent and independent variables, leading to unreliable coefficients and predictions.

Question 18

One of the assumptions in multiple regression with regard to the raw scale variables is that the IVs are normally distributed.

Accepted Answer

The assumption in multiple regression is not that the independent variables (IVs) need to be normally distributed, but rather that the residuals (errors) from the regression model are normally distributed.

Question 19

Another assumption in multiple regression with regard to the residuals is that the errors are correlated with the IVs.

Accepted Answer

In multiple regression, the assumption is that the residuals (errors) are not correlated with the independent variables (IVs). This assumption ensures that the model estimates unbiased and consistent coefficients.

Question 20

In cases that involve moderate violations of linearity and homoscedasticity, one should be aware that these violations weaken and invalidate the regression analysis.

Accepted Answer

Moderate violations of linearity and homoscedasticity do not necessarily invalidate regression analysis; they may weaken the predictive power or the accuracy of the estimates, but statistical techniques and transformations can often be used to address these issues and still provide useful results.

Quiz 7: Multiple Regression