Question 1

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

Accepted Answer

The coefficient of determination is not the square root of the coefficient of correlation, but the square of it.

Question 2

If 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 always between 0 and 1. However, it is often expressed as a percentage by multiplying the value by 100, making its range 0% to 100%.

Question 3

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

Accepted Answer

Y or vertical axis

Question 4

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 magnitude (absolute value) of the coefficient of correlation, not on the sign. The sign indicates the direction of the relationship (positive or negative), but not the strength.

Question 5

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

The regression equation is a mathematical formula used to estimate or predict the value of the dependent variable Y based on a selected value of the independent variable X. It is also known as a prediction equation or a forecasting model. Therefore, statement A is true.

Question 6

One assumption underlying linear regression is that the Y values are statistically dependent. This means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X value.

Accepted Answer

Linear regression assumes that the Y values are statistically independent, meaning the Y values for one X value do not depend on the Y values for any other X value.

Question 7

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

Accepted Answer

The hypothesis to test the slope of a regression equation is H0: β = 0, where β represents the slope, not α.

Question 8

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

Accepted Answer

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

Question 9

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 variance in the dependent variable (Y) that can be explained by the independent variable(s) (X). Therefore, option A is true.

Question 10

If the coefficient of determination is 0.81, what is the coefficient of correlation? ______

Accepted Answer

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

Question 11

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

The answer of An economist is interested in predicting the...

Question 12

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

Accepted Answer

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

Question 13

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 how two variables relate to each other. The independent variable is plotted on the x-axis and the dependent variable is plotted on the y-axis. The pattern of points on the graph can reveal the nature of the correlation between the two variables, such as whether it is positive or negative, strong or weak.

Question 14

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 specific value of X using a regression model. This can help provide a range of values within which the true mean value of Y is likely to fall for that particular value of X.

Question 15

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 least squares.

Question 16

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

Accepted Answer

The values of a and b in the regression equation (y = a + bx) are indeed called the regression coefficients.

Question 17

In regression analysis, error is defined as (  - Y).

Accepted Answer

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

Question 18

If the coefficient of correlation is 0.80, what is the coefficient of determination? ______

Accepted Answer

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

Question 19

How do we designate the population correlation coefficient? _____

Accepted Answer

The answer of How do we designate the population correlation...

Question 20

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

Accepted Answer

The standard error of estimate measures the variability or spread of the actual data points around the predicted values. It gives an indication of how close the predicted values are to the actual values and therefore measures the accuracy of a prediction.

Quiz 13: Correlation and Linear Regression