Question 1

Lumber Weight Narrative
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
-Refer to Lumber Weight Narrative. What is the least-squares best-fitting regression line?

Accepted Answer

= 3.3 + 6.5x

Question 2

Blacktop
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
-Refer to Blacktop statement. What is the estimated amount of time it takes to apply 2400 square metres of blacktop?

Accepted Answer

= 81.6 + 0.207 (2400) = 578.4 minutes

Question 3

Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.  s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
-Refer to Salary and Years Narrative. Does a linear relationship exist between x and y? Test using  = 0.05.

Accepted Answer

Since p-value = 0.0 <  , reject the null hypothesis and conclude that a linear relationship does exist between x and y.

Question 4

Delivery Time Narrative
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
-Refer to Delivery Time Narrative. Use the least-squares regression line to estimate the time it takes to deliver ten pieces of furniture. (You may assume that ten is in the range of the data.)

Accepted Answer

The answer of Delivery Time Narrative
Let x be the number...

Question 5

Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.  s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
-Refer to Salary and Years Narrative. What are the values of  and the sum of squares for error?

Accepted Answer

The answer of Salary and Years Narrative
A company manager is...

Question 6

Lumber Weight Narrative
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
-Refer to Lumber Weight Narrative. What is the estimated time it takes to load 9 tonnes of lumber?

Accepted Answer

The answer of Lumber Weight Narrative
Let x be the weight...

Question 7

Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.  s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
-Refer to Salary and Years Narrative. What is the least-squares regression equation?

Accepted Answer

The answer of Salary and Years Narrative
A company manager is...

Question 8

Delivery Time Narrative
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
-Refer to Delivery Time Narrative. Identify and interpret the slope of the equation.

Accepted Answer

The answer of Delivery Time Narrative
Let x be the number...

Question 9

Delivery Time Narrative
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
-Refer to Delivery Time Narrative. Identify and interpret the y-intercept. Does this make sense?

Accepted Answer

The answer of Delivery Time Narrative
Let x be the number...

Question 10

Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.  s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
-Refer to Salary and Years Narrative. What are the least-squares estimates of the slope and the y-intercept?

Accepted Answer

The answer of Salary and Years Narrative
A company manager is...

Question 11

Blacktop
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
-Refer to Blacktop statement. What is the average change in time per one square metre increase in area?

Accepted Answer

The answer of Blacktop
Let x be the area (in square...

Question 12

Lumber Weight Narrative
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
-Refer to Lumber Weight Narrative. What is the average change in time per one tonne increase in weight?

Accepted Answer

The answer of Lumber Weight Narrative
Let x be the weight...

Question 13

Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.  s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
-Refer to Salary and Years Narrative. Find and interpret the coefficient of determination.

Accepted Answer

The answer of Salary and Years Narrative
A company manager is...

Question 14

Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.  s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
-Refer to Salary and Years Narrative. Find and interpret the correlation coefficient.

Accepted Answer

The answer of Salary and Years Narrative
A company manager is...

Question 15

Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company. 
-Refer to Advertising and Money Spent Narrative. Use a statistical software package of your choice and report the regression analysis results.

Accepted Answer

The answer of Advertising and Money Spent Narrative
A marketing analyst...

Question 16

Lumber Weight Narrative
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
-Refer to Lumber Weight Narrative. Interpret the y-intercept of the regression line.

Accepted Answer

The answer of Lumber Weight Narrative
Let x be the weight...

Question 17

Delivery Time Narrative
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
-Refer to Delivery Time Narrative. What is the least-squares best-fitting regression line?

Accepted Answer

The answer of Delivery Time Narrative
Let x be the number...

Question 18

Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.  s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
-Refer to Salary and Years Narrative. Interpret the estimated slope and y-intercept for this .

Accepted Answer

The answer of Salary and Years Narrative
A company manager is...

Question 19

Blacktop
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
-Refer to Blacktop statement. What is the least-squares best-fitting regression line?

Accepted Answer

The answer of Blacktop
Let x be the area (in square...

Question 20

Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company. 
-Refer to Advertising and Money Spent Narrative. Develop a scatterplot and determine whether a linear relationship appears to provide a good fit to this data set.

Accepted Answer

The answer of Advertising and Money Spent Narrative
A marketing analyst...

Quiz 12: B: linear Regression and Correlation