Question 1

In regression analysis, which of the following is not a required assumption about the error term $\varepsilon$?
A)The expected value of the error term is one.
B)The variance of the error term is the same for all values of X.
C)The values of the error term are independent.
D)The error term is normally distributed.

Accepted Answer

The expected value of the error term is not a required assumption in regression analysis. The other three choices (B, C, and D) are all required assumptions.

Question 2

In regression analysis, the model in the form  is called
A)regression equation
B)correlation equation
C)estimated regression equation
D)regression model

Accepted Answer

D

Question 3

The value of the coefficient of correlation (R) A)can be equal to the value of the coefficient of determination (R²) B)can never be equal to the value of the coefficient of determination (R²) C)is always smaller than the value of the coefficient of determination D)is always larger than the value of the coefficient of determination

Accepted Answer

The coefficient of determination (R-squared) is the square of the coefficient of correlation (R), which means that R-squared can never be smaller than R. In some cases, R-squared can be equal to R. Therefore, the value of the coefficient of correlation (R) can be equal to the value of the coefficient of determination (R-squared).

Question 4

The interval estimate of the mean value of y for a given value of x is
A)prediction interval estimate
B)confidence interval estimate
C)average regression
D)x versus y correlation interval

Accepted Answer

A confidence interval estimate is used to estimate the true population mean with a certain level of confidence. It is commonly used in regression analysis to estimate the mean value of y for a given value of x. A prediction interval estimate is used to predict the value of an individual observation, which is different from estimating the mean value. "Average regression" is not a commonly used term in statistical analysis. "X versus y correlation interval" is not a valid term in statistics.

Question 5

Regression analysis is a statistical procedure for developing a mathematical equation that describes how
A)one independent and one or more dependent variables are related
B)several independent and several dependent variables are related
C)one dependent and one or more independent variables are related
D)None of these alternatives is correct.

Accepted Answer

Regression analysis is used to model the relationship between a dependent variable and one or more independent variables. Therefore, choice C is the correct answer as it states that regression analysis is used to describe how one dependent and one or more independent variables are related.

Question 6

If the coefficient of determination is a positive value, then the coefficient of correlation
A)must also be positive
B)must be zero
C)can be either negative or positive
D)must be larger than 1

Accepted Answer

The answer of If the coefficient of determination is a...

Question 7

In the following estimated regression equation A)b₁ is the slope B)b₁ is the intercept C)b₀ is the slope D)None of these alternatives is correct.

Accepted Answer

The answer of In the following estimated regression equation A)b₁...

Question 8

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = $\beta$₀ + $\beta$₁x, is known as A)regression equation B)correlation equation C)estimated regression equation D)regression model

Accepted Answer

The answer of The mathematical equation relating the independent variable...

Question 9

In a regression analysis, the error term $\varepsilon$ is a random variable with a mean or expected value of
A)zero
B)one
C)any positive value
D)any value

Accepted Answer

The error term is the difference between the observed value and the predicted value of the dependent variable. It represents the part of the dependent variable that is not explained by the independent variable(s) included in the regression model. As a random variable, it can take on any value, positive or negative, but on average, it is expected to be zero since the regression line is designed to minimize the sum of squared errors. Therefore, the best choice for the mean or expected value of the error term is A) zero.

Question 10

In regression analysis, the unbiased estimate of the variance is
A)coefficient of correlation
B)coefficient of determination
C)mean square error
D)slope of the regression equation

Accepted Answer

The unbiased estimate of the variance in regression analysis is the mean square error, which is calculated by dividing the sum of squared errors by the degrees of freedom. It is an unbiased estimate because it takes into account the sample size and the number of variables in the model, and it provides a measure of how well the regression equation fits the data. The coefficient of correlation and determination and the slope of the regression equation are all measures of the strength and direction of the relationship between the variables, but do not provide an estimate of the variance.

Question 11

If only MSE is known, you can compute the
A)r square
B)coefficient of determination
C)standard error
D)all of these alternatives are correct

Accepted Answer

The answer of If only MSE is known, you can...

Question 12

The standard error is the
A)t-statistic squared
B)square root of SSE
C)square root of SST
D)square root of MSE

Accepted Answer

The standard error is defined as the standard deviation of the sampling distribution of a statistic, and for the purposes of linear regression analysis, it is the square root of the mean squared error (MSE).

Question 13

In regression analysis, the variable that is being predicted is the
A)dependent variable
B)independent variable
C)intervening variable
D)is usually x

Accepted Answer

The dependent variable is the variable that is being predicted in regression analysis. The independent variable(s) are used to predict the values of the dependent variable. Intervening variables are variables that come between the independent and dependent variables and affect the relationship between them. "Usually x" is not a correct answer as it implies that the independent variable is always x, which is not true.

Question 14

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called
A)the correlation model
B)the regression model
C)correlation analysis
D)None of these alternatives is correct.

Accepted Answer

The equation that relates the dependent variable (y) to the independent variable (x) is called the regression model. Correlation analysis simply measures the relationship between two variables, but does not provide an equation. The correlation model is not a commonly used term.

Question 15

The coefficient of determination
A)cannot be negative
B)is the square root of the coefficient of correlation
C)is the same as the coefficient of correlation
D)can be negative or positive

Accepted Answer

The coefficient of determination, often denoted as R^2, represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is a measure of the goodness of fit of a model and ranges from 0 to 1, meaning it cannot be negative.

Question 16

In a simple regression analysis (where Y is a dependent and X an independent variable), if the Y intercept is positive, then
A)there is a positive correlation between X and Y
B)if X is increased, Y must also increase
C)if Y is increased, X must also increase
D)None of these alternatives is correct.

Accepted Answer

The Y intercept being positive only indicates the value of Y when X is zero. It does not provide any information about the correlation or causal relationship between X and Y, or the direction of change when one variable is increased or decreased.

Question 17

The model developed from sample data that has the form of  is known as
A)regression equation
B)correlation equation
C)estimated regression equation
D)regression model

Accepted Answer

The form of the model provided includes both the sample data and the estimated regression equation. Therefore, the correct answer is C, the estimated regression equation.

Question 18

The interval estimate of an individual value of y for a given value of x is
A)prediction interval estimate
B)confidence interval estimate
C)average regression
D)x versus y correlation interval

Accepted Answer

The prediction interval estimate provides an interval within which a future observation of y for a given value of x is expected to fall. This involves taking into account both the variability of the data points around the regression line as well as the uncertainty in estimating the true regression line. The other options (B, C, D) are not appropriate for estimating an individual value of y for a given x. Confidence interval estimates provide a range of plausible values for a population parameter, such as the slope or intercept of the regression line. Average regression is not a statistical term, and x versus y correlation does not involve interval estimation.

Question 19

A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation  = 30,000 + 4 X
The above equation implies that an
A)increase of $4 in advertising is associated with an increase of $4,000 in sales
B)increase of $1 in advertising is associated with an increase of $4 in sales
C)increase of $1 in advertising is associated with an increase of $34,000 in sales
D)increase of $1 in advertising is associated with an increase of $4,000 in sales

Accepted Answer

The coefficient of X in the equation is 4, which means that for every $1 increase in advertising, there is an increase in sales of $4,000 (not $4 or $34,000). Therefore, the correct choice is (D).

Question 20

In a regression analysis the standard error is determined to be 4. In this situation the MSE
A)is 2
B)is 16
C)depends on the sample size
D)depends on the degrees of freedom

Accepted Answer

The mean squared error (MSE) is equal to the sum of squared residuals divided by the degrees of freedom. The standard error is the square root of the MSE multiplied by the square root of the number of observations (which is assumed to be large enough to approximate the standard error as the population standard deviation). Therefore, MSE = (standard error)^2 / n. Plugging in the given values, MSE = (4)^2 / n. There is no information provided about the sample size or degrees of freedom, so we cannot determine those values. However, we can calculate the MSE using the formula and the provided standard error, which gives us MSE = 16/n. Therefore, the best choice is B.

Quiz 12: Simple Linear Regression

In regression analysis, which of the following is not a required assumption about the error term $\varepsilon$ ?

In regression analysis, the model in the form is called

The value of the coefficient of correlation (R)

The interval estimate of the mean value of y for a given value of x is

Regression analysis is a statistical procedure for developing a mathematical equation that describes how

If the coefficient of determination is a positive value, then the coefficient of correlation

In the following estimated regression equation

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = $\beta$ ₀ + $\beta$ ₁x, is known as

In a regression analysis, the error term $\varepsilon$ is a random variable with a mean or expected value of

In regression analysis, the unbiased estimate of the variance is

If only MSE is known, you can compute the

The standard error is the

In regression analysis, the variable that is being predicted is the

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

The coefficient of determination

In a simple regression analysis (where Y is a dependent and X an independent variable) , if the Y intercept is positive, then

The model developed from sample data that has the form of is known as

The interval estimate of an individual value of y for a given value of x is

A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation = 30,000 + 4 X The above equation implies that an

In a regression analysis the standard error is determined to be 4. In this situation the MSE