Question 1

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable?
A)Salesperson
B)Number of contacts
C)Amount of sales
D)Sales manager

Accepted Answer

The independent variable is the variable that is manipulated or changed by the researcher, and in this case, the number of contacts made by a salesperson is the independent variable. The amount of sales earned is the dependent variable, which is affected by the independent variable (number of contacts). The salesperson, amount of sales, and sales manager are not the variables that are being manipulated or changed, therefore they cannot be the independent variable.

Question 2

What is the general form of the regression equation?
A)Ŷ = ab
B)Ŷ = a+(bX)
C)Ŷ = (a+b)X
D)Ŷ = abX

Accepted Answer

The general form of the regression equation is Ŷ = a + bX, where Ŷ is the predicted value of the dependent variable, X is the independent variable, a is the intercept, and b is the slope. This is the most commonly used form of the regression equation.

Question 3

In the least squares equation, Ŷ = 10 + 20X the value of 20 indicates ____________.
A)The Y-intercept increases by 20 units for each unit increase in X
B)That Y increases by 20 units for each unit increase in X
C)That X increases by 20 units for each unit increase in Y
D)The error in prediction

Accepted Answer

The value of 20 in the least squares equation indicates that Y (predicted value) increases by 20 units for each unit increase in X (independent variable).

Question 4

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results:  What is the Y-intercept of the linear equation?
A)-12.201
B)2.195
C)-1.860
D)12.505

Accepted Answer

The answer of A sales manager for an advertising agency...

Question 5

The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the test-statistic to test the significance of the slope?
A)z = -2.560
B)z = +2.639
C)t = +2.560
D)t = +2.639

Accepted Answer

Since the sample size is less than 30, we have to use a t-distribution instead of a z-distribution. We can use the formula t = (b1 - 0)/SE(b1), where b1 is the slope coefficient and SE(b1) is the standard error of the slope.

Substituting the values, we get t = (2.56 - 0)/0.97 = 2.639.

Therefore, the test-statistic to test the significance of the slope is t = +2.639. The correct answer is D.

Question 6

Which of the following are the same between a confidence interval and a prediction interval?
A)The formulas are the same.
B)They both use the standard error of estimate.
C)They both provide a confidence interval for the mean.
D)A confidence interval and prediction interval are the same width.

Accepted Answer

Both confidence intervals and prediction intervals use the standard error of estimate. However, the other statements are not true: A) the formulas for calculating the intervals are not the same, C) prediction intervals provide an interval for individual observations, not just the mean, and D) the width of a prediction interval is typically wider than that of a confidence interval.

Question 7

The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level?
A)z = ±1.96
B)t = ±2.179
C)t = ±2.145
D)t = +2.145

Accepted Answer

To test the significance of the slope, we need to use a t-test since the sample size is less than 30. The critical value for a two-tailed t-test at the 0.05 significance level with 12 degrees of freedom (n-2) is ±2.179.

Question 8

Which of the following are true assumptions underlying linear regression? (1) For each value of X, there is a group of Y values that is normally distributed. (2) The means of these normal distributions of Y values all lie on the regression line. (3) The standard deviations of these normal distributions are equal.
A)Only (1)
B)Only (2)
C)Only (3)
D)All of them

Accepted Answer

All three assumptions are true underlying linear regression. Assumption (1) is necessary to ensure that the residuals (the difference between the predicted Y values and the actual Y values) are normally distributed. Assumption (2) is necessary to ensure that the regression line accurately represents the relationship between X and Y, and assumption (3) is necessary for the accuracy of the standard errors used in testing the significance of the regression coefficients.

Question 9

Given the least squares regression equation, Ŷ = 1,202 + 1,133X, when X = 3, what does Ŷ equal?
A)5,734
B)8,000
C)4,601
D)4,050

Accepted Answer

Substitute X=3 into the equation: Ŷ = 1,202 + 1,133X
Ŷ = 1,202 + 1,133(3)
Ŷ = 1,202 + 3,399
Ŷ = 4,601

Question 10

In the equation, Ŷ = a + bX, what is Ŷ?
A)It is the slope of the line.
B)It is the Y intercept.
C)It is the predicted value of Y, given a specific X value.
D)It is the value of Y when X = 0.

Accepted Answer

Ŷ represents the predicted value of Y, given a specific X value. It is also known as the dependent variable or the response variable. The equation is a linear regression equation, where a is the Y intercept and b is the slope of the line.

Question 11

Which of the following is true about the standard error of estimate?
A)It is a measure of the accuracy of the prediction.
B)It is based on squared vertical deviations between Y and X.
C)It can be negative.
D)It is calculated using the regression mean square.

Accepted Answer

The standard error of estimate is a measure of the accuracy of the prediction.

Question 12

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the dependent variable?
A)Salesperson
B)Number of contacts
C)Amount of sales dollars
D)Sales manager

Accepted Answer

The dependent variable is the variable that is being measured or tested in an experiment, and in this case, it is the amount of sales dollars earned. The independent variable, which is not given in the question, is the number of contacts made by the salesperson. Therefore, the best choice is C, which represents the dependent variable in the relationship between the number of contacts made and the amount of sales dollars earned.

Question 13

If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?
A)-1
B)+1
C)0
D)Infinity

Accepted Answer

If all the plots on a scatter diagram lie on a straight line, there is no variability or deviation from the line, indicating a perfect fit. Therefore, the standard error of estimate will be 0.

Question 14

The regression equation is Ŷ = 29.29 - 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the test-statistic to test the significance of the slope?
A)z = -4.364
B)z = +4.364
C)t = -4.364
D)t = -0.960

Accepted Answer

To test the significance of the slope, we need to perform a t-test. The formula for the t-test is:

t = (b - β) / (SE(b))

where b is the slope coefficient, β is the hypothesized population slope (usually 0), and SE(b) is the standard error of the slope.

In this case, b = -0.96, β = 0 (since we want to test if the slope is significantly different from 0), and SE(b) = 0.22.

Plugging in the values, we get:

t = (-0.96 - 0) / (0.22) = -4.364

Since the sample size is small (n < 30), we use a t-distribution instead of a standard normal distribution. The degrees of freedom for the t-distribution is n - 2 = 8 - 2 = 6.

Looking up the t-distribution table with 6 degrees of freedom, we find that the critical value for a two-tailed test at α = 0.05 is ±2.447.

Since our calculated t-value of -4.364 is outside the range of -2.447 to +2.447, we reject the null hypothesis that the slope is equal to 0 and conclude that the slope is significantly different from 0.

Question 15

When comparing the 95% confidence and prediction intervals for a given regression analysis ______________.
A)The confidence interval is wider than a prediction interval
B)The confidence interval is narrower than a prediction interval
C)There is no difference between confidence and prediction intervals
D)The prediction interval has a higher level of confidence

Accepted Answer

The confidence interval estimates the mean of the dependent variable for given values of the independent variables, while the prediction interval predicts the value of the dependent variable for individual observations. The prediction interval is wider because it accounts for the error in estimating the mean (as the confidence interval does) plus the variability (error) associated with individual observations.

Question 16

In regression, the difference between the confidence interval and prediction interval formulas is ________________. A)The prediction interval is the square root of the confidence interval B)The addition of "1" to the quantity under the radical sign C)The prediction interval uses r² and the confidence interval uses r D)No difference

Accepted Answer

The prediction interval accounts for the uncertainty in predicting a single response value, which includes the error in estimating the mean response (as in the confidence interval) plus the variability of the response around its mean. This is mathematically represented by adding "1" to the quantity under the radical sign in the formula, distinguishing it from the confidence interval formula.

Question 17

Assume the least squares equation is Ŷ = 10 + 20X. What does the value of 10 in the equation indicate?
A)When X = 0, Y = 10.
B)X increases by 10 for each unit increase in Y.
C)Y increases by 10, for each unit increase in X.
D)It is the error of estimation.

Accepted Answer

The value of 10 in the equation represents the intercept, which is the predicted value of Y when X equals zero. Therefore, when X = 0, Y = 10.

Question 18

What is the variable used to predict another variable called?
A)Independent variable
B)Dependent variable
C)Important variable
D)Causal variable

Accepted Answer

The independent variable is the variable used to predict another variable. It is also known as the predictor variable.

Question 19

The regression equation is Ŷ = 29.29 - 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the critical value to test the significance of the slope at the 0.01 significance level?
A)z = +2.576
B)t = +3.707
C)t = +3.355
D)t = ±3.707

Accepted Answer

Given the sample size (n = 8) and the significance level (0.01), we use a t-distribution because the population standard deviation is unknown. With n - 2 = 6 degrees of freedom, the critical value for a two-tailed test at the 0.01 significance level is ±3.707.

Question 20

Based on the regression equation, we can _______________.
A)Predict the value of the dependent variable given a value of the independent variable
B)Predict the value of the independent variable given a value of the dependent variable
C)Measure the association between two variables
D)Measure cause and effect

Accepted Answer

The regression equation is used to predict the value of the dependent variable (Y) based on the value of the independent variable (X). Therefore, choice A is the correct answer. Choice B is incorrect because the regression equation cannot predict the value of the independent variable given a value of the dependent variable; this would require a different type of analysis, such as inverse regression. Choice C is partially correct, as the regression equation does measure the association between the two variables, but this is not its primary purpose. Choice D is incorrect, as regression analysis cannot establish cause and effect relationships due to the presence of confounding variables and the possibility of reverse causation.

Quiz 13: Correlation and Linear Regression

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable?

What is the general form of the regression equation?

In the least squares equation, Ŷ = 10 + 20X the value of 20 indicates ____________.

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the Y-intercept of the linear equation?

The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the test-statistic to test the significance of the slope?

Which of the following are the same between a confidence interval and a prediction interval?

The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level?

Given the least squares regression equation, Ŷ = 1,202 + 1,133X, when X = 3, what does Ŷ equal?

In the equation, Ŷ = a + bX, what is Ŷ?

Which of the following is true about the standard error of estimate?

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the dependent variable?

If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?

The regression equation is Ŷ = 29.29 - 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the test-statistic to test the significance of the slope?

When comparing the 95% confidence and prediction intervals for a given regression analysis ______________.

In regression, the difference between the confidence interval and prediction interval formulas is ________________.

Assume the least squares equation is Ŷ = 10 + 20X. What does the value of 10 in the equation indicate?

What is the variable used to predict another variable called?

The regression equation is Ŷ = 29.29 - 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the critical value to test the significance of the slope at the 0.01 significance level?

Based on the regression equation, we can _______________.