Question 1

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

Accepted Answer

Both confidence intervals and prediction intervals use the standard error of estimate in their calculations.

Question 2

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

Accepted Answer

The standard error of estimate is a measure of the accuracy of the prediction, which indicates how far the observed values are from the predicted values. It is typically a positive value and is calculated based on the squared vertical deviations between Y and X. It is not calculated using the regression mean square, and cannot be negative. Therefore, A is the correct choice.

Question 3

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?

Accepted Answer

The independent variable is the variable that is being manipulated or changed by the researcher. In this scenario, the number of contacts is the variable being changed to see if it has an effect on the amount of sales dollars. Therefore, the independent variable is the number of contacts.

Question 4

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

Accepted Answer

The value of 10 in the equation represents the Y-intercept, where X is 0. Therefore, when X = 0, Y = 10.

Question 5

A sales manager for an advertising agency believes 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 slope of the linear equation?

Accepted Answer

The slope of the linear equation is the coefficient of the independent variable, which is 2.195 in this case.

Question 6

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?

Accepted Answer

Since the sample size is small, we need to use the t-distribution to test the significance of the slope. The critical value for a two-tailed test at the 0.05 significance level with 12 degrees of freedom (14-2=12) is t=±2.179. Therefore, the best choice is B.

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.

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

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

Accepted Answer

If all the plots on a scatter diagram lie on a straight line, then the regression line is a perfect fit and the standard error of estimate equals zero. Therefore, the best choice is C, which indicates zero standard error of estimate.

Question 9

What is the general form of the regression equation?

Accepted Answer

The general form of the regression equation is typically y = a + bX, where y is the dependent variable, X is the independent variable, a is the intercept, and b is the slope. Choice B represents this general form.

Question 10

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?

Accepted Answer

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

Question 11

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

Accepted Answer

The value of 20 indicates that for each unit increase in X, the predicted value of Y increases by 20 units. Therefore, option B is the correct choice. Option A is incorrect because the Y-intercept is already given as 10 and does not change with the increase in X. Option C is incorrect since it is the inverse of the correct relationship. Option D is also incorrect because the value of 20 is not related to the error in 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?

Accepted Answer

The dependent variable is the variable that is being measured and affected by the independent variable. In this case, the sales dollars earned are being affected by the number of contacts made. Therefore, the dependent variable is the amount of sales dollars.

Question 13

Based on the regression equation,we can ________.

Accepted Answer

The regression equation allows us to predict the value of the dependent variable based on a given value of the independent variable. It does not allow us to predict the value of the independent variable based on a given value of the dependent variable. It also measures the association between the two variables, but it does not measure cause and effect.

Question 14

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

Accepted Answer

The confidence interval estimates the mean of future observations whereas the prediction interval estimates an individual observation. Therefore, the prediction interval must account for additional sources of variation beyond what is included in the confidence interval. As a result, prediction intervals are wider than confidence intervals.

Question 15

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

Accepted Answer

The given equation is in the form of y = a + bx, where 11ea71e6_5bbb_0049_91e5_cf4907471a93_TB2636_11 is the y-intercept (a), and b is the slope of the line. Therefore, 11ea71e6_5bbb_004a_91e5_b118ed57ffe7_TB2636_11 is the predicted value of Y, given a specific X value.

Question 16

A sales manager for an advertising agency believes 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 standard error of the slope?

Accepted Answer

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

Question 17

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

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 18

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?

Accepted Answer

To test the significance of the slope, we need to calculate the t-statistic using the formula: 
t = (b - 0) / SEb 
where b is the regression coefficient (slope), SEb is the standard error of the slope, and 0 is the hypothesized value of the slope (in this case, it is 0 because we want to test if the slope is significantly different from 0). 
Substituting the given values: 
t = (2.56 - 0) / 0.97 = 2.639 
Since the sample size is 14, the degrees of freedom are n-2 = 12. Using a t-distribution table with 12 degrees of freedom, the critical value for a two-tailed test at 5% level of significance is ±2.179. Since our calculated t-statistic (2.639) is greater than the critical value (2.179), we can reject the null hypothesis and conclude that the slope is significantly different from 0. Hence, the answer is D.

Question 19

What is the variable used to predict another variable called?

Accepted Answer

The independent variable is the variable that is manipulated or changed in order to see its effect on the dependent variable. It is the variable that is used to predict another variable. The dependent variable, on the other hand, is the variable that is being predicted or measured. The other options, important variable and causal variable, may also have a role in the analysis, but they are not specifically used to predict another variable.

Question 20

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

Accepted Answer

To find the value of 11ea71e6_5bba_8b13_91e5_c56506a7d4e2_TB2636_11, we simply substitute X = 3 into the equation:
11ea71e6_5bba_8b13_91e5_c56506a7d4e2_TB2636_11 = 1,202 + 1,133(3) = 4,601. Therefore, the answer is C.

Quiz 13: Correlation and Linear Regression

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

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 independent variable?

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

A sales manager for an advertising agency believes 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 slope 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 critical value to test the significance of the slope at the 0.05 significance level?

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

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. A regression analysis shows the following results: What is the Y-intercept of the linear equation?

In the least squares equation, = 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. What is the dependent variable?

Based on the regression equation,we can ________.

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

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

A sales manager for an advertising agency believes 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 standard error of the slope?

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

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?

What is the variable used to predict another variable called?

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