A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.  Use the estimated regression equation developed in part (c) to develop a 95% confidence interval for the expected number of days absent for employees living 5 miles from the company (to 1 decimal). Least squares equation from part c:
Days Absent = 7.269 + -0.194 Distance

Write MATLAB script programs to perform the following conversions, taking a value in SI units as the input argument and returning the value to US Customary Units.

a. Length: Centimeters to inches

b. Temperature: °C to °F

c. Force: Newton to Pound-force

d. Speed: Meters per second to miles per hour

Write MATLAB functions to perform the following conversions, taking a value in SI units as the input argument and returning the value to US Customary Units.

a. Length: Centimeters to inches

b. Temperature: °C to °F

c. Force: Newton to Pound-force

d. Speed: Meters per second to miles per hour

Provide the source code and use the following data:

a. 5 centimeter

b. 10 °C

c. 100 Newtown

d. 100 Meters per second

R-Studio (R Programming Language)

1. How would you create a vector `V` containing the values 0, 0.25, 0.5, 0.75, and 1?
  
```{r}
#insert your code
```

2. Name the elements of `V`: first, second, middle, fourth, last. Describe two ways of naming elements in `V`

```{r}
#insert your code
```

3. Suppose you keep track of your mileage each time you fill up. At your last 6 fill-ups the mileage was
65311 65624 65908 66219 66499 66821 67145 67447. Enter these numbers into R as vector `miles`. Use the function `diff` on the data `miles`. What does it give? Use `sum` on the computed differences to find the total travelled distance.

```{r}
#insert your code
```

5. In detail, summarize what the information that a five-number summary for the variable Per Capita Income provides for the City of Chicago.

Let a firm’s production function be given by K^0.7 L^0.3.
(i) Sketch (without specific numbers) the shape of the long run average and long-run marginal cost curves of the firm; explain the key features of the sketch.
(ii) in the same graph, please also sketch the firm’s short run average and marginal cost curves (when the amount of capital is fixed). Comment on the relationship between the long- and the short-run curves depicted in your graph.

The price elasticity of demand has been identified for nine markets: Salt: 0.1; Gasoline, short-run: 0.2; Gasoline, long-run: 0.7; Automobiles, long-run: 0.2; Chevrolet automobiles: 4; Coffee: 0.25; Restaurant meals: 2.3; Airline travel, short-run: 0.1; Airline travel, long-run: 2.4.

Which of the goods listed would be considered price elastic? Price inelastic? What do the goods that are price inelastic have in common? Why is the price elasticity of demand for automobiles 0.2, but the price elasticity of demand for Chevrolet automobiles is 4.0? Why is the long-run elasticity of demand for gasoline different from the short-run elasticity of demand?

i.Based on the Fama-French model, calculate the required return for HSU Limited using these estimates. Assume that the Treasury billrate is 5 percent. (4marks)

ii. What do you know about HSU Limitedbased on its factor sensitivities?(6marks)

For a newsvendor product the probability distribution of demand X (in units) is as follows:

xi 0 1 2 3 4 5 6
pi 0.05 0.1 0.2 0.3 0.2 0.1 0.05

The newsvendor orders Q = 4 units.

a) Derive the probability distributions and the cumulative distribution functions of lost sales as well as leftover inventory.

b) Knowing that the expected total cost function is convex in the order quantity Q, demonstrate that Q = 4 gives the minimal expected total cost.

The number X of cars that Linda hopes to sell has the distribution:

Cars sold    0   1    2   3

Probability 0.2 0.1      0.3    0.4

Find the mean and standard deviation of X.

A cereal manufacturer has two new brands of cereal which it would like to produce. Because resources are limited, the cereal manufacturer can only afford to produce one of the new brands. A marketing study produced the following probability distributions for the amount of sales for each of the new brands of cereal.

a. What are the expected sales of each of the new brands of cereal?

b. What is the standard deviation of the sales for each of the brands of cereal?

c. If both of the brands of cereal cost the same amount to produce, which brand of cereal do you think the cereal manufacturer should produce? Explain.