Question 1

The standard error of the estimate is the
A) standard deviation of t.
B) square root of SSE.
C) square root of SST.
D) square root of MSE.

Accepted Answer

The standard error of the estimate is calculated as the square root of the mean squared error (MSE). Therefore, the correct choice is D, which is "square root of MSE."  Choices A and B are incorrect because they refer to the standard deviation of t and the square root of SSE, respectively, which are not used to calculate the standard error of the estimate. Choice C is incorrect because it refers to the square root of SST, which represents the total variation in the dependent variable and is not directly used to calculate the standard error of the estimate.

Question 2

In the following estimated regression equation = b₀ + b₁x, A) b₁ is the slope. B) b₁ is the intercept. C) b₁x is the slope. D) b₁x is the intercept.

Accepted Answer

A

Question 3

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

Accepted Answer

The MSE (mean squared error) is equal to the SSE (sum of squared errors) divided by the degrees of freedom. The standard error of the estimate is equal to the square root of the MSE. Therefore, MSE = (standard error of the estimate)^2 = 4^2 = 16. It does not depend on the sample size and does not require knowledge of SSE.

Question 4

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 (r²). D) is always larger than the value of the coefficient of determination (r²).

Accepted Answer

The coefficient of correlation (r) is the square root of the coefficient of determination (r^2), so it can definitely be equal to the value of the coefficient of determination (r^2 = r²).

Question 5

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

Accepted Answer

Prediction interval estimate is used to estimate the range within which a single observation is expected to fall. This type of interval estimate provides an estimate of the uncertainty around a single future observation.

Question 6

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 7

The model developed from sample data that has the form of = b₀ + b₁x is known as the A) regression equation. B) correlation model. C) estimated regression equation. D) regression model.

Accepted Answer

The model developed from the sample data is known as the estimated regression equation because it is created from the calculated estimates of the population parameters. It is not the true regression equation since it is based on sample data and is likely to have some degree of error.

Question 8

In regression analysis, the model in the form y =  +  x + ε is called the
A) regression equation.
B) correlation model.
C) estimated regression equation.
D) regression model

Accepted Answer

The answer of In regression analysis, the model in the...

Question 9

The coefficient of correlation
A) is the square of the r-square.
B) is the square root of the r-square.
C) can never be equal to r-square.
D) can never be negative.

Accepted Answer

The coefficient of correlation (r) is the square root of the r-square (R²). Therefore, option B is correct. Option A is incorrect because the r-square is the square of the correlation coefficient, not the other way around. Option C is incorrect because in some cases, the coefficient of correlation can be equal to the r-square. Option D is incorrect because the coefficient of correlation can be negative, indicating a negative correlation between variables.

Question 10

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

Accepted Answer

The interval estimate of the mean value of y for a given value of x is called the confidence interval estimate. The prediction interval estimate is used to estimate individual values of y, not the mean value. The other options (average regression interval and x versus y correlation interval) are not well-defined statistical terms.

Question 11

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: ​  = 30,000 + 5x
​
The above equation implies that an
A) increase of $4 in advertising is associated with an increase of $5000 in sales.
B) increase of $1 in advertising is associated with an increase of $5 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 $5000 in sales.

Accepted Answer

The coefficient of advertising (x) is 5 which means that for every increase in advertising by $1, there is an increase in sales by $5, as stated in option D. Option A is incorrect as it assumes a non-existent coefficient of 5000/4. Option B is partly correct as its coefficient of 5 matches with the given equation but it assumes an increase of $1 in advertising instead of $4. Option C is incorrect as it wrongly assumes a coefficient of 34,000 instead of 5.

Question 12

In regression analysis, which of the following assumptions is not true about the error term ε?
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 assumed to be zero, not one. The other assumptions listed (B, C, and D) are all true assumptions about the error term in regression analysis.

Question 13

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the​
A) ​correlation coefficient.
B) ​standard error of the estimate.
C) ​coefficient of determination.
D) ​confidence interval estimate.

Accepted Answer

The coefficient of determination (also known as R-squared) measures the proportion of variation in the y variable that is explained by the estimated regression equation. It ranges from 0 to 1, with higher values indicating a better fit of the equation to the data. The correlation coefficient (A) measures the strength and direction of the linear relationship between two variables, but does not account for the variation in y explained by the regression equation. The standard error of the estimate (B) measures the average deviation between the predicted y values and the actual y values, but does not directly measure the proportion of variation in y explained by the equation. The confidence interval estimate (D) provides a range of plausible values for the true population regression coefficient, but again does not directly measure the proportion of variation in y explained by the equation.

Question 14

In regression analysis, the error term ε is a random variable with a mean or expected value of
A) 0.
B) 1.
C) μ.
D)  .

Accepted Answer

The error term ε represents the difference between the actual dependent variable value and the predicted value by the regression equation. Since the regression equation is trying to fit the best line or curve to the data points, the error term should ideally have a mean or expected value of 0. This means that on average, the predicted value should be equal to the actual value. In other words, the errors should cancel each other out over many observations. Therefore, choice A, which states that the mean of the error term is 0, is the best choice.

Question 15

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) one dependent, one independent, and several error variables are related.

Accepted Answer

Regression analysis is a statistical procedure used to develop a mathematical equation that describes how one dependent variable is related to one or more independent variables. The goal of regression analysis is to find the best fit line or curve that predicts the relationship between the dependent and independent variables. Therefore, option C, which states that one dependent and one or more independent variables are related, is the correct choice.

Question 16

If only MSE is known, you can compute the
A) r-square.
B) coefficient of correlation.
C) standard error.
D) ith residual.

Accepted Answer

The standard error can be computed using only the MSE, as it is the square root of the MSE divided by the sample size. The coefficient of correlation and r-square both require information on both the dependent and independent variables, while the ith residual requires information on the specific data point in question.

Question 17

In simple linear regression, r² is the A) mean square error. B) correlation coefficient. C) squared residual. D) coefficient of determination.

Accepted Answer

The coefficient of determination, denoted as r², measures the proportion of the variance in the dependent variable that is predictable from the independent variable in a regression model.

Question 18

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β₀ + β₁x, is known as the A) regression equation. B) correlation model. C) estimated regression equation. D) regression model.

Accepted Answer

The equation E(y) = β₀ + β₁x is the regression equation, which represents the relationship between the independent variable x and the expected value of the dependent variable y.

Question 19

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 positive or negative.
D) can be larger than 1.

Accepted Answer

The coefficient of determination (R^2) indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s), but it does not indicate the direction of the relationship. The coefficient of correlation (r) indicates both the strength and the direction of the linear relationship between two variables. Since R^2 is the square of r, if R^2 is positive, r can be either positive or negative, reflecting either a direct or inverse relationship, respectively.

Question 20

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 mean square error is the unbiased estimate of the variance in regression analysis.

Quiz 14: Simple Linear Regression

The standard error of the estimate is the

In the following estimated regression equation = b₀ + b₁x,

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

The value of the coefficient of correlation (r)

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

The coefficient of determination

The model developed from sample data that has the form of = b₀ + b₁x is known as the

In regression analysis, the model in the form y = + x + ε is called the

The coefficient of correlation

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

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: = 30,000 + 5x The above equation implies that an

In regression analysis, which of the following assumptions is not true about the error term ε?

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the

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

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

If only MSE is known, you can compute the

In simple linear regression, r² is the

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β₀ + β₁x, is known as the

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

In regression analysis, the unbiased estimate of the variance is