Question 1

If r = -1,then we can conclude that there is a perfect relationship between X and Y.

Accepted Answer

This relationship is an inverse relationship.

Question 2

The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).

Accepted Answer

The slope of the simple linear regression equation represents the change in the value of the dependent variable that is predicted to occur for every unit change in the independent variable. Therefore, the correct answer is A.

Question 3

A significant positive correlation between X and Y implies that changes in X cause Y to change.

Accepted Answer

Correlation does not assume or imply causation.

Question 4

The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.

Accepted Answer

The error term is the difference between the observed and predicted values of the dependent variable.

Question 5

The least squares simple linear regression line minimizes the sum of the vertical deviations between the line and the data points.

Accepted Answer

The least squares simple linear regression line minimizes the sum of the squared deviations.

Question 6

The notation Ŷ refers to the average value of the dependent variable Y.

Accepted Answer

This notation refers to the estimated or predicted value of the dependent variable.

Question 7

In simple linear regression analysis,if the error terms exhibit a positive or negative autocorrelation over time,then the assumption of constant variance is violated.

Accepted Answer

When error terms exhibit a positive or negative autocorrelation over time, the assumption of independence is violated.

Question 8

In simple regression analysis,r² is a percentage measure and measures the proportion of the variation explained by the simple linear regression model.

Accepted Answer

The coefficient of determination, r-squared (r²) is indeed a percentage measure that represents the proportion of total variation in the dependent variable that can be explained by the independent variable(s) in the simple linear regression model.

Question 9

When using simple regression analysis,if there is a strong correlation between the independent and dependent variables,then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.

Accepted Answer

Correlation does not assume or predict causation or direction.

Question 10

In simple linear regression analysis,we assume that the variance of the independent variable (X)is equal to the variance of the dependent variable (Y).

Accepted Answer

In simple linear regression analysis, we do not assume that the variance of the independent variable (X) is equal to the variance of the dependent variable (Y). We only assume that the errors or residuals have constant variance, which is known as homoscedasticity.

Question 11

The standard error of the estimate (standard error)is the estimated standard deviation of the distribution of the independent variable (X)for all values of the dependent variable (Y).

Accepted Answer

The standard error of the estimate (standard error) is actually the estimated standard deviation of the residuals (actual Y - predicted Y) for all values of X. It is used to determine how well the regression line fits the data points.

Question 12

The dependent variable is the variable that is being described,predicted,or controlled.

Accepted Answer

The dependent variable is the variable that is being affected and measured in an experiment, and is therefore being described, predicted, or controlled.

Question 13

When there is positive autocorrelation,over time,negative error terms are followed by positive error terms and positive error terms are followed by negative error terms.

Accepted Answer

Positive autocorrelation implies positive error terms followed by positive error terms and negative error terms followed by negative error terms.

Question 14

In a simple linear regression model,the coefficient of determination not only indicates the strength of the relationship between the independent and dependent variables,but also shows whether the relationship is positive or negative.

Accepted Answer

The coefficient of determination is r² and therefore can only take a positive value.

Question 15

The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line.

Accepted Answer

This statement is true. The estimated simple linear regression equation is chosen in such a way that it minimizes the sum of the squared deviations between the predicted values of Y and the actual values of Y. This is also known as the method of least squares.

Question 16

The simple coefficient of determination is the proportion of total variation explained by the regression line.

Accepted Answer

The coefficient of determination, also known as R-squared, is the proportion of total variation in the dependent variable that can be explained by the independent variable(s) in the regression equation. Therefore, the statement is true.

Question 17

A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.

Accepted Answer

This is a true statement. A simple linear regression model is a type of statistical model that uses a linear function to describe the relationship between a dependent variable and one independent variable. The equation for a simple linear regression model is typically written as y = a + bx, where y is the dependent variable, x is the independent variable, b is the slope of the line, and a is the y-intercept.

Question 18

The correlation coefficient is the ratio of explained variation to total variation.

Accepted Answer

The correlation coefficient measures the strength and direction of the linear relationship between two variables, and it ranges between -1 and 1. It is not a ratio of explained variation to total variation, although it can be interpreted as the proportion of variability in one variable that is accounted for by the other variable.

Question 19

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

Accepted Answer

This is the definition of residual in regression analysis.

Question 20

The experimental region is the range of the previously observed values of the dependent variable.

Accepted Answer

The experimental region is the range of values of the independent variable that will be tested in an experiment. The range of previously observed values of the dependent variable is called the range or distribution, but it is not specifically referred to as the experimental region.

Quiz 14: Simple Linear Regression Analysis