Question 1

When does multicollinearity occur in a multiple regression analysis?

Accepted Answer

Multicollinearity occurs when the independent variables in a multiple regression analysis are highly correlated with each other. This makes it difficult to determine the true relationship between each independent variable and the dependent variable, as the effect of one independent variable cannot be separated from that of another. Highly correlated independent variables can also result in unstable or inconsistent regression coefficients. Therefore, having highly correlated independent variables can be problematic and should be avoided whenever possible.

Question 2

If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what does this indicate?

Accepted Answer

A correlation of 0.11 between the independent variables suggests a weak relationship between them. However, if both independent variables are highly correlated with the dependent variable, it is important to include both in the regression analysis to capture their individual effects on the dependent variable. Therefore, both independent variables should be used to predict the dependent variable.

Question 3

If a data set of ten observations is used in a multiple regression analysis with ten independent variables, then

Accepted Answer

In a multiple regression analysis with the same number of observations as independent variables, the model will perfectly fit the data, resulting in an R² of 1.0.

Question 4

To evaluate the assumption of linearity, a multiple regression analysis should include

Accepted Answer

Scatter diagrams of the dependent variable plotted as a function of each independent variable is the best choice to evaluate the assumption of linearity. This helps to visually inspect if there is a linear relationship between the dependent variable and each independent variable, allowing identification of potential issues such as curvilinear relationships or outliers. Variance inflation factors, hypothesis tests of individual coefficients, and ANOVA tables are useful for other aspects of multiple regression analysis, but not specifically for evaluating linearity assumptions.

Question 5

In multiple regression analysis, when the independent variables are highly correlated, this situation is called ___________________.

Accepted Answer

Multicollinearity occurs when there is a high correlation between independent variables in a regression model. This can lead to difficulties in interpreting the importance of individual independent variables and can cause instability in the estimates of regression coefficients. Autocorrelation refers to the correlation of error terms in a time series regression, homoscedasticity refers to the equal variance of error terms, and curvilinearity refers to the relationship between the dependent variable and independent variables not being linear.

Question 6

In multiple regression analysis, testing the global null hypothesis that all regression coefficients are zero is based on

Accepted Answer

The global null hypothesis that all regression coefficients are zero can be tested using an F statistic in multiple regression analysis. This is done by comparing the ratio of the explained variance (sum of squares due to regression) to the unexplained variance (residual sum of squares) with an F distribution.

Question 7

If the coefficient of multiple determination is 0.81, what percent of variation is not explained?

Accepted Answer

The coefficient of multiple determination, usually denoted as R-squared, represents the proportion of variation in the dependent variable that is explained by the independent variables in a regression model. Therefore, if R-squared is 0.81, 81% of the total variation is explained, and the remaining 19% (100% - 81%) is not explained by the model. Therefore, the correct answer is A) 19%.

Question 8

If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what does this indicate?

Accepted Answer

A correlation of 0.11 between the two independent variables indicates a very low level of multicollinearity, which is beneficial for regression analysis. The fact that each independent variable is highly correlated with the dependent variable suggests that including both in the regression equation could lead to an effective model in explaining the variation in the dependent variable.

Question 9

In the general multiple regression equation, which of the following variables represents the Y-intercept?

Accepted Answer

In the general multiple regression equation, "a" represents the Y-intercept or the constant term.

Question 10

What does the multiple standard error of estimate measure?

Accepted Answer

The multiple standard error of estimate measures the variability or "error" in predicting the dependent variable (Y) based on the independent variable(s) used in the regression model.

Question 11

If a multiple regression analysis is based on ten independent variables collected from a sample of 125 observations, what will be the value of the denominator in the calculation of the multiple standard error of estimate?

Accepted Answer

The denominator for the calculation of the multiple standard error of estimate is given by n - k -1, where n is the number of observations and k is the number of independent variables. Thus, the denominator in this case would be 125 - 10 - 1 = 114. Therefore, the correct answer is C.

Question 12

A valid multiple regression analysis assumes or requires that

Accepted Answer

Multiple regression analysis assumes or requires that the independent variables and the dependent variable have a linear relationship. The other options are not necessarily required for a valid multiple regression analysis.

Question 13

In multiple regression analysis, how is the degree of association between a set of independent variables and a dependent variable measured?

Accepted Answer

The degree of association between a set of independent variables and a dependent variable in multiple regression analysis is measured by the coefficient of multiple determination, which is also known as R-squared. It represents the proportion of variance in the dependent variable that is explained by the independent variables. This measure ranges from 0 to 1, where a value of 1 indicates a perfect fit and 0 indicates no relationship between the variables. Confidence intervals, autocorrelation, and standard error of estimate are not direct measures of the degree of association in multiple regression analysis.

Question 14

The adjusted R² accounts for the number of independent variables by?

Accepted Answer

The adjusted R² (also known as R-squared adjusted) takes into account the number of independent variables in the model by using the degrees of freedom. This is done through a formula that adjusts the original R² value based on the sample size and the number of independent variables.

Question 15

The variance inflation factor can be used to

Accepted Answer

The variance inflation factor (VIF) measures how much the variance of a regression coefficient is inflated due to collinearity among the predictor variables. A high VIF indicates that the corresponding predictor variable is strongly correlated with at least one other predictor variable and may need to be eliminated from the model. Therefore, the VIF can be used to select or eliminate variables for a multiple regression model.

Question 16

If there are four independent variables in a multiple regression equation, there are also four

Accepted Answer

For each independent variable in a multiple regression equation, there is a corresponding regression coefficient. The number of independent variables has no impact on the number of Y-intercepts, dependent variables, or constant terms in the equation.

Question 17

In multiple regression analysis, residual analysis is used to test the requirement that

Accepted Answer

Residual analysis is used to check whether the assumptions of the regression model are met. One of the assumptions is homoscedasticity, which means that the variation in the residuals should be the same for all values of the predicted variable Y. Therefore, choice A is the correct answer. B is incorrect because residual analysis cannot directly test causality. C is related to model specification, which is a different issue. D is related to model fit, which is also different from residual analysis.

Question 18

What is the range of values for multiple R²?

Accepted Answer

Multiple R² can only output a range of 0% to +100% inclusive, since it takes an input signal and multiplies it by a value between 0 and 1 (RS1), and then adds that to the original signal (U1), resulting in an output that is always equal to or greater than the original signal (S1), up to a maximum of double the original signal (P0). Therefore, the output range is limited to 0% to +100% inclusive.

Question 19

In a multiple regression ANOVA table, explained variation is represented by

Accepted Answer

The regression sum of squares in a multiple regression ANOVA table represents the variation explained by the model, or the extent to which the predictors are able to account for the variation in the dependent variable. The total sum of squares represents the overall variation in the dependent variable, while the residual mean square represents the variation that is not accounted for by the model. The p-value is a measure of the probability of observing the results of the analysis by chance.

Question 20

In multiple regression analysis, before testing the significance of the individual regression coefficients,

Accepted Answer

Before testing the significance of individual regression coefficients, the overall null hypothesis that all regression coefficients equal zero should be rejected to ensure that the model has some predictive power.

Quiz 14: Multiple Regression Analysis

When does multicollinearity occur in a multiple regression analysis?

If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what does this indicate?

If a data set of ten observations is used in a multiple regression analysis with ten independent variables, then

To evaluate the assumption of linearity, a multiple regression analysis should include

In multiple regression analysis, when the independent variables are highly correlated, this situation is called ___________________.

In multiple regression analysis, testing the global null hypothesis that all regression coefficients are zero is based on

If the coefficient of multiple determination is 0.81, what percent of variation is not explained?

If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what does this indicate?

In the general multiple regression equation, which of the following variables represents the Y-intercept?

What does the multiple standard error of estimate measure?

If a multiple regression analysis is based on ten independent variables collected from a sample of 125 observations, what will be the value of the denominator in the calculation of the multiple standard error of estimate?

A valid multiple regression analysis assumes or requires that

In multiple regression analysis, how is the degree of association between a set of independent variables and a dependent variable measured?

The adjusted R2 accounts for the number of independent variables by?

The variance inflation factor can be used to

If there are four independent variables in a multiple regression equation, there are also four

In multiple regression analysis, residual analysis is used to test the requirement that

What is the range of values for multiple R2?

In a multiple regression ANOVA table, explained variation is represented by

In multiple regression analysis, before testing the significance of the individual regression coefficients,

The adjusted R² accounts for the number of independent variables by?

What is the range of values for multiple R²?