Question 1

The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X.

Accepted Answer

This is a correct statement about the purpose of regression analysis.

Question 2

In plotting paired data in a scatter diagram, the dependent variable is scaled on the __________________.

Accepted Answer

Y or vertical axis

Question 3

The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

Accepted Answer

The strength of the correlation between two variables depends on the absolute value of the coefficient of correlation, not the sign. A positive sign indicates a positive correlation (as one variable increases, so does the other) while a negative sign indicates a negative correlation (as one variable increases, the other decreases), but the strength is determined by the magnitude of the coefficient, which ranges from -1 to 1.

Question 4

The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.

Accepted Answer

This is the definition of the least squares technique.

Question 5

Because the coefficient of determination is expressed as a percent, its value is between 0% and 100%.

Accepted Answer

The coefficient of determination, also known as R-squared, is expressed as a percentage between 0% and 100%.

Question 6

If there is absolutely no relationship between two variables, Pearson's r will equal _____.

Accepted Answer

The answer of If there is absolutely no relationship between...

Question 7

If the coefficient of determination is 0.81, the coefficient of correlation is _____.

Accepted Answer

The answer of If the coefficient of determination is 0.81,...

Question 8

The hypothesis to test the slope of a regression equation is H₀: α = 0.

Accepted Answer

The correct hypothesis to test the slope of a regression equation is usually stated as H0: β = 0, where β represents the slope.

Question 9

The values of a and b in the regression equation are called the regression coefficients.

Accepted Answer

The coefficients in a regression equation are the values of the intercept (b) and the slope (a).

Question 10

A confidence interval can be determined for the mean value of Y for a given value of X.

Accepted Answer

A confidence interval can be calculated for the mean value of Y for a given value of X using regression analysis. This interval is based on the sample mean and standard error of the estimate, and provides a range of likely values for the population mean at a given level of confidence.

Question 11

The coefficient of determination is the square root of the coefficient of correlation.

Accepted Answer

The coefficient of determination is actually equal to the coefficient of correlation squared, not the square root of the coefficient of correlation.

Question 12

If the coefficient of correlation is 0.80, the coefficient of determination is _____.

Accepted Answer

The answer of If the coefficient of correlation is 0.80,...

Question 13

The standard error of estimate measures the accuracy of a prediction.

Accepted Answer

The standard error of estimate is a measure of the variability or dispersion of the observed values around the predicted values in a regression analysis. It can be used to assess the accuracy of predictions made by the regression model. Therefore, statement A is true.

Question 14

An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product.

Accepted Answer

In this context, the independent variable is the gross domestic product (GDP) because it is used to predict the dependent variable, which is the unemployment rate.

Question 15

In regression analysis, error is defined as  .

Accepted Answer

The answer of In regression analysis, error is defined as...

Question 16

A scatter diagram is a graph that portrays the correlation between a dependent variable and an independent variable.

Accepted Answer

A scatter diagram is a graph that shows the relationship between two variables, with one variable typically considered the dependent variable and the other variable considered the independent variable. The scatter plot can be used to determine if there is a correlation between the two variables, and if so, what type of correlation exists (positive, negative, or no correlation).

Question 17

One assumption underlying linear regression is that the X values are normally distributed.

Accepted Answer

The assumption underlying linear regression is that the error or residual terms are normally distributed and not the X values. The X values can have any distribution.

Question 18

If the coefficient of correlation is -0.81, the coefficient of determination is ______.

Accepted Answer

The answer of If the coefficient of correlation is -0.81,...

Question 19

The coefficient of determination is the proportion of total variation in Y that is explained by X.

Accepted Answer

The coefficient of determination, also known as R-squared, measures the proportion of total variation in the dependent variable (Y) that is explained by the independent variable(s) (X). It ranges between 0 and 1, where 0 means none of the variation is explained by X and 1 means all of the variation is explained by X. Therefore, the statement is true.

Question 20

Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables.

Accepted Answer

Correlation analysis is used to measure the strength and direction of the relationship between two variables.

Quiz 13: Correlation and Linear Regression