Question 1

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
The regression equation is Y = 72.9 - 0.519 X
 
-What is the sample slope for this model?
A) 72.909
B) 2.037
C) -0.5195
D) 0.1946

Accepted Answer

C

Question 2

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
The regression equation is Y = 72.9 - 0.519 X
 
-What is the sample intercept for this model?
A) 72.909
B) 2.037
C) -0.5195
D) 0.1946

Accepted Answer

The sample intercept is the constant term in the regression equation, which is 72.909 in this context.

Question 3

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
The regression equation is Y = 72.9 - 0.519 X
 
-What is the standard error of the sample slope?
A) 72.909
B) 2.037
C) -0.519
D) 0.1946

Accepted Answer

The standard error of the sample slope is a measure of the variability of the slope estimate, and it is typically a small positive value. Among the options, 0.1946 is the most reasonable value for a standard error.

Question 4

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
The regression equation is Y = 72.9 - 0.519 X
 
-What is the p-value for testing if the slope in the population is different from zero?
A) 0.5195
B) 0.1946
C) p < 0.001
D) 0.008

Accepted Answer

The answer of Use the following to answer the questions...

Question 5

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
The regression equation is Y = 72.9 - 0.519 X
 
-The sample size in this situation is n = 157. What are the degrees of freedom for constructing a confidence interval for, or performing a test about, the population slope?
A) 157
B) 156
C) 155
D) 153

Accepted Answer

The degrees of freedom for a confidence interval or hypothesis test about the population slope in simple linear regression is n - 2, which is 157 - 2 = 155.

Question 6

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
The regression equation is Y = 72.9 - 0.519 X
 
-The sample size in this situation is n = 157. Construct a 95% confidence interval for the population slope. Round the margin of error to four decimal places.
A) -0.9038 to -0.1352
B) -0.9009 to -0.1381
C) -0.8976 to -0.1414
D) -0.9138 to -0.1252

Accepted Answer

t* = 1.975 (df = 155)
-0.5195 ± 1.975(0.1946)
-0.5195 ± 0.3843
-0.9038 to -0.1352

Question 7

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
The regression equation is Y = 72.9 - 0.519 X
 
-Use the p-value for testing if the slope in the population is different from zero (and a 5% significance level) to make a clear conclusion about the effectiveness of the model.
A) p-value = 0.008 There is very strong evidence that the population slope differs from zero, and thus is an effective model for predicting this response variable.
B) p-value = 0.008 There is not enough evidence that the population slope differs from zero, and thus this is not an effective model for predicting this response variable.

Accepted Answer

Since the p-value (0.008) is less than the significance level (0.05), there is strong evidence to reject the null hypothesis, indicating that the slope is significantly different from zero, making the model effective.

Question 8

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
 
-What is the sample slope for this model?
A) 1.6370
B) 0.5453
C) 7.2960
D) 14.5444

Accepted Answer

The sample slope is 1.6370. This is the value of the coefficient for the independent variable in the regression equation.

Question 9

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
 
-What is the sample intercept for this model?
A) 1.6370
B) 0.5453
C) 7.2960
D) 14.5444

Accepted Answer

The answer of Use the following to answer the questions...

Question 10

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
 
-What is the standard error of the sample slope?
A) 1.6370
B) 0.5453
C) 7.2960
D) 14.5444

Accepted Answer

The standard error of the sample slope is a measure of the variability or dispersion of the sample slope estimate. It is typically calculated using statistical software or formulas based on the sample data. In this context, 0.5453 is the correct standard error value.

Question 11

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
 
-What is the p-value for testing if the slope in the population is different from zero?
A) 0.502
B) 0.622
C) 0.5453
D) 0.00765

Accepted Answer

A p-value of 0.00765 indicates strong evidence against the null hypothesis, suggesting that the slope in the population is significantly different from zero.

Question 12

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
 
-The sample size in this situation is n = 20. What are the degrees of freedom for constructing a confidence interval, or performing a test about, the population slope?
A) 17
B) 18
C) 19
D) 20

Accepted Answer

The answer of Use the following to answer the questions...

Question 13

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
 
-The sample size in this situation is n = 20. Construct a 95% confidence interval for the population slope. Round the margin of error to three decimal places.
A) 0.491 to 2.783
B) 0.568 to 2.706
C) 0.578 to 2.697
D) 0.5327 to 2.741

Accepted Answer

t* = 2.101 (df = 18)
1.637 ± 2.101(0.5453)
1.637 ± 1.146
0.491 to 2.783

Question 14

Use the following to answer the questions below:
Computer output from a regression analysis is provided.
 
-Use the p-value for testing if the slope in the population is different from zero (and a 5% significance level) to make a clear conclusion about the effectiveness of the model.
A) p-value = 0.00765
There is very strong evidence that the population slope differs from zero, and thus is an effective model for predicting this response variable.
B) p-value = 0.00765
There is not enough evidence that the population slope differs from zero, and thus is not an effective model for predicting this response variable.

Accepted Answer

The p-value of 0.00765 is less than the 5% significance level, indicating strong evidence that the population slope differs from zero, suggesting the model is effective.

Question 15

The website for the Quantitative Environmental Learning Project (funded by the National Science Foundation) describes data they collected on the lengths and widths of Puget Sound Butter Clams. A scatterplot of the data (with the regression line) is provided. 
  
Use the scatterplot to check each of the conditions for using a linear model with this data. Is using a linear model appropriate for these data?

Accepted Answer

The answer of The website for the Quantitative Environmental Learning...

Question 16

In a random sample of 41 students, the correlation between Math SAT score and college GPA is 0.289. Is there a significant linear association between Math SAT score and college GPA? Use α = 0.05. Include all details of the test. Round the test statistic to two decimal places.

Accepted Answer

The answer of In a random sample of 41 students,...

Question 17

In a random sample of 41 students, the correlation between Verbal SAT score and college GPA is 0.574. Is there evidence of a positive correlation between Verbal SAT score and college GPA? Use a 5% significance level. Include all details of the test. Round the test statistic to two decimal places.

Accepted Answer

The answer of In a random sample of 41 students,...

Question 18

In a random sample of 41 college students, the correlation between number of hours of television watched in a typical week and college GPA is -0.125. Is there evidence of a negative correlation between the amount of television watched and college GPA? Use a 5% significance level. Include all details of the test. Round the test statistic to three decimal places.

Accepted Answer

The answer of In a random sample of 41 college...

Question 19

Use the following to answer the questions below:
In a regression analysis based on a sample of size n = 30, SSModel = 750 and SSTotal = 2,500.
-Use this information to fill in all values in an analysis of variance table as shown.

Accepted Answer

The answer of Use the following to answer the questions...

Question 20

Use the following to answer the questions below:
In a regression analysis based on a sample of size n = 30, SSModel = 750 and SSTotal = 2,500.
-Compute  .
A) 30%
B) 83%
C) 1.2%
D) 5.5%

Accepted Answer

The answer of Use the following to answer the questions...

Quiz 9: Inference for Regression

Use the following to answer the questions below: Computer output from a regression analysis is provided. The regression equation is Y = 72.9 - 0.519 X -What is the sample slope for this model?

Use the following to answer the questions below: Computer output from a regression analysis is provided. The regression equation is Y = 72.9 - 0.519 X -What is the sample intercept for this model?

Use the following to answer the questions below: Computer output from a regression analysis is provided. The regression equation is Y = 72.9 - 0.519 X -What is the standard error of the sample slope?

Use the following to answer the questions below: Computer output from a regression analysis is provided. The regression equation is Y = 72.9 - 0.519 X -What is the p-value for testing if the slope in the population is different from zero?

Use the following to answer the questions below: Computer output from a regression analysis is provided. -What is the sample slope for this model?

Use the following to answer the questions below: Computer output from a regression analysis is provided. -What is the sample intercept for this model?

Use the following to answer the questions below: Computer output from a regression analysis is provided. -What is the standard error of the sample slope?

Use the following to answer the questions below: Computer output from a regression analysis is provided. -What is the p-value for testing if the slope in the population is different from zero?

Use the following to answer the questions below: Computer output from a regression analysis is provided. -The sample size in this situation is n = 20. What are the degrees of freedom for constructing a confidence interval, or performing a test about, the population slope?

Use the following to answer the questions below: Computer output from a regression analysis is provided. -The sample size in this situation is n = 20. Construct a 95% confidence interval for the population slope. Round the margin of error to three decimal places.

Use the following to answer the questions below: Computer output from a regression analysis is provided. -Use the p-value for testing if the slope in the population is different from zero (and a 5% significance level) to make a clear conclusion about the effectiveness of the model.

In a random sample of 41 students, the correlation between Math SAT score and college GPA is 0.289. Is there a significant linear association between Math SAT score and college GPA? Use α = 0.05. Include all details of the test. Round the test statistic to two decimal places.

In a random sample of 41 students, the correlation between Verbal SAT score and college GPA is 0.574. Is there evidence of a positive correlation between Verbal SAT score and college GPA? Use a 5% significance level. Include all details of the test. Round the test statistic to two decimal places.

Use the following to answer the questions below: In a regression analysis based on a sample of size n = 30, SSModel = 750 and SSTotal = 2,500. -Use this information to fill in all values in an analysis of variance table as shown.

Use the following to answer the questions below: In a regression analysis based on a sample of size n = 30, SSModel = 750 and SSTotal = 2,500. -Compute .