You are an accountant for a large department store and have been given the assignment of developing a model to predict the amount of time it takes to process invoices. Data is collected daily for 32 consecutive working days, and the number of invoices processed and completion time (in hours) are stored under the tab Invoice in the Excel data file for this homework.

a. Create the appropriate scatter plot and calculate the coefficient of correlation. Comment on the results. Does it appear a linear relationship exists?

b. Use the least-squares method to compute the regression coefficients b₀ and b₁.

c. Interpret the meaning of b₀ and b₁ in this problem.

d. What if the predicted mean amount of time it would take to process 150 invoices? Include a confidence interval for this prediction.

e. Determine the coefficient of determination, R², and explain its meaning in this problem.  

g. Perform a complete residual analysis. Does the analysis support all the assumptions required for a valid model? Explain.

h. Based on your results in part g, what can you say about the validity of the prediction you made in part c?

h. What conclusions can you reach about the relationship between then number of invoices processed and the completion time? What actions, if any, would you take next?

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

1. Choose the scatter diagram that best fits the data.

• Scatter diagram 1

• Scatter diagram 2

• Scatter diagram 3

2. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

1. c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

1. c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

1. c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.01 significance level.

4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

c-1. State the decision rule for 0.025 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.)

c-2Compute the value of the test statistic. (Round your answer to 2 decimal places.)

c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.025 significance level.

What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

1. Choose the scatter diagram that best fits the data.

• Scatter diagram 1

• Scatter diagram 2

• Scatter diagram 3

2. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

Pearson correlation _______

1. c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

Reject H0 if t > ________

1. c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic ______

4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

_____ % of the variation in revenue is explained by variation in occupied rooms.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

1. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

Pearson Correlation:

2.

c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

c-2. Compute the value of the test statistic.

D. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

________% of the variation in revenue is explained by variation in occupied rooms.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

a. Choose the scatter diagram that best fits the data.

b. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

1. c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

1. c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

1. c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.01 significance level.

d.

4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

1. Choose the scatter diagram that best fits the data.

• Scatter diagram 1

• Scatter diagram 2

• Scatter diagram 3

2. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

Pearson correlation _____

1. c-1. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

Reject H0 if T> _____

1. c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic _________

1. c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.01 significance level.

______ H0, it ______ reasonable to conclude that there is a positive relationship between revenue and occupied rooms.

4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

_____ % of the variation in revenue is explained by variation occupied rooms.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied. Day Revenue Occupied Day Revenue Occupied 1 $ 1,452 32 14 $ 1,425 29 2 1,361 30 15 1,445 31 3 1,426 33 16 1,439 33 4 1,470 33 17 1,348 30 5 1,456 33 18 1,450 34 6 1,430 29 19 1,431 30 7 1,354 29 20 1,446 30 8 1,442 30 21 1,485 30 9 1,394 32 22 1,405 32 10 1,459 30 23 1,461 32 11 1,399 33 24 1,490 32 12 1,458 31 25 1,426 33 13 1,537 34

Click here for the Excel Data File

Choose the scatter diagram that best fits the data.

Scatter diagram 1 Scatter diagram 2 Scatter diagram 3

Scatter diagram 1 Scatter diagram 2 Scatter diagram 3

Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.)

c-1. State the decision rule for 0.05 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.)

c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

c-3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.05 significance level. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.)

  
Click here for the Excel Data File