Question 1

The least-squares regression line minimizes the sum of the squared deviations of the actual values from the predicted values in the regression line.

Accepted Answer

This is the definition of the least-squares regression line. It is designed to minimize the sum of the squared deviations between the actual values and the predicted values in the regression line.

Question 2

Covariance is the extent to which one variable causes a change in another variable.

Accepted Answer

Covariance measures the relationship between two variables, but not the causation. Therefore, it would be incorrect to say that covariance measures the extent to which one variable causes a change in another variable.

Question 3

In regression analysis, the equation of a straight line is Y = a + b X.

Accepted Answer

This statement is true. The equation of a straight line in regression analysis is Y = a + b X, where Y is the dependent variable, X is the independent variable, a is the intercept, and b is the slope of the line.

Question 4

In regression, the standardized Y-intercept term is always 0.

Accepted Answer

The standardized Y-intercept term, also known as the standardized coefficient or beta coefficient, represents the expected change in the dependent variable for a one-unit change in the independent variable, while holding all other independent variables constant. It is not always 0 in regression, but it depends on the specific model and data. However, the intercept term itself (which is not standardized) represents the expected value of the dependent variable when all independent variables are 0, and it can be any value.

Question 5

In a correlation matrix, the main diagonal contains correlations of 1.00 because it represents a variable's correlation with itself.

Accepted Answer

The main diagonal of a correlation matrix represents the correlation of a variable with itself, which is always 1.00 as it is a perfect correlation.

Question 6

In a regression equation, the slope of the line, b, is the change in X that is due to a corresponding change of one unit of Y.

Accepted Answer

The slope of the line, b, is the change in Y that is due to a corresponding change of one unit of X.

Question 7

Measure of association is a general term that refers to causality.

Accepted Answer

Measure of association does not necessarily refer to causality. It simply quantifies the relationship between two variables. While a strong measure of association may suggest a causal relationship, it does not prove causation.

Question 8

A Spearman correlation is more appropriate for interval and ratio data than is the Pearson product-moment correlation.

Accepted Answer

A Spearman correlation is more appropriate for ordinal level data.

Question 9

If r = -0.88, this indicates a weak relationship between the two variables under study.

Accepted Answer

A correlation coefficient (r) of -0.88 indicates a strong negative relationship between the two variables.

Question 10

In simple regression, standardized parameter estimates reflect the measurement scale range.

Accepted Answer

Standardized parameter estimates in simple regression are not affected by the measurement scale range because the predictor variable (X) is standardized before computing the regression coefficients. This means that the units of X are converted to standard deviation units, and therefore the standardized parameter estimates are comparable across different scales.

Question 11

The correlation coefficient, r, indicates the magnitude of the linear relationships but not the direction of that relationship.

Accepted Answer

The correlation coefficient, r, indicates both the magnitude and direction of the linear relationship between two variables. A positive r value indicates a positive linear relationship (increases in one variable are associated with increases in the other variable), while a negative r value indicates a negative linear relationship (increases in one variable are associated with decreases in the other variable).

Question 12

In most business research, the estimate of b in a regression equation is most important.

Accepted Answer

The estimate of b in a regression equation represents the coefficient or slope, which is the measure of the relationship between the independent variable and dependent variable. Thus, it is important in interpreting and predicting the impact of changes in the independent variable on the dependent variable.

Question 13

If the purpose of the regression analysis is forecasting, then standardized regression estimates must be used.

Accepted Answer

Standardized regression estimates are useful when comparing the strength and direction of the relationship between variables. However, if the purpose is forecasting, unstandardized regression estimates are typically used because they provide values in their original units, allowing for easier interpretation and application to future predictions.

Question 14

One way to determine the relationship between X and Y is to simply visually draw the best-fit straight line through the points in the figure.

Accepted Answer

The best-fit straight line through the points in a scatter plot can help determine the relationship between X and Y.

Question 15

A correlation coefficient is a measure of the covariance, or association, between two at-least interval variables.

Accepted Answer

A correlation coefficient measures the strength and direction of the linear relationship between two quantitative variables. It ranges from -1 to +1, with 0 indicating no linear relationship and values closer to -1 or +1 indicating a stronger linear relationship. It is calculated using the covariance of the two variables divided by the product of their standard deviations. Therefore, it is a measure of association between two interval variables.

Question 16

The ordinary least-squares method of regression analysis is based on the logic of how much better a regression line can predict values of Y compared to simply using the standard deviation as a prediction.

Accepted Answer

The ordinary least-squares method minimizes the sum of the squared differences between observed and predicted values, not comparing to the standard deviation.

Question 17

The square of the correlation coefficient indicates the part of the total variance of dependent variable that can be accounted for by the independent variable.

Accepted Answer

This statement is true. The square of the correlation coefficient (also known as the coefficient of determination) represents the proportion of variance in the dependent variable that is explained by the independent variable, or the amount of variance that is shared by the two variables.

Question 18

The statistical significance of a correlation can be tested using the t-test.

Accepted Answer

The t-test can be used to test the statistical significance of a correlation coefficient.

Question 19

A correlation matrix is the standard form for reporting observed correlations between two variables.

Accepted Answer

A correlation matrix displays the observed correlation coefficients between multiple variables, not just two. It is the standard format for reporting the correlations between more than two variables in a single table.

Question 20

The symbol for the Pearson product-moment correlation coefficient is b.

Accepted Answer

The symbol for the Pearson product-moment correlation coefficient is typically denoted by the letter "r".

Quiz 23: Bivariate Statistical Analysis: Measures of Association