Question 1

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 lie on a straight line, it means that there is no variation or error in the data. Therefore, the standard error of estimate is 0.

Question 2

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 allows us to predict the value of the dependent variable (the variable we are trying to explain) based on the value of the independent variable (the variable we are using to explain it). Therefore, option A is the best choice. Option B is not possible as the regression equation does not predict the value of the independent variable. Option C may be partially correct as regression measures the strength of association between two variables, but it does not quantify this association in the same way as a correlation coefficient. Option D is not possible as regression does not determine causation, but rather examines the relationship between variables.

Question 3

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 is the predicted value of Y, given a specific X value. It represents the value of the dependent variable (Y) that is estimated based on the value of the independent variable (X) and the coefficients (a and b) of the equation.

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

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 estimates the range for individual observations. Prediction intervals are wider because they account for both the uncertainty in estimating the mean and the variability of individual observations around the mean.

Question 6

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 Ŷ = 10 +20X indicates that Y increases by 20 units for each unit increase in X. This is the slope or coefficient of X in the equation.

Question 7

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. (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. These assumptions are necessary for the linear regression model to be valid and for accurate interpretation of the results.

Question 8

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 in the given least squares regression equation:

Ŷ = 1,202 + 1,133(3)

Ŷ = 1,202 + 3,399

Ŷ = 4,601

Therefore, when X = 3, Ŷ equals 4,601. Option C is the correct choice.

Question 9

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 should use a t-test to test the significance of the slope. The formula for the t-test is t = (b - 0) / SE(b), where b is the estimate of the slope, SE(b) is the standard error of the slope, and 0 is the null hypothesis value of the slope. Substituting the given values, we get t = (2.56 - 0) / 0.97 = 2.639. Therefore, the test-statistic is t = +2.639.

Question 10

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 a confidence interval and a prediction interval use the standard error of estimate to calculate the bounds of the interval. However, they differ in their interpretations - a confidence interval provides a range of values in which the true population mean is likely to fall, while a prediction interval provides a range of values in which individual future observations are likely to fall. The formulas used and the width of the intervals may also differ between the two.

Question 11

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 variable used to predict another variable is called the independent variable. The dependent variable is the outcome variable that is being predicted or measured. The important variable may refer to any variable that is relevant to the research question but may not necessarily be the predictor variable. The causal variable refers to a variable that has a causal effect on another variable, which may or may not be the predictor variable.

Question 12

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, while the confidence interval estimates the uncertainty around the mean response for given x-values. The key difference in their formulas is the addition of 1 to the quantity under the radical sign in the prediction interval formula, reflecting the extra variability associated with predicting a single response rather than the mean response.

Question 13

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 and affected by the independent variable. In this case, the amount of sales dollars earned is the dependent variable as it is the variable that is being affected by the number of contacts made by the salesperson, which is the independent variable. Therefore, the best choice is C.

Question 14

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). This includes both an intercept (a) and a slope (b) term, allowing for a more accurate prediction of Y based on X. Options A, C, and D do not include an intercept term or include the slope term in a different location.

Question 15

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 being manipulated and is expected to cause a change in the dependent variable. In this case, the number of contacts made by the salesperson is the independent variable because it is being manipulated by the salesperson and is expected to cause a change in the dependent variable (amount of sales earned). The other options, such as the salesperson, sales manager, and amount of sales, are not being manipulated in this scenario and therefore cannot be independent variables.

Question 16

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

Since the sample size is less than 30, we use a t-test instead of a z-test. The test-statistic is calculated as: 
t = (slope - null hypothesis value of slope) / standard error of the slope
Here, the null hypothesis is that the slope is 0 (i.e. no linear relationship between X and Y). 
Substituting the given values, we get: 
t = (-0.96 - 0) / 0.22 = -4.364
Therefore, the test-statistic is -4.364, which corresponds to choice C.

Question 17

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

Since the sample size is less than 30, we need to use a t-distribution to test the significance of the slope. At the 0.05 significance level with 12 degrees of freedom (14-2), the critical value is ±2.179, which is the closest option to 2.145. Therefore, the answer is B.

Question 18

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

The critical value for a two-tailed t-test with 6 degrees of freedom (n-2) at the 0.01 significance level is approximately ±3.707.

Question 19

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.

Question 20

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.

Quiz 13: Correlation and Linear Regression

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

Based on the regression equation, we can _______________.

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

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?

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

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

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

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?

What is the variable used to predict another variable called?

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

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?

What is the general form of the regression equation?

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?

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?

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?

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?

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

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