There are many restaurants in northeastern South Carolina. They serve beach vacationers in the summer, golfers in the fall and spring, and snowbirds in the winter. Bill and Joyce Tune all manage several restaurants in the North Jersey area and are considering moving to Myrtle Beach, SC, to open a new restaurant. Before making a final decision, they wish to investigate existing restaurants and what variables seem to be related to profitability. They gather sample information where profit (reported in $000) is the dependent variable and the independent variables are: x 1 the number of parking spaces near the restaurant. x 2 the number of hours the restaurant is open per week. x 3 the distance from the SkyWheel, a landmark in Myrtle Beach. x 4 the number of servers employed. x 5 the number of years the current owner operated the restaurant. The following is part of the output obtained using statistical software. (a) What is the amount of profit for a restaurant with 40 parking spaces that is open 72 hours per week, is 10 miles from the SkyWheel, has 20 servers, and has been operated by the current owner for 5 years? (b) Interpret the values of b 2 and b 3 in the multiple regression equation.

Question

Want to see more full solutions like this?

Answer 1

Textbook Question

Chapter 14, Problem 1SR

There are many restaurants in northeastern South Carolina. They serve beach vacationers in the summer, golfers in the fall and spring, and snowbirds in the winter. Bill and Joyce Tune all manage several restaurants in the North Jersey area and are considering moving to Myrtle Beach, SC, to open a new restaurant. Before making a final decision, they wish to investigate existing restaurants and what variables seem to be related to profitability. They gather sample information where profit (reported in $000) is the dependent variable and the independent variables are:

x₁ the number of parking spaces near the restaurant.

x₂ the number of hours the restaurant is open per week.

x₃ the distance from the SkyWheel, a landmark in Myrtle Beach.

x₄ the number of servers employed.

x₅ the number of years the current owner operated the restaurant.

The following is part of the output obtained using statistical software.

Chapter 14, Problem 1SR, There are many restaurants in northeastern South Carolina. They serve beach vacationers in the

(a) What is the amount of profit for a restaurant with 40 parking spaces that is open 72 hours per week, is 10 miles from the SkyWheel, has 20 servers, and has been operated by the current owner for 5 years?
(b) Interpret the values of b₂ and b₃ in the multiple regression equation.

a.

Expert Solution

To determine

Find the amount of profit for a restaurant with the given conditions.

Answer to Problem 1SR

The amount of profit for a restaurant with the given conditions is $389,500.

Explanation of Solution

Calculation:

Multiple linear regression model:

A multiple linear regression model is given as y^=a+b1x1+b2x2+b3x3+...+bkxk where y is the response or dependent variable, and x1,x2,...,xk are the k quantitative independent variables where k is a positive integer.

Here, a is the intercept term of the regression model, that is, the value of predicted value of y when X’s are 0 and bi’s are the slopes, that is, the amount of change of the predicted value of y for one unit increase in xi when all other independent variables are constant.

In the given problem the predicted dependent variable y is the amount of profit in $1,000. The number of parking space near the restaurant, the number of hours the restaurant is opened per week, the distance from the landmark in Beach M, the number of servers and the number of years the current owner operated the restaurant are defined as x1,x2,x3,x4 and x5, respectively.

Hence, using the given information the regression equation is y^=2.50+3x1+4x2−3x3+0.20x4+x5.

Thus, the amount of profit for a restaurant with 40 parking spaces which is open 72 hours per week, 10 mile from a landmark of Beach M with 20 servers and has been operated by the current owner for 5 years, is calculated as follows:

y^=2.50+3(40)+4(72)−3(10)+0.20(20)+5=2.50+120+288−30+4+5=389.5

Therefore, the amount of profit for a restaurant with the given conditions is $389,500.

b.

Expert Solution

To determine

Explain the values of b2 and b3 in the multiple regression equation.

Explanation of Solution

It is clear that, the value b2 is 4 which is the coefficient of x2, the number of hours the restaurant is opened per week.

Hence, it can be concluded that if the restaurant is opened one more hour per week, then the amount of profit for the restaurant would be increased by $4,000, when all the other factors are constant.

It is clear that, the value b3 is –3 which is the coefficient of x3, the distance from the landmark in Beach M.

Hence, it can be concluded that if the restaurant is opened one more mile away from the landmark of Beach M, then the amount of profit for the restaurant would be decreased by $3,000, when all the other factors are constant.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Cycles to failure Position in ascending order 0.5 f(x)) (x;) Problem 44 Marsha, a renowned cake scientist, is trying to determine how long different cakes can survive intense fork attacks before collapsing into crumbs. To simulate real-world cake consumption, she designs a test where cakes are subjected to repeated fork stabs and bites, mimicking the brutal reality of birthday parties. After rigorous testing, Marsha records 10 observations of how many stabs each cake endured before structural failure. Construct P-P plots for (a.) a normal distribution, (b.) a lognormal distribution, and (c.) a Weibull distribution (using the information included in the table below). Which distribution seems to be the best model for the cycles to failure for this material? Explain your answer in detail. Observation Empirical cumulative Probability distribution Cumulative distribution Inverse of cumulative distribution F-1 (-0.5) F(x)) (S) n 4 3 1 0.05 9 5 2 0.15 7 7 3 0.25 1 10 4 0.35 3 12 5 0.45 Normal…

Problem 3 In their lab, engineer Daniel and Paulina are desperately trying to perfect time travel. But the problem is that their machine still struggles with power inconsistencies-sometimes generating too little energy, other times too much, causing unstable time jumps. To prevent catastrophic misjumps into the Jurassic era or the far future, they must calibrate the machine's power output. After extensive testing, they found that the time machine's power output follows a normal distribution, with an average energy level of 8.7 gigawatts and a standard deviation of 1.2 gigawatts. The Time Travel Safety Board has set strict guidelines: For a successful time jump, the machine's power must be between 8.5 and 9.5 gigawatts. What is the probability that a randomly selected time jump meets this precision requirement? Daniel suggests that adjusting the mean power output could improve time-travel accuracy. Can adjusting the mean reduce the number of dangerous misjumps? If yes, what should the…

Problem 5 ( Marybeth is also interested in the experiment from Problem 2 (associated with the enhancements for Captain America's shield), so she decides to start a detailed literature review on the subject. Among others, she found a paper where they used a 2"(4-1) fractional factorial design in the factors: (A) shield material, (B) throwing mechanism, (C) edge modification, and (D) handle adjustment. The experimental design used in the paper is shown in the table below. a. Run A B с D 1 (1) -1 -1 -1 1 2 a 1 -1 -1 1 3 bd -1 1 -1 1 4 abd 1 1 -1 1 5 cd -1 -1 1 -1 6 acd 1 -1 1 -1 7 bc -1 1 1 -1 abc 1 1 1 -1 paper? s) What was the generator used in the 2"(4-1) fractional factorial design described in the b. Based on the resolution of this design, what do you think about the generator used in the paper? Do you think it was a good choice, or would you have selected a different one? Explain your answer in detail.

Answer 2

Textbook Question

Chapter 14, Problem 1SR

There are many restaurants in northeastern South Carolina. They serve beach vacationers in the summer, golfers in the fall and spring, and snowbirds in the winter. Bill and Joyce Tune all manage several restaurants in the North Jersey area and are considering moving to Myrtle Beach, SC, to open a new restaurant. Before making a final decision, they wish to investigate existing restaurants and what variables seem to be related to profitability. They gather sample information where profit (reported in $000) is the dependent variable and the independent variables are:

x₁ the number of parking spaces near the restaurant.

x₂ the number of hours the restaurant is open per week.

x₃ the distance from the SkyWheel, a landmark in Myrtle Beach.

x₄ the number of servers employed.

x₅ the number of years the current owner operated the restaurant.

The following is part of the output obtained using statistical software.

Chapter 14, Problem 1SR, There are many restaurants in northeastern South Carolina. They serve beach vacationers in the

(a) What is the amount of profit for a restaurant with 40 parking spaces that is open 72 hours per week, is 10 miles from the SkyWheel, has 20 servers, and has been operated by the current owner for 5 years?
(b) Interpret the values of b₂ and b₃ in the multiple regression equation.

a.

Expert Solution

To determine

Find the amount of profit for a restaurant with the given conditions.

Answer to Problem 1SR

The amount of profit for a restaurant with the given conditions is $389,500.

Explanation of Solution

Calculation:

Multiple linear regression model:

A multiple linear regression model is given as y^=a+b1x1+b2x2+b3x3+...+bkxk where y is the response or dependent variable, and x1,x2,...,xk are the k quantitative independent variables where k is a positive integer.

Here, a is the intercept term of the regression model, that is, the value of predicted value of y when X’s are 0 and bi’s are the slopes, that is, the amount of change of the predicted value of y for one unit increase in xi when all other independent variables are constant.

In the given problem the predicted dependent variable y is the amount of profit in $1,000. The number of parking space near the restaurant, the number of hours the restaurant is opened per week, the distance from the landmark in Beach M, the number of servers and the number of years the current owner operated the restaurant are defined as x1,x2,x3,x4 and x5, respectively.

Hence, using the given information the regression equation is y^=2.50+3x1+4x2−3x3+0.20x4+x5.

Thus, the amount of profit for a restaurant with 40 parking spaces which is open 72 hours per week, 10 mile from a landmark of Beach M with 20 servers and has been operated by the current owner for 5 years, is calculated as follows:

y^=2.50+3(40)+4(72)−3(10)+0.20(20)+5=2.50+120+288−30+4+5=389.5

Therefore, the amount of profit for a restaurant with the given conditions is $389,500.

b.

Expert Solution

To determine

Explain the values of b2 and b3 in the multiple regression equation.

Explanation of Solution

It is clear that, the value b2 is 4 which is the coefficient of x2, the number of hours the restaurant is opened per week.

Hence, it can be concluded that if the restaurant is opened one more hour per week, then the amount of profit for the restaurant would be increased by $4,000, when all the other factors are constant.

It is clear that, the value b3 is –3 which is the coefficient of x3, the distance from the landmark in Beach M.

Hence, it can be concluded that if the restaurant is opened one more mile away from the landmark of Beach M, then the amount of profit for the restaurant would be decreased by $3,000, when all the other factors are constant.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 14, Problem 1SR

There are many restaurants in northeastern South Carolina. They serve beach vacationers in the summer, golfers in the fall and spring, and snowbirds in the winter. Bill and Joyce Tune all manage several restaurants in the North Jersey area and are considering moving to Myrtle Beach, SC, to open a new restaurant. Before making a final decision, they wish to investigate existing restaurants and what variables seem to be related to profitability. They gather sample information where profit (reported in $000) is the dependent variable and the independent variables are:

x₁ the number of parking spaces near the restaurant.

x₂ the number of hours the restaurant is open per week.

x₃ the distance from the SkyWheel, a landmark in Myrtle Beach.

x₄ the number of servers employed.

x₅ the number of years the current owner operated the restaurant.

The following is part of the output obtained using statistical software.

Chapter 14, Problem 1SR, There are many restaurants in northeastern South Carolina. They serve beach vacationers in the

(a) What is the amount of profit for a restaurant with 40 parking spaces that is open 72 hours per week, is 10 miles from the SkyWheel, has 20 servers, and has been operated by the current owner for 5 years?
(b) Interpret the values of b₂ and b₃ in the multiple regression equation.

a.

Expert Solution

To determine

Find the amount of profit for a restaurant with the given conditions.

Answer to Problem 1SR

The amount of profit for a restaurant with the given conditions is $389,500.

Explanation of Solution

Calculation:

Multiple linear regression model:

A multiple linear regression model is given as y^=a+b1x1+b2x2+b3x3+...+bkxk where y is the response or dependent variable, and x1,x2,...,xk are the k quantitative independent variables where k is a positive integer.

Here, a is the intercept term of the regression model, that is, the value of predicted value of y when X’s are 0 and bi’s are the slopes, that is, the amount of change of the predicted value of y for one unit increase in xi when all other independent variables are constant.

In the given problem the predicted dependent variable y is the amount of profit in $1,000. The number of parking space near the restaurant, the number of hours the restaurant is opened per week, the distance from the landmark in Beach M, the number of servers and the number of years the current owner operated the restaurant are defined as x1,x2,x3,x4 and x5, respectively.

Hence, using the given information the regression equation is y^=2.50+3x1+4x2−3x3+0.20x4+x5.

Thus, the amount of profit for a restaurant with 40 parking spaces which is open 72 hours per week, 10 mile from a landmark of Beach M with 20 servers and has been operated by the current owner for 5 years, is calculated as follows:

y^=2.50+3(40)+4(72)−3(10)+0.20(20)+5=2.50+120+288−30+4+5=389.5

Therefore, the amount of profit for a restaurant with the given conditions is $389,500.

b.

Expert Solution

To determine

Explain the values of b2 and b3 in the multiple regression equation.

Explanation of Solution

It is clear that, the value b2 is 4 which is the coefficient of x2, the number of hours the restaurant is opened per week.

Hence, it can be concluded that if the restaurant is opened one more hour per week, then the amount of profit for the restaurant would be increased by $4,000, when all the other factors are constant.

It is clear that, the value b3 is –3 which is the coefficient of x3, the distance from the landmark in Beach M.

Hence, it can be concluded that if the restaurant is opened one more mile away from the landmark of Beach M, then the amount of profit for the restaurant would be decreased by $3,000, when all the other factors are constant.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 14, Problem 1SR

There are many restaurants in northeastern South Carolina. They serve beach vacationers in the summer, golfers in the fall and spring, and snowbirds in the winter. Bill and Joyce Tune all manage several restaurants in the North Jersey area and are considering moving to Myrtle Beach, SC, to open a new restaurant. Before making a final decision, they wish to investigate existing restaurants and what variables seem to be related to profitability. They gather sample information where profit (reported in $000) is the dependent variable and the independent variables are:

x₁ the number of parking spaces near the restaurant.

x₂ the number of hours the restaurant is open per week.

x₃ the distance from the SkyWheel, a landmark in Myrtle Beach.

x₄ the number of servers employed.

x₅ the number of years the current owner operated the restaurant.

The following is part of the output obtained using statistical software.

Chapter 14, Problem 1SR, There are many restaurants in northeastern South Carolina. They serve beach vacationers in the

(a) What is the amount of profit for a restaurant with 40 parking spaces that is open 72 hours per week, is 10 miles from the SkyWheel, has 20 servers, and has been operated by the current owner for 5 years?
(b) Interpret the values of b₂ and b₃ in the multiple regression equation.

a.

Expert Solution

To determine

Find the amount of profit for a restaurant with the given conditions.

Answer to Problem 1SR

The amount of profit for a restaurant with the given conditions is $389,500.

Explanation of Solution

Calculation:

Multiple linear regression model:

A multiple linear regression model is given as y^=a+b1x1+b2x2+b3x3+...+bkxk where y is the response or dependent variable, and x1,x2,...,xk are the k quantitative independent variables where k is a positive integer.

Here, a is the intercept term of the regression model, that is, the value of predicted value of y when X’s are 0 and bi’s are the slopes, that is, the amount of change of the predicted value of y for one unit increase in xi when all other independent variables are constant.

In the given problem the predicted dependent variable y is the amount of profit in $1,000. The number of parking space near the restaurant, the number of hours the restaurant is opened per week, the distance from the landmark in Beach M, the number of servers and the number of years the current owner operated the restaurant are defined as x1,x2,x3,x4 and x5, respectively.

Hence, using the given information the regression equation is y^=2.50+3x1+4x2−3x3+0.20x4+x5.

Thus, the amount of profit for a restaurant with 40 parking spaces which is open 72 hours per week, 10 mile from a landmark of Beach M with 20 servers and has been operated by the current owner for 5 years, is calculated as follows:

y^=2.50+3(40)+4(72)−3(10)+0.20(20)+5=2.50+120+288−30+4+5=389.5

Therefore, the amount of profit for a restaurant with the given conditions is $389,500.

b.

Expert Solution

To determine

Explain the values of b2 and b3 in the multiple regression equation.

Explanation of Solution

It is clear that, the value b2 is 4 which is the coefficient of x2, the number of hours the restaurant is opened per week.

Hence, it can be concluded that if the restaurant is opened one more hour per week, then the amount of profit for the restaurant would be increased by $4,000, when all the other factors are constant.

It is clear that, the value b3 is –3 which is the coefficient of x3, the distance from the landmark in Beach M.

Hence, it can be concluded that if the restaurant is opened one more mile away from the landmark of Beach M, then the amount of profit for the restaurant would be decreased by $3,000, when all the other factors are constant.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Find the amount of profit for a restaurant with the given conditions.

Answer to Problem 1SR

The amount of profit for a restaurant with the given conditions is $389,500.

Explanation of Solution

Calculation:

Multiple linear regression model:

A multiple linear regression model is given as y^=a+b1x1+b2x2+b3x3+...+bkxk where y is the response or dependent variable, and x1,x2,...,xk are the k quantitative independent variables where k is a positive integer.

Here, a is the intercept term of the regression model, that is, the value of predicted value of y when X’s are 0 and bi’s are the slopes, that is, the amount of change of the predicted value of y for one unit increase in xi when all other independent variables are constant.

In the given problem the predicted dependent variable y is the amount of profit in $1,000. The number of parking space near the restaurant, the number of hours the restaurant is opened per week, the distance from the landmark in Beach M, the number of servers and the number of years the current owner operated the restaurant are defined as x1,x2,x3,x4 and x5, respectively.

Hence, using the given information the regression equation is y^=2.50+3x1+4x2−3x3+0.20x4+x5.

Thus, the amount of profit for a restaurant with 40 parking spaces which is open 72 hours per week, 10 mile from a landmark of Beach M with 20 servers and has been operated by the current owner for 5 years, is calculated as follows:

y^=2.50+3(40)+4(72)−3(10)+0.20(20)+5=2.50+120+288−30+4+5=389.5

Therefore, the amount of profit for a restaurant with the given conditions is $389,500.

b.

Expert Solution

To determine

Explain the values of b2 and b3 in the multiple regression equation.

Explanation of Solution

It is clear that, the value b2 is 4 which is the coefficient of x2, the number of hours the restaurant is opened per week.

Hence, it can be concluded that if the restaurant is opened one more hour per week, then the amount of profit for the restaurant would be increased by $4,000, when all the other factors are constant.

It is clear that, the value b3 is –3 which is the coefficient of x3, the distance from the landmark in Beach M.

Hence, it can be concluded that if the restaurant is opened one more mile away from the landmark of Beach M, then the amount of profit for the restaurant would be decreased by $3,000, when all the other factors are constant.

Answer 8

a.

Expert Solution

To determine

Find the amount of profit for a restaurant with the given conditions.

Answer to Problem 1SR

The amount of profit for a restaurant with the given conditions is $389,500.

Explanation of Solution

Calculation:

Multiple linear regression model:

A multiple linear regression model is given as y^=a+b1x1+b2x2+b3x3+...+bkxk where y is the response or dependent variable, and x1,x2,...,xk are the k quantitative independent variables where k is a positive integer.

Here, a is the intercept term of the regression model, that is, the value of predicted value of y when X’s are 0 and bi’s are the slopes, that is, the amount of change of the predicted value of y for one unit increase in xi when all other independent variables are constant.

In the given problem the predicted dependent variable y is the amount of profit in $1,000. The number of parking space near the restaurant, the number of hours the restaurant is opened per week, the distance from the landmark in Beach M, the number of servers and the number of years the current owner operated the restaurant are defined as x1,x2,x3,x4 and x5, respectively.

Hence, using the given information the regression equation is y^=2.50+3x1+4x2−3x3+0.20x4+x5.

Thus, the amount of profit for a restaurant with 40 parking spaces which is open 72 hours per week, 10 mile from a landmark of Beach M with 20 servers and has been operated by the current owner for 5 years, is calculated as follows:

y^=2.50+3(40)+4(72)−3(10)+0.20(20)+5=2.50+120+288−30+4+5=389.5

Therefore, the amount of profit for a restaurant with the given conditions is $389,500.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Find the amount of profit for a restaurant with the given conditions.

Answer 13

Answer to Problem 1SR

The amount of profit for a restaurant with the given conditions is $389,500.

Answer 14

Explanation of Solution

Calculation:

Multiple linear regression model:

A multiple linear regression model is given as y^=a+b1x1+b2x2+b3x3+...+bkxk where y is the response or dependent variable, and x1,x2,...,xk are the k quantitative independent variables where k is a positive integer.

Here, a is the intercept term of the regression model, that is, the value of predicted value of y when X’s are 0 and bi’s are the slopes, that is, the amount of change of the predicted value of y for one unit increase in xi when all other independent variables are constant.

In the given problem the predicted dependent variable y is the amount of profit in $1,000. The number of parking space near the restaurant, the number of hours the restaurant is opened per week, the distance from the landmark in Beach M, the number of servers and the number of years the current owner operated the restaurant are defined as x1,x2,x3,x4 and x5, respectively.

Hence, using the given information the regression equation is y^=2.50+3x1+4x2−3x3+0.20x4+x5.

Thus, the amount of profit for a restaurant with 40 parking spaces which is open 72 hours per week, 10 mile from a landmark of Beach M with 20 servers and has been operated by the current owner for 5 years, is calculated as follows:

y^=2.50+3(40)+4(72)−3(10)+0.20(20)+5=2.50+120+288−30+4+5=389.5

Therefore, the amount of profit for a restaurant with the given conditions is $389,500.

Answer 15

b.

Expert Solution

To determine

Explain the values of b2 and b3 in the multiple regression equation.

Explanation of Solution

It is clear that, the value b2 is 4 which is the coefficient of x2, the number of hours the restaurant is opened per week.

Hence, it can be concluded that if the restaurant is opened one more hour per week, then the amount of profit for the restaurant would be increased by $4,000, when all the other factors are constant.

It is clear that, the value b3 is –3 which is the coefficient of x3, the distance from the landmark in Beach M.

Hence, it can be concluded that if the restaurant is opened one more mile away from the landmark of Beach M, then the amount of profit for the restaurant would be decreased by $3,000, when all the other factors are constant.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Explain the values of b2 and b3 in the multiple regression equation.

Answer 20

Explanation of Solution

It is clear that, the value b2 is 4 which is the coefficient of x2, the number of hours the restaurant is opened per week.

Hence, it can be concluded that if the restaurant is opened one more hour per week, then the amount of profit for the restaurant would be increased by $4,000, when all the other factors are constant.

It is clear that, the value b3 is –3 which is the coefficient of x3, the distance from the landmark in Beach M.

Hence, it can be concluded that if the restaurant is opened one more mile away from the landmark of Beach M, then the amount of profit for the restaurant would be decreased by $3,000, when all the other factors are constant.

Answer 21

Ch. 14 - There are many restaurants in northeastern South...Ch. 14 - Prob. 1E Ch. 14 - Thompson Photo Works purchased several new, highly...Ch. 14 - A consulting group was hired by the Human...Ch. 14 - Cellulon, a manufacturer of home insulation, wants...Ch. 14 - Refer to Self-Review 141 on the subject of...Ch. 14 - Prob. 5E Ch. 14 - Prob. 6E Ch. 14 - Prob. 3SR Ch. 14 - Given the following regression output, answer the...

Concept explainers

Videos

Answer to Problem 1SR

Explanation of Solution

Explanation of Solution

Want to see more full solutions like this?

Chapter 14 Solutions