Question 1

We check for normality by drawing a(n) ____________________ of the residuals.

Accepted Answer

histogram

Question 2

The variance of the error variable  is required to be constant.When this requirement is satisfied, the condition is called homoscedasticity.

Accepted Answer

This statement is true. When the variance of the error variable is constant, the condition is called homoscedasticity. If the variance is not constant, the condition is called heteroscedasticity.

Question 3

When the error variable does not have constant variance, this condition is called ____________________.

Accepted Answer

heteroscedasticity

Question 4

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y, then look for a change in the spread of the plotted values.

Accepted Answer

This is a correct method to diagnose heteroscedasticity in a regression model. A change in the spread of the residuals plotted against the predicted values indicates that the variance of the errors is not constant across different levels of the independent variables.

Question 5

Error terms that are autocorrelated ____________________ (are/are not) independent.

Accepted Answer

The answer of Error terms that are autocorrelated ____________________ (are/are...

Question 6

If you take the residuals, subtract their mean and divide by their standard deviation, the result is called the ____________________ residuals.

Accepted Answer

The answer of If you take the residuals, subtract their...

Question 7

If the plot of the residuals vs.the predicted values resembles a straight line with non-zero slope, then the regression line fits well.

Accepted Answer

If the plot of residuals vs. predicted values resembles a straight line with non-zero slope, it indicates the presence of a pattern or structure in the data that the regression line is not capturing. This means that the regression line does not fit well and may not be a good model for the data. A random scatter of points around the horizontal line at zero is what we are looking for in a good regression model.

Question 8

If the plot of the residuals is fan shaped, which assumption of regression analysis (if any) is violated?
A) No assumptions are violated.
B) Independence of errors
C) Homoscedasticity
D) Normality

Accepted Answer

A fan-shaped plot of residuals indicates that the variance of the errors is not constant across all levels of the predictor variable, violating the assumption of homoscedasticity.

Question 9

The plot of residuals vs.predicted values should show no patterns if the conditions of a regression analysis are met.

Accepted Answer

If the conditions of a regression analysis are met, the residuals should be randomly scattered around the horizontal line of zero in the plot of residuals vs. predicted values, with no discernible patterns such as curvature or funnel shape. If patterns are observed, it may indicate a violation of assumptions, such as nonlinearity, heteroscedasticity, or outliers.

Question 10

When the variance  of the error variable  is a constant no matter what the value of x is, this condition is called:
A) heterocausality.
B) homoscedasticity.
C) homocausality.
D) heteroscedasticity.

Accepted Answer

When the variance of the error term is constant across all values of x, it is known as homoscedasticity. Therefore, option B is the correct answer. The other options are incorrect as they do not describe this condition.

Question 11

We check for normality by drawing a pie chart of the residuals.

Accepted Answer

A pie chart is not an appropriate way to check for normality. Normality can be checked using a histogram or a Q-Q plot of the residuals.

Question 12

The variance of the error variable  is required to be constant.When this requirement is violated, the condition is called heteroscedasticity.

Accepted Answer

Heteroscedasticity refers to a violation of the constant variance assumption in the error term. When the variance of the error term is not constant, it leads to heteroscedasticity.

Question 13

An outlier is an observation that is unusually small or unusually large.

Accepted Answer

An outlier is indeed an observation that is unusually small or unusually large compared to other observations in the same dataset.

Question 14

The least squares method requires that the variance  of the error  is a constant no matter what the value of x is.When this requirement is violated, the condition is called:
A) heteroscedasticity.
B) homoscedasticity.
C) influential observation.
D) non-independence of .

Accepted Answer

When the variance of the error variable is not constant, it is called heteroscedasticity. This violates the assumption of the least squares method and can lead to biased estimates and incorrect inferences. Homoscedasticity, on the other hand, means that the variance of the error variable is constant, which is the required assumption for the least squares method to work properly. Influential observation and non-independence of the error variable are different issues that may affect the results of the least squares method, but they are not directly related to the assumption of homoscedasticity.

Question 15

We standardize residuals by subtracting their mean and dividing by their variance.

Accepted Answer

We standardize residuals by subtracting their mean (which is usually zero in regression models) and dividing by their standard deviation, not their variance.

Question 16

Data that exhibit an autocorrelation effect violate the regression assumption of independence.

Accepted Answer

Autocorrelation refers to the correlation between a variable and its previous values. When autocorrelation is present, it violates the assumption of independence, which assumes that the residuals or errors of a regression model are independent of each other. Autocorrelation in the residuals indicates that there is information in the data that has not been captured by the model, and can lead to biased and inefficient estimates of the regression coefficients.

Question 17

If the variance of the errors is constant for each predicted y value, the condition is called ____________________.

Accepted Answer

The answer of If the variance of the errors is...

Question 18

The spread in the residuals should increase as the predicted value of y increases.

Accepted Answer

The spread in the residuals should be approximately constant across all levels of the predicted value of y for the assumptions of homoscedasticity to be met in a linear regression model.

Question 19

The standardized residual is defined as:
A) residual multiplied by the square root of the standard error of estimate.
B) residual multiplied by the standard error of estimate.
C) residual divided by the square of the standard error of estimate.
D) residual divided by the standard error of estimate.

Accepted Answer

The standardized residual is defined as the residual divided by the standard error of estimate. This calculation standardizes the residual by taking into account the variability in the dependent variable around the regression line. It allows for easy comparison of outliers or influential points in the data by comparing their standardized residuals to a threshold value, typically ±2 or ±3.

Question 20

Error terms that are correlated over time are said to be ____________________.

Accepted Answer

The answer of Error terms that are correlated over time...

Quiz 16: Simple Linear Regression and Correlation