Question 1

The objective typically used in the tree types of equation-building procedures is to: A) find the equation with a small s_e B) find the equation with a large R² C) find the equation with a small s_e and a large R² D) find the equation with the smallest F-ratio

Accepted Answer

The goal is to find an equation that minimizes the standard error (s_e) and maximizes the coefficient of determination (R²), indicating a good fit with minimal error.

Question 2

Which of the following would be considered a definition of an outlier?
A) an extreme value for one or more variables
B) a value whose residual is abnormally large in magnitude
C) values for individual explanatory variables that fall outside the general pattern of the other observations
D) all of these choices

Accepted Answer

An outlier can be defined as an extreme value for one or more variables, a value whose residual is abnormally large in magnitude, or values for individual explanatory variables that fall outside the general pattern of the other observations. Therefore, all of the choices are correct definitions of an outlier.

Question 3

Determining which variables to include in regression analysis by estimating a series of regression equations by successively adding or deleting variables according to prescribed rules is referred to as:
A) elimination regression
B) forward regression
C) backward regression
D) stepwise regression

Accepted Answer

Stepwise regression is the process of identifying the most relevant variables by testing and examining the statistical significance of each variable and their combinations. It starts with all potential variables and then removes or adds them one by one based on their p-values and contribution to the model's prediction. This method is considered more efficient and accurate than forward or backward regression, which only add or remove variables based on their individual significance.

Question 4

Which approach can be used to test for autocorrelation?
A) regression coefficient
B) correlation coefficient
C) Durbin-Watson statistic
D) F-test or t-test

Accepted Answer

The Durbin-Watson statistic is specifically designed to test for the presence of autocorrelation in a regression model. The other options (regression coefficient, correlation coefficient, F-test or t-test) may also provide information about autocorrelation, but they are not specifically designed for this purpose.

Question 5

When the error variance is nonconstant, it is common to see the variation increases as the explanatory variable increases (you will see a "fan shape" in the scatterplot). There are two ways you can deal with this phenomenon. These are:
A) the weighted least squares and a logarithmic transformation
B) the partial F and a logarithmic transformation
C) the weighted least squares and the partial F
D) stepwise regression and the partial F

Accepted Answer

Weighted least squares is a technique used to account for heteroscedasticity (nonconstant error variance) in regression analysis. It involves assigning weights to each observation based on the magnitude of its error variance. A logarithmic transformation on the explanatory variable can also help address nonconstant error variance, as it can compress extreme values and reduce the impact of outliers. Partial F and stepwise regression have no direct relationship to dealing with nonconstant error variance.

Question 6

Suppose you forecast the values of all of the independent variables and insert them into a multiple regression equation and obtain a point prediction for the dependent variable. You could then use the standard error of the estimate to obtain an approximate:
A) confidence interval
B) prediction interval
C) hypothesis test
D) independence test

Accepted Answer

The standard error of the estimate measures the amount of variability or "noise" in the dependent variable that is not explained by the independent variables in the model. Therefore, when using the point prediction from the regression equation, we can use the standard error of the estimate to construct a prediction interval, which estimates the range within which the actual value of the dependent variable is likely to fall with a certain level of confidence. Confidence intervals are used to estimate the true value of a population parameter, such as the population mean, whereas prediction intervals are used to estimate the value of a future observation or outcome. Therefore, the best choice is B, prediction interval.

Question 7

In regression analysis, homoscedasticity refers to constant error variance.

Accepted Answer

Homoscedasticity in regression analysis means that the variance of the errors (residuals) is constant across all levels of the predictor variable.

Question 8

In regression analysis, extrapolation is performed when you:
A) attempt to predict beyond the limits of the sample
B) have to estimate some of the explanatory variable values
C) have to use a lag variable as an explanatory variable in the model
D) do not have observations for every period in the sample

Accepted Answer

Extrapolation means predicting values beyond the range of the sample data. It is a risky practice as it assumes that the relationships between variables will hold even outside the observed range.

Question 9

A point that "tilts" the regression line toward it, is referred to as a(n):
A) magnetic point
B) influential point
C) extreme point
D) explanatory point

Accepted Answer

An influential point is a point that has a large effect on the slope of the regression line. This point "tilts" the line toward it, hence making it an appropriate choice for the given question. A magnetic point is not a statistical term. An extreme point may or may not have an effect on the regression line and is a vague term. An explanatory point is also not a statistical term.

Question 10

The assumptions of regression are: 1) there is a population regression line, 2) the dependent variable is normally distributed, 3) the standard deviation of the response variable remains constant as the explanatory variables increase, and 4) the errors are probabilistically independent.

Accepted Answer

These are the four main assumptions of regression.

Question 11

If you can determine that the outlier is not really a member of the relevant population, then it is appropriate and probably best to:
A) average it
B) reduce it
C) delete it
D) leave it

Accepted Answer

If the outlier is not a member of the relevant population and is an extreme value due to error or unusual circumstances, it can significantly influence the results of the analysis. Therefore, it is appropriate to delete it from the dataset to obtain more accurate and reliable results.

Question 12

When determining whether to include or exclude a variable in regression analysis, if the p-value associated with the variable's t-value is above some accepted significance value, such as 0.05, then the variable:
A) is a candidate for inclusion
B) is a candidate for exclusion
C) is redundant
D) does not fit the guidelines of parsimony

Accepted Answer

If the p-value associated with the variable's t-value is above some accepted significance value, such as 0.05, then the variable is not statistically significant and is a candidate for exclusion from the regression model. This is because if the variable is not contributing significantly to the model, it can add noise and reduce the accuracy of the model. Therefore, option B is the correct choice.

Question 13

Multiple regression represents an improvement over simple regression because it allows any number of response variables to be included in the analysis.

Accepted Answer

Multiple regression allows for multiple predictor variables to be included in the analysis, but it still only allows for one response variable to be analyzed.

Question 14

In a simple linear regression model, testing whether the slope  of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

Accepted Answer

Yes, testing whether the slope of the population regression line could be zero is essentially testing whether there is a significant linear relationship between the response variable Y and the explanatory variable X. If the slope is zero, then there is no linear relationship between the two variables.

Question 15

Residuals separated by one period that are autocorrelated indicate:
A) simple autocorrelation
B) redundant autocorrelation
C) time 1 autocorrelation
D) lag 1 autocorrelation

Accepted Answer

Residuals separated by one period that are autocorrelated indicate lag 1 autocorrelation.

Question 16

A researcher can check whether the errors are normally distributed by using:
A) a t-test or an F-test
B) the Durbin-Watson statistic
C) a frequency distribution or the value of the regression coefficient
D) a histogram or a Q-Q plot

Accepted Answer

A histogram or Q-Q plot can visually display whether the distribution of errors is approximately normal. The other options listed do not specifically assess the normality of the errors.

Question 17

Forward regression:
A) begins with all potential explanatory variables in the equation and deletes them one at a time until further deletion would do more harm than good
B) adds and deletes variables until an optimal equation is achieved
C) begins with no explanatory variables in the equation and successively adds one at a time until no remaining variables make a significant contribution
D) randomly selects the optimal number of explanatory variables to be used

Accepted Answer

Forward regression starts with no explanatory variables in the equation and adds them one at a time until no remaining variables make a significant contribution. This approach is also known as stepwise forward regression.

Question 18

In time series data, errors are often not probabilistically independent.

Accepted Answer

In time series data, errors can exhibit autocorrelation, which means that the error in one time period may be related to the error in a previous time period. Therefore, the errors are not probabilistically independent.

Question 19

Many statistical packages have three types of equation-building procedures. They are:
A) forward, linear, and non-linear
B) forward, backward, and stepwise
C) simple, complex, and stepwise
D) inclusion, exclusion, and linear

Accepted Answer

The three types of equation-building procedures commonly used in statistical packages are forward (addition of predictors one at a time), backward (elimination of predictors one at a time), and stepwise (combination of forward and backward methods). Choice B includes all three of these methods. Therefore, B is the best choice.

Question 20

If exact multicollinearity exists, redundancy exists in the data.

Accepted Answer

Exact multicollinearity means that one or more independent variables in a regression model can be perfectly predicted by the other independent variables, which indicates redundancy in the data.

Quiz 11: Regression Analysis: Statistical Inference

The objective typically used in the tree types of equation-building procedures is to:

Which of the following would be considered a definition of an outlier?

Determining which variables to include in regression analysis by estimating a series of regression equations by successively adding or deleting variables according to prescribed rules is referred to as:

Which approach can be used to test for autocorrelation?

When the error variance is nonconstant, it is common to see the variation increases as the explanatory variable increases (you will see a "fan shape" in the scatterplot) . There are two ways you can deal with this phenomenon. These are:

Suppose you forecast the values of all of the independent variables and insert them into a multiple regression equation and obtain a point prediction for the dependent variable. You could then use the standard error of the estimate to obtain an approximate:

In regression analysis, homoscedasticity refers to constant error variance.

In regression analysis, extrapolation is performed when you:

A point that "tilts" the regression line toward it, is referred to as a(n) :

The assumptions of regression are: 1) there is a population regression line, 2) the dependent variable is normally distributed, 3) the standard deviation of the response variable remains constant as the explanatory variables increase, and 4) the errors are probabilistically independent.

If you can determine that the outlier is not really a member of the relevant population, then it is appropriate and probably best to:

When determining whether to include or exclude a variable in regression analysis, if the p-value associated with the variable's t-value is above some accepted significance value, such as 0.05, then the variable:

Multiple regression represents an improvement over simple regression because it allows any number of response variables to be included in the analysis.

In a simple linear regression model, testing whether the slope of the population regression line could be zero is the same as testing whether or not the linear relationship between the response variable Y and the explanatory variable X is significant.

Residuals separated by one period that are autocorrelated indicate:

A researcher can check whether the errors are normally distributed by using:

Forward regression:

In time series data, errors are often not probabilistically independent.

Many statistical packages have three types of equation-building procedures. They are:

If exact multicollinearity exists, redundancy exists in the data.