Question 1

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

Accepted Answer

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

Question 2

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

The model assumptions of a simple linear regression are independence of the error terms and constant variation of the error terms.

Question 3

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 4

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

Accepted Answer

Experimental region is the range of values of the independent variable.

Question 5

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

Accepted Answer

Also known as the response variable.

Question 6

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

It is a measure of the potential usefulness of a simple linear regression model.

Question 7

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 8

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 9

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

Standard error is the standard deviation of the population of the error terms.

Question 10

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

Accepted Answer

The independent variable on the x-axis while the dependent variable is on the y-axis.

Question 11

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 12

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

Accepted Answer

It is a measure of the potential usefulness of a simple linear regression model.

Question 13

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 is the change - the amount of increase or decrease.

Question 14

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 15

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 16

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 17

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 18

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

Accepted Answer

The residual is how far the observed y value you saw is from the predicted y value on the graph.

Question 19

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 20

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

Accepted Answer

That is why it is called the least squares model.

Quiz 14: Simple Linear Regression Analysis