When you determine if there is an association between two variables, it is also important for you to determine how strong or weak that association is. This is why, when you have data for two quantitative variables, you calculate what is called the coefficient for correlation.

Instructions

1. Suppose you are determining the association between the weight of a car and the miles per gallon that the car gets. Answer the following questions in a Word document:

• define correlation and explain how you can use correlation to determine the relationship between these two variables.
• Before you look at some data, what kind of association do you think will exist between the weight of a car and the miles per gallon that the car gets? Will it be positive or negative?
• Given the data below, use Excel or other technology to calculate the correlation coefficient for this data:

Model

City MPG

Weight

Mazda MX-5 Miata

25

2365

Mercedes/Benz SLK

22

3020

Mitsubishi Eclipse

23

3235

Pontiac Firebird

18

3545

Porsche Boxster

19

2905

Saturn SC

27

2420

• Now that you have calculated the correlation, what does this value represent? What does it tell you about the relationship between these two variables?

The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are as follows:

^{a)Using a 2-year moving average, the forecast for year 6 (round your response to the nearest whole number)?.
b) If a 2-year moving average is used to make the forecast, the MAD based on this (round your response to one decimal place). (Hint: You will have only 3 years of matched data.)?}

^{c)The forecast for year 6 using a weighted 2-year moving average with weights of 0.40 and 0.60 (the weight of 0.60 is for the most recent period) = miles (round your response to the nearest whole number).?
The MAD for the forecast developed using a weighted 2-year moving average with weights of 0.40 and 0.60 (round your response to one decimal place). (Hint: You will have only 3 years of matched data.)?}

^{d) Using exponential smoothing with alpha ? 0.30 and the forecast for year 1 being 3,050, the forecast for year 6 (round your response to the nearest whole number).?}

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).

given Σx = 301, Σy = 168, Σx² = 12,089, Σy² = 3802, Σxy = 5906, and r ≈ −0.907.

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.)

=

+ ???? x

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 = 31 (hundred pounds). What does the least-squares line forecast for y = miles per gallon? (Round your answer to two decimal places.)
? mpg

Toby used 40 pounds of fertilizer that she bought in bulk ($1,000 for 2,000 pounds). It took her employee 1.5 hours to spread the fertilizer (she is paid $15/hour) with the motorized spreader. Toby paid $4,000 for the spreader three years ago and it is estimated to last 10 years or 10,000 pounds. To get to the job site, a company truck and trailer was used (cost: $40,000 expected to last 10 years or 200,000 miles, the site visit was 30 miles round trip). This was the only use of the truck, trailer, and spreader for that day. Additional employee costs include 10% payroll tax and $730 per year in worker’s compensation insurance. You may assume an employee works 2,000 hours per year and Toby currently charges $2.12 per pound to spread fertilizer. Calculate the ROI for this job using the Dupont method, compare this to the RI (assuming a 10% required return). What is the required return to earn zero RI? Find this rate using Excel’s Solver function. Given this information, what would your recommendation to Toby be regarding the maximum interest rate on a loan for expanding the fertilizer operation? PLEASE SHOW FORMULAS IN EXCEL

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².

(Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)ŷ =

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

Using the Motor Trend Car Road Tests dataset mtcars, in faraway R package, fit a model with mpg: Miles/(US) gallon as the response and the other variables as predictors. (a) Which variables are statistically significant at the 5% level? For each and every test provide the null and alternative hypotheses, critical region (or rejection region), test statistics and your conclusions. (30) (b) What interpretation should be given to the coefficient for vs: Engine? (3) (c) Compute 90 and 95% confidence intervals for the parameter associated with hp: Gross horsepower and interpret the results. (6) (d) Compute and display a 95% joint confidence region for the parameters associated with wt: Weight (1000 lbs) and hp: Gross horsepower. Plot the origin on this display. The location of the origin on the display tells us the outcome of a certain hypothesis test. State that test and its outcome. (5) (e) Fit a model with just mpg: Miles/(US) gallon; cyl: Number of cylinders; and disp: Displacement (cu.in.) as predictors and use an F-test to compare it to the full model. For this test provide the null and alternative hypotheses, critical region (or rejection region), test statistics and your conclusions. Please use R, Dataset mtcars(faraway)

Lafayette Public School System has three high schools to serve a district divided into five areas. The capacity of each high school, the student population in each area, and the distance (in miles) between each school and the center of each area are listed in the table below:

(Part a - 8 points) Formulate and list the linear program for the above problem to minimize the total student-miles traveled per day. You do NOT need to solve your listed linear program.  

(Part b - 2 points) If Capedot High School will be closed to conserve the school system’s resources and its budget, how will you efficiently revise your linear program to cope with this school closing?

Please use Word or something to write your answer and show work. Thank you very much! :D

China's Galanz built a new complex at the expected cost of 2 billion yuan in order to produce 12 million air-conditioning units annually. The site was completed in 2004.
1 Make the following assumptions:

•The actual investment cost is either 1.9, 2.0, or 2.1 billion yuan, with respective probabilities of 0.25,0.50, and 0.25.
•The plant operates for 15 years, with the salvage value being either 50 million, 0, or-100 million(remediation costs) yuan at that time, with probabilities of 0.20,0.50, and 0.30, respectively.
•Finally, the net cash flow resulting from operations and sales is 60 yuan per unit. The number of units sold in each year is either 9 (0.1), 10 (0.2), 11 (0.3), or 12 (0.4) million. The figures in
parentheses represent the probabilities of the given level of production.

Assume that these are the only relevant cash flows and the interest rate is 18% per year.

a) Find an expression for the present worth (PW).

b) Find the expected value of the PW(if possible).

c) Find the standard deviation of the PW(if possible).

d)Find Pr(PW >0) (if possible).

e)Perform 200 simulations, and find the sample mean, standard deviation, as well as the probability that the investment will have a positive PW (point & interval estimates). Finally, summarize your process (which will naturally include all the appropriate steps) and results

7.15 Channel equalization. We suppose that u1, . . . , um is a signal (time series) that is trans- mitted (for example by radio). A receiver receives the signal y = c ∗ u, where the n-vector c is called the channel impulse response. In most applications n is small, e.g., under 10, and m is much larger. An equalizer is a k-vector h that satisfies h∗c ≈ e1, the first unit vector of length n + k − 1. The receiver equalizes the received signal y by convolving it with the equalizer to obtain z = h ∗ y.

(a) How are z (the equalized received signal) and u (the original transmitted signal) related? Hint. Recall that h∗(c∗u) = (h∗c)∗u.

(b) Numerical example. Generate a signal u of length m = 50, with each entry a random value that is either −1 or +1. Plot u and y = c ∗ u, with c = (1,0.7,−0.3). Also plot the equalized signal z = h ∗ y, with

h = (0.9, −0.5, 0.5, −0.4, 0.3, −0.3, 0.2, −0.1).