1. *The following another set of data that looking at how long it takes to get to work. Let x= commuting distance (miles) and y= commuting time (minutes)

1. Give a scatterplot of this data and comment on the direction, form and strength of this relationship.
2. Determine the least-squares estimate equation for this data set.
3. Give the r², comment on what that means.
4. Give the residual plot based on the least-squares estimate equation.
5. Test if this least-squares estimate equation specify a useful relationship between commuting distance and commuting time.

answer all questions

Rachel bought a car from the Beautiful Used Car Agency under a written contract. She purchased the car in reliance on Beautiful's agent's oral representations that it had never been in a wreck and could be driven at least two thousand miles without adding oil. Thereafter, Rachel discovered that the car had, in fact, been previously wrecked and rebuilt, that it used excessive quantities of oil, and that Beautiful's agent was aware of these facts when the car was sold. Rachel brings an action to rescind the contract and recover the purchase price. Beautiful objects to the introduction of oral testimony concerning representations of its agent, contending that the written contract alone governed the rights of the parties. Decision on the objection?

Fire Damage: A fire insurance company is interested in investigating the effect of the distance between the burning house and the nearest fire station (miles) on the amount of fire damage (thousands of dollars) in major residential fire. A random sample of 15 recent fires in a suburb is selected. The data set can be found in the excel file Fire with variables name Distance and Damage. Source: McClave, J. & Sincich, T. (2015). Statistics. (12th edition). M. A.: Pearson.

Part 1: Describe a scatterplot to learn the association between the distance between the burning house and the nearest fire station (miles) and the amount of fire damage (thousands of dollars) in major residential fire. (36 points total, 9 points each criterion)

Direction of association:

Form of association:

Strength of association:

Presence of outlier:

Note: Save R codes, outputs, and scatterplot on your machine for future reference

Part 2: Interpret regression parameters in context: (44 points total, 22 points each parameter)

Interpretation of y-intercept (b_0):

Interpretation of slope of regression line (b_1):

Note: Save R code and output on your machine for future reference

Part 3: Interpret the coefficient of determination (R^2) in context: (20 points)

Interpretation:

Note: Save R code and output on your machine for future reference

Distance Damage
1   3.4   26.2
2   1.8   17.8
3   4.6   31.3
4   2.3   23.1
5   3.1   27.5
6   5.5   36.0
7   0.7   14.1
8   3.0   22.3
9   2.6   19.6
10   4.3   31.3
11   2.1   24.0
12   1.1   17.3
13   6.1   43.2
14   4.8   36.4
15   3.8   26.1

The car dealer gave Unicorn a $2,000 cash discount off the $31,000 list price. However, Unicorn paid an additional $6,000 to equip the car with a more luxurious interior and high tech lighting so it would have greater appeal. Unicorn Company expected the car to have a five-year useful life and a $5,000 salvage value. Unicorn also expected to use the car for 150,000 miles before disposing of it. Unicorn used the car, and it was driven 50,000 / 10,000 / 40,000 / 30,000 / 20,000 miles during each use year respectively. Unicorn sold the car on January 1, 2020, for $7,500 cash. (SHOW ALL CALUCUALTIONS)

1. What is the cost of the car that Unicorn Company will record?

1. Under the straight line method of depreciation, how much depreciation expense will Unicorn have each year of the car’s use?

1. Under the double declining balance method of depreciation
   1. What is the percentage depreciation Unicorn will use?

1. At the end of the first year, how much depreciation expense will Unicorn have for the car?

1. At the end of the first year, what will be the book value the car?

1. At the end of the second year, how much depreciation expense will Unicorn have for the car?

1. At the end of the second year, what will be the book value the car?

1. Under the units of production method of depreciation
   1. How much depreciation will Unicorn have for each mile driven of the car?

1. How much depreciation expense will Unicorn have in the last three years under this method?

1. When Unicorn sold the car, what did it recognize as a gain or loss and for how much? Show calculation in proper format and put into the accounting equation.

Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg).

Complete parts (b) through (e), given Σx = 296, Σy = 172, Σx² = 11,676, Σy² = 4006, Σxy = 5924, and

r ≈ −0.932.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

(f) Suppose a car weighs x = 42 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
mpg

Gallatin Carpet Cleaning-the company has always charged a flat fee per hundred square feet of carpet cleaned. The current fee is $23.50 per hundred square feet.

The total cost of operating the company for the year is $370,000

1. Prepare the first-stage allocation of costs to the activity cost pools.

2. Compute the activity rates for the activity cost pools.

3. The company recently completed a 400 square foot carpet-cleaning job at the Flying N Ranch—a 53-mile round-trip journey from the company’s offices in Bozeman. Compute the cost of this job using the activity-based costing system.

4. The revenue from the Flying N Ranch was $94.00 (400 square feet @ $23.50 per hundred square feet). Calculate the customer margin

Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 26 47 30 47 23 40 34 52 y 30 20 23 13 29 17 21 14 Complete parts (a) through (e), given Σx = 299, Σy = 167, Σx2 = 11,983, Σy2 = 3765, Σxy = 5810, and r ≈ −0.909.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

(f) Suppose a car weighs x = 40 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
mpg

For the test of significance questions, clearly indicate each of the formal steps in the test of significance.

Step 1: State the null and alternative hypothesis.
Step 2: Calculate the test statistic.
Step 3: Find the p-value.

Step 4: State your conclusion. (Do not just say “Reject H0” or “Do not reject H0”, state the conclusion in the context of the problem.)

Does using premium gas increase your miles per gallon? A study was conducted with nine vehicles that can run on regular gas to see if using premium gas will get better gas mileage. Each car in our sample was randomly filled first with either regular or premium gasoline, and the mileage for that tankful recorded. The mileage was recorded again for the same cars for a tankful of the other kind of gasoline. Is there evidence to suggest that using premium gas will increase your miles per gallon? (Use 10% significance level.)

Vehicle 1: Prem: 19 Reg: 20 Difference: -1

Vehicle 2: Prem: 35 Reg: 32 Difference: 3

Vehicle 3: Prem: 34 Reg: 33 Difference: 1

Vehicle 4: Prem: 18 Reg: 19 Difference: -1

Vehicle 5: Prem: 40 Reg: 37 Difference: 3

Vehicle 6: Prem: 26 Reg: 27 Difference: -1

Vehicle 7: Prem: 36 Reg: 33 Difference: 3

Vehicle 8: Prem: 28 Reg: 29 Difference: -1

Vehicle 9: Prem: 34 Reg: 31 Difference: 3

Mean: Prem: 30 Reg: 29 Difference: 1

St. Dev: Prem: 7.7 Reg: 6.1 Difference: 2.0

. Hoverboards and the Factory Market Area: Suppose there is a single shoe factory in the region. The factory competes with homemade shoes and will sell shoes to any household for which the net price of factory shoes is less than the cost of homemade shoes. The cost of a homemade shoe is the opportunity cost of the time required to make the shoe at home, that is, the one gallon of milk that could be produced instead. Suppose the higher cost of living and commuting requires compensation of 0.80 gallons of milk per hour. Each worker produces 10 shoes per hour, so the average labor and capital cost are 0.18 gallons of milk and 0.12 gallons of milk respectively. The factory price of shoe (equal to the average production cost, sum of the average labor cost and the average capital cost) is 0.30 gallons of milk. A round-trip mile involves one mile of travel to a location and one mile back, for a total distance of two miles. Linear travel cost 20 miles /hour. Therefore, the typical person takes 1/10 of an hour per round- trip mile. The changes are not cumulative.

a) Calculate the market area of the shoe factory. Draw the graph.
b) Suppose hoverboards decrease travel time for consumers from 1/10 per round-trip mile to 1/20 per round-trip mile. Illustrate the implications for the radius of the market area of the factory, including a value for the new radius. Draw the graph.
c) Suppose hoverboards also decrease the commuting cost of factory workers, decreasing the cost of urban living from 0.80 gallons to 0.30 gallons. Illustrate the effect on radius of the market area of the factory, including a value for the new radius. Draw the graph.

Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:

1. b-1. Fill in the blanks. (Round your answers to 3 decimal places. Negative values should be indicated by minus sign.)

1. b-2. State the decision rule for 0.10 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

1. b-3. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

1. b-4. Can we conclude that there is a positive correlation between distance and time? Use the 0.10 significance level.