Question 1

In regression, the line that runs through the points on a scatter diagram is positioned to minimize the vertical distances away from the line of the various points because of the "least squares criterion."

Accepted Answer

The least squares criterion means that the line is positioned to minimize the squared vertical distances away from the line of the various points. This is a standard technique used in regression analysis.

Question 2

Multiple regression requires specification of a general conceptual model that identifies independent and dependent variables and shows their expected relationships.

Accepted Answer

Multiple regression analysis involves identifying a conceptual model that specifies the variables of interest and their hypothesized relationships. The model guides the selection of variables and the interpretation of the results.

Question 3

The VIF is useful for identifying multicollinearity.

Accepted Answer

VIF (Variance Inflation Factor) is a statistical method used to detect and quantify the severity of multicollinearity in a regression analysis. Therefore, it is true that VIF is useful for identifying multicollinearity.

Question 4

A regression line using the "least squares criterion" will result in high residuals.

Accepted Answer

A regression line using the "least squares criterion" is created to minimize the sum of squared residuals, so it should result in low residuals.

Question 5

Multicollinearity refers to correlations among the dependent variables and makes predictions much more accurate because predicting one variable also allows you to predict the correlated variable(s).

Accepted Answer

Multicollinearity actually decreases the accuracy of predictions because it makes it difficult to determine the individual effect of each independent variable on the dependent variable. It also leads to unstable regression coefficients and inflated standard errors.

Question 6

If the ANOVA F test is not significant in bivariate regression analysis, we must trim the model by eliminating the insignificant dependent variable(s).

Accepted Answer

The ANOVA F test in bivariate regression analysis only tests the significance of the overall model, not individual variables. Therefore, if the F test is not significant, it does not necessarily mean that any variables should be eliminated. We would need to examine the significance of each variable separately using t-tests or other techniques.

Question 7

If the tests of the significance of the slope and the intercept are significant, this means that the straight-line relationship depicted by the slope and the intercept actually exists in the population and, therefore, the regression equation may be used as a prediction device.

Accepted Answer

If both the tests of significance of the slope and the intercept are significant, it means that there is evidence to suggest that the relationship between the dependent and independent variables exists in the population. This means that the regression equation can be used as a prediction tool for future observations.

Question 8

The standard error of the estimate is used to help predict a range within which we would expect an actual result to fall.

Accepted Answer

The standard error of the estimate is a measure of the accuracy of predictions made with a regression analysis. It helps to estimate the range within which the actual result is likely to fall. Therefore, the statement is true.

Question 9

One of the assumptions of regression analysis is that the plots on a scatter diagram will be spread uniformly and in accord with the normal curve assumptions over the regression line. This means that the points will be diffused and spread out near the line and become closer together as you move away from the line.

Accepted Answer

The assumption of regression analysis is not that the scatter plot will be spread uniformly and in accordance with the normal curve assumptions over the regression line. Rather, the assumption is that the residuals (the differences between the observed values and the predicted values) will be normally distributed and have a constant variance (homoscedasticity) along the regression line. The scatter plot may or may not demonstrate these characteristics.

Question 10

The standard error of the estimate is used as a measure of the accuracy of the predictions in regression; it is analogous to the standard error of the mean used in estimating a population mean from a sample.

Accepted Answer

The statement is true. The standard error of the estimate measures the variability of the predicted values around the regression line and is used as an indicator of how well the regression model fits the data. The standard error of the mean, on the other hand, measures the variability of sample means around the population mean and is used as an indicator of the precision of the sample mean as an estimator of the population mean. Both standard errors provide information about the accuracy or precision of an estimate, but in different contexts.

Question 11

We can sometimes improve a regression analysis finding by removing outliers and rerunning the regression analysis.

Accepted Answer

Outliers can greatly affect the regression results and removing them can help improve the accuracy of the analysis.

Question 12

In multiple regression analysis, we are trying to predict an independent variable using more than two dependent variables.

Accepted Answer

The answer of In multiple regression analysis, we are trying...

Question 13

In bivariate regression analysis, t tests are used to test the significance of the slope and the intercept of the multiple dependent variables.

Accepted Answer

In bivariate regression analysis, t tests are used to test the significance of the slope coeficient (β) and not the intercept (α).

Question 14

A regression plane is the shape of the independent variable in multiple regression analysis.

Accepted Answer

A regression plane is the plane that represents the predicted values of the dependent variable based on the values of the independent variables in a multiple regression analysis. It is a three-dimensional shape, not a two-dimensional shape like a plane.

Question 15

In bivariate regression, we can calculate an upper and lower range within which we could expect the values of the independent values to fall if they were calculated.

Accepted Answer

The answer of In bivariate regression, we can calculate an...

Question 16

VIF is an acronym for "Very InFrequent."

Accepted Answer

VIF actually stands for "Variance Inflation Factor," which is a statistical measure used in regression analysis.

Question 17

The multiple R, also called the coefficient of determination, in multiple regression ranges from 0 to +1.00 and represents the amount of the dependent variable "explained" by the combined independent variables.

Accepted Answer

The statement is true.

Question 18

The R Square value is very important because it tells us how well our regression line fits the scatter of data points. It may range from 0 to +1.00 because it is the square of the correlation coefficient, which may range from -1.00 to +1.00.

Accepted Answer

The R Square value is indeed the square of the correlation coefficient and may range from 0 to +1.00.

Question 19

Immediately in bivariate analysis the researcher must find out whether or not a linear relationship
exists in the population.

Accepted Answer

Bivariate analysis involves examining the relationship between two variables. The first step in bivariate analysis is to determine whether there is a linear relationship between the two variables. This is important because if a linear relationship exists, then further statistical tests can be done to determine the strength and significance of the relationship. If no linear relationship exists, then other types of analysis may be more appropriate.

Question 20

An outlier refers to Multiple Rs that are above expected norms such as above 95 or 100.

Accepted Answer

An outlier refers to values that are significantly higher or lower than the majority of the data points, but there is no specific threshold such as 95 or 100.

Quiz 19: Regression Analysis in Marketing Research