Question 1

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 are indeed known as regression coefficients.

Question 2

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

Accepted Answer

In this scenario, the economist is using gross domestic product (GDP) to predict the unemployment rate, making GDP the independent variable because it is the predictor or the variable that is manipulated or changed to observe its effect on the dependent variable, which in this case is the unemployment rate.

Question 3

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

Accepted Answer

False

Question 4

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

Accepted Answer

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

Question 5

What is the chart called when the paired data (the dependent and independent variables)are plotted?
A)A scatter diagram
B)A bar chart
C)A pie chart
D)A histogram

Accepted Answer

A scatter diagram is used to plot paired data with the dependent variable on the y-axis and the independent variable on the x-axis. It is used to visualize the relationship between the two variables, such as whether they have a positive or negative correlation. Bar charts, pie charts, and histograms are used for different types of data, such as categorical data or frequency distributions.

Question 6

What is the range of values for a coefficient of correlation?
A)0 to +1.0
B)−3 to +3 inclusive
C)−1.0 to +1.0 inclusive
D)Unlimited range

Accepted Answer

The coefficient of correlation ranges from -1.0 to +1.0, inclusive. A correlation coefficient of +1.0 represents a perfect positive correlation, a coefficient of -1.0 represents a perfect negative correlation, and a coefficient of 0 represents no correlation. Therefore, the best choice is C because it includes the entire range of possible correlation coefficients.

Question 7

What does a coefficient of correlation of 0.70 infer?
A)There is almost no correlation because 0.70 is close to 1.0.
B)Seventy percent of the variation in one variable is explained by the other variable.
C)The coefficient of determination is 0.49.
D)The coefficient of nondetermination is 0.30.

Accepted Answer

The coefficient of determination is the square of the correlation coefficient, so 0.70 squared is 0.49.

Question 8

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 a proportion which can be expressed as a decimal between 0 and 1 or as a percentage between 0% and 100%. Therefore, the statement is true.

Question 9

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 true. The regression equation is a mathematical formula that relates the dependent variable (Y) to one or more independent variables (X) and allows us to estimate a value of Y for a given value of X.

Question 10

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 11

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. The sign only indicates the direction of the relationship (positive or negative).

Question 12

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 scatter of prediction errors. It is calculated as the standard deviation of the difference between the predicted values and the actual values. Therefore, it reflects the accuracy of prediction by indicating how much the predicted values deviate from the actual values on average. A smaller standard error of estimate means that the predicted values are generally closer to the actual values, indicating a more accurate prediction.

Question 13

In regression analysis,what is the predictor variable called?
A)Independent variable
B)Dependent variable
C)Correlation variable
D)Variable of determination

Accepted Answer

The predictor variable is also known as the independent variable in regression analysis. It is the variable that is being used to predict or explain changes in the dependent variable.

Question 14

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 15

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, is the proportion of total variation in Y that can be explained by the independent variable X. Thus, option A is correct.

Question 16

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 statement correctly describes the process of least squares regression. The goal is to minimize the sum of the squared residuals (vertical distances between the actual Y values and the predicted values of Y) in order to find the best fitting line or curve to the data.

Question 17

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

Accepted Answer

This statement is true. A scatter diagram is a graphical representation of the relationship between two variables, where one variable is plotted on the x-axis (independent variable) and the other on the y-axis (dependent variable). It provides a visual way to identify the correlation between the two variables.

Question 18

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 19

Which of the following statements regarding the coefficient of correlation is true?
A)It ranges from 0.0 to + 1.0 inclusive.
B)It describes the relationship between two variables.
C)A value of 0.00 indicates two variables are related.
D)It is calculated as the square of the slope.

Accepted Answer

The coefficient of correlation describes the strength and direction of the relationship between two variables. It ranges from -1.0 to +1.0, where a value of -1.0 indicates a perfect negative correlation, 0 indicates no correlation, and +1.0 indicates a perfect positive correlation. It is not calculated as the square of the slope, and a value of 0.00 does not indicate that two variables are related.

Question 20

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 determined for the mean value of Y for a given value of X by calculating the standard error of the mean and using it to construct a margin of error around the estimated mean. This interval provides a range of plausible values for the population mean of Y at the given value of X, based on the sample data and the level of confidence selected.

Quiz 13: Correlation and Linear Regression

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

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

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

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

What is the chart called when the paired data (the dependent and independent variables) are plotted?

What is the range of values for a coefficient of correlation?

What does a coefficient of correlation of 0.70 infer?

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

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

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

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

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

In regression analysis,what is the predictor variable called?

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

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

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.

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

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

Which of the following statements regarding the coefficient of correlation is true?

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

Quiz 13: Correlation and Linear Regression

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

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

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

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

What is the chart called when the paired data (the dependent and independent variables) are plotted?

What is the range of values for a coefficient of correlation?

What does a coefficient of correlation of 0.70 infer?

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

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

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

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

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

In regression analysis,what is the predictor variable called?

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

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

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.

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

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

Which of the following statements regarding the coefficient of correlation is true?

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

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