Question 1

When does multicollinearity occur in a multiple regression analysis?
A)The dependent variables are highly correlated
B)The independent variables are minimally correlated
C)The independent variables are highly correlated
D)The independent variables have no correlation

Accepted Answer

Multicollinearity occurs when the independent variables in a multiple regression analysis are highly correlated with each other. This can cause problems in the regression analysis, such as inflated standard errors and unstable coefficients. Therefore, it is important to check for multicollinearity before conducting a multiple regression analysis.

Question 2

What are the degrees of freedom associated with the regression sum of squares?
A)Number of independent variables
B)1
C)F-ratio
D)(n - 2)

Accepted Answer

The degrees of freedom associated with the regression sum of squares is equal to the number of independent variables in the model.

Question 3

If there are four independent variables in a multiple regression equation,there are also four
A)Y-intercepts.
B)regression coefficients.
C)dependent variables.
D)constant terms.

Accepted Answer

The number of regression coefficients in a multiple regression equation will always be equal to the number of independent variables included in the equation.

Question 4

If the coefficient of multiple determination is 0.81,what percent of variation is not explained?
A)19%
B)90%
C)66%
D)81%

Accepted Answer

The coefficient of multiple determination, R-squared, gives the proportion of the total variation in the dependent variable that is explained by the independent variables. Therefore, if R-squared is 0.81, it means that 81% of the variation in the dependent variable is explained by the independent variables. The remaining variation (100% - 81% = 19%) is not explained by the model. Hence, the correct choice is A (19%).

Question 5

In multiple regression analysis,when the independent variables are highly correlated,this situation is called ____________________.
A)Autocorrelation
B)Multicollinearity
C)Homoscedasticity
D)Curvilinearity

Accepted Answer

When the independent variables in multiple regression analysis are highly correlated, it creates a problem of multicollinearity. This means that the independent variables are not independent of each other and it becomes difficult to isolate the effect of each variable on the dependent variable. Autocorrelation refers to the correlation between observations within a single variable over time, homoscedasticity refers to the assumption of equal variances across different levels of the independent variable, and curvilinearity refers to the presence of a curved relationship between the independent and dependent variables. While these may also be issues in regression analysis, they are not directly related to the problem of multicollinearity.

Question 6

A valid multiple regression analysis assumes or requires that
A)the dependent variable is measured using an ordinal,interval,or ratio scale
B)the residuals follow an F-distribution
C)the independent variables and the dependent variable have a linear relationship
D)the observations are autocorrelated

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 7

What can we conclude if the global test of regression rejects the null hypothesis?
A)Strong correlations exist among the variables.
B)No relationship exists between the dependent variable and any of the independent variables.
C)At least one of the net regression coefficients is not equal to zero.
D)Good predictions are not possible.

Accepted Answer

If the global test of regression rejects the null hypothesis, it indicates that at least one of the net regression coefficients is not equal to zero, which means that there is significant relationship between the dependent variable and at least one of the independent variables.

Question 8

What is the range of values for multiple R?
A)-100% to -100% inclusive
B)-100% to 0% inclusive
C)0% to +100% inclusive
D)Unlimited range

Accepted Answer

The multiple R value, also known as the correlation coefficient, measures the strength and direction of the relationship between two or more variables. The correlation coefficient can range from -1.00 to +1.00, where -1.00 indicates a perfect negative correlation, 0.00 indicates no correlation, and +1.00 indicates a perfect positive correlation. Therefore, the range of values for multiple R is 0% to +100% inclusive.

Question 9

What does the correlation matrix for a multiple regression analysis contain?
A)Multiple correlation coefficients
B)Simple correlation coefficients
C)Multiple coefficients of determination
D)Multiple standard errors of estimate

Accepted Answer

The correlation matrix in a multiple regression analysis contains simple correlation coefficients, which measure the linear relationship between each pair of variables.

Question 10

Which of the following is a characteristic of the F-distribution?
A)Normally distributed
B)Positively skewed
C)Negatively skewed
D)Equal to the t-distribution

Accepted Answer

The F-distribution is positively skewed, meaning it has a longer tail to the right. This is because the F-distribution is the ratio of two chi-squared distributions, which are themselves positively skewed.

Question 11

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?
A)Only one of the independent variables should be used in the regression equation.
B)The independent variables are strongly related.
C)Two separate regression equations are required.
D)Both independent variables should be used to predict the dependent variable.

Accepted Answer

A correlation coefficient of 0.11 indicates a weak and positive relationship between the two independent variables, which suggests that both variables could be included in the regression model. Additionally, if each independent variable is highly correlated with the dependent variable, it is important to include both variables in the regression model to obtain the most accurate predictions of the dependent variable. Therefore, the best choice would be to use both independent variables to predict the dependent variable (choice D).

Question 12

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)125
B)10
C)114
D)115

Accepted Answer

The denominator in the calculation of the multiple standard error of estimate is (n - k - 1), where n is the sample size and k is the number of independent variables. Therefore, the denominator in this case would be (125 - 10 - 1) = 114.

Question 13

In multiple regression analysis,testing the global null hypothesis that the multiple regression coefficients are all zero is based on
A)a z statistic
B)a t statistic
C)a F statistic
D)binomial distribution

Accepted Answer

Testing the global null hypothesis in multiple regression analysis requires an F test. The F statistic evaluates the overall significance of the regression model and indicates whether at least one of the independent variables is significantly related to the dependent variable.

Question 14

In the general multiple regression equation which of the following variables represents the Y intercept?
A)b1
B)x1
C) 
D)a

Accepted Answer

In the general multiple regression equation, the Y intercept is represented by the constant term, which is denoted by the symbol "a". Option D represents the constant term or Y intercept of the regression equation.

Question 15

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?
A)Multicollinearity between these two independent variables
B)A negative relationship is not possible
C)Only one of the two independent variables will explain a high percent of the variation
D)An effective regression equation

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 16

In a regression analysis,three independent variables are used in the equation based on a sample of forty observations.What are the degrees of freedom associated with the F-statistic?
A)3 and 39
B)4 and 40
C)3 and 36
D)2 and 39

Accepted Answer

The degrees of freedom associated with the F-test are calculated as follows: numerator degrees of freedom = number of independent variables in the model, which is 3 in this case; denominator degrees of freedom = sample size minus the number of independent variables, which is 40 - 3 = 37. Therefore, the correct choice is C, which shows the numerator degrees of freedom as 3 and denominator degrees of freedom as 36.

Question 17

What can we conclude if the global test of regression does not reject the null hypothesis?
A)A strong relationship exists among the variables
B)No relationship exists between the dependent variable and any of the independent variables
C)The independent variables are good predictors
D)Good forecasts are possible

Accepted Answer

If the global test of regression does not reject the null hypothesis, it means that there is not enough evidence to suggest that there is a relationship between the dependent variable and any of the independent variables. Therefore, choice B is the best answer. The other choices suggest that there is a relationship between the variables, which is not supported by the results of the test.

Question 18

How is the degree of association between a set of independent variables and a dependent variable measured?
A)Confidence intervals.
B)Autocorrelation.
C)Coefficient of multiple determination.
D)Standard error of estimate.

Accepted Answer

The coefficient of multiple determination, also known as R-square, is the best measure of degree of association between a set of independent variables and a dependent variable. It measures the proportion of variation in the dependent variable explained by the independent variables. Confidence intervals and standard error of estimate are measures of statistical significance and precision, while autocorrelation measures the correlation between a variable and its lagged values.

Question 19

What does the multiple standard error of estimate measure? A)Change in for a change in X₁ B)The "error" or variability in predicting Y C)The regression mean square error in the ANOVA table D)Amount of explained variation

Accepted Answer

The multiple standard error of estimate measures the "error" or variability in predicting Y, which is the overall model's ability to predict the outcome variable based on the predictor variables.

Question 20

In a multiple regression ANOVA table,explained variation is represented by
A)the regression sum of squares
B)the total sum of squares
C)the regression coefficients
D)the correlation matrix

Accepted Answer

The regression sum of squares (RSS) represents the explained variation in a multiple regression ANOVA table. The RSS measures the amount of variability in the dependent variable that is explained by the independent variables in the model. The total sum of squares (TSS) represents the total variation in the dependent variable, and the remaining variation, not explained by the independent variables, is represented by the residual sum of squares (RSS). The regression coefficients are the estimates of the effects of the independent variables on the dependent variable, and the correlation matrix is a matrix of correlations between the variables in the model.

Quiz 14: Multiple Regression and Correlation Analysis

When does multicollinearity occur in a multiple regression analysis?

What are the degrees of freedom associated with the regression sum of squares?

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

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

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

A valid multiple regression analysis assumes or requires that

What can we conclude if the global test of regression rejects the null hypothesis?

What is the range of values for multiple R?

What does the correlation matrix for a multiple regression analysis contain?

Which of the following is a characteristic of the F-distribution?

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 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?

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

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

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 a regression analysis,three independent variables are used in the equation based on a sample of forty observations.What are the degrees of freedom associated with the F-statistic?

What can we conclude if the global test of regression does not reject the null hypothesis?

How is the degree of association between a set of independent variables and a dependent variable measured?

What does the multiple standard error of estimate measure?

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