***Use R/STATA to perform the following analysis

Data: ShareValue.xlsx contains data on N=309 firms which sold new shares. Data on the following variables is provided. All variables are measured in millions of US dollars. ShrVal is the dependent variable and the all the remaining variables are the explanatory variables.

ShareValue: the total value of all shares outstanding, calculated as the price per share times the number of shares outstanding.

FirmDebt: firm’s long-term debt

TotalSales: sales of the firm.

Net_Income: net income of the firm.

TotalAssets: book value of the assets of the firm

1. Undertake appropriate basic data analytics to motivate the regression model above.

2. Using the dataset provided, run the above described regression model and interpret all regression coefficients.

3. Do you suspect any multicollinearity problem could affect the regression coefficients?

5. Use graphical method or a test of heteroscedasticity to check for evidence of heteroscedasticity in part 2.

6. Test the following hypothesis:

(a)     Is your regression model a significant predictor of share value variations for the sample of firms you are given?

(b)     Test that increasing sales by 20 million dollars, everything else held constant, would raise the share value by at least 5 million dollars;

(c)      Test the fact that jointly, a firm’s total assets and its outstanding debts better left out of this regression (Beta_TotAssets = Beta_Debt =0)

Use the Breusch-Pagan test to see if there is heteroskedasticity in this regression.

Use the White test to see if there is heteroskedasticity in this regression.

You should have found that heteroskedasticity is present. Using the strategy for "Log transforming the Model" investigate whether using a “double-log model” fixes the heteroscedasticity problem? For your transformed regression, state how the coefficients should be interpreted.

Does dividing the original (“levels”) model’s all variables by the FirmDebt variable fix the heteroskedasticity problem? For your transformed regression, state how the coefficients should be interpreted.

Using heteroskedasticity consistent estimator (HCE or White robust estimator). Estimate the regression model using one HCE.

Of the regressions in questions 9, 10, 11, which would you use as your preferred specification for inclusion for this particular project?

Before each class, I either drink a cup of coffee, a cup of tea, or a cup of water. The probability of coffee is 0.7, the probability of tea is 0.2, and the probability of water is 0.1. If I drink coffee, the probability that the lecture ends early is 0.3. If I drink tea, the probability that the lecture ends early is 0.2. If I drink water, the lecture never ends early.
1) What’s the probability that I drink tea and finish the lecture early?
2) What’s the probability that I finish the lecture early?
3) Given the lecture finishes early, what’s the probability I drank coffee?

Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow:

Required:

Use the step method to allocate the service costs, using the following:

a. The order of allocation starts with Maintenance.

b. The allocations are made in the reverse order (starting with Cafeteria).

The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it​ best? Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not?

Tar   Nicotine   CO
5   0.5   3
15   1.0   19
17   1.1   16
14   0.7   19
14   0.8   19
14   1.0   13
15   1.0   16
14   1.1   14
15   1.2   15
8   0.8   12
13   0.8   18
12   0.8   16
12   0.8   18
15   1.0   17
2   0.3   3
16   1.1   17
15   1.0   14
13   0.7   19
13   1.1   14
15   0.9   16
15   1.1   14
15   1.1   16
8   0.6   8
18   1.3   17
14   1.1   13

Find the best regression equation for predicting the amount of nicotine in a cigarette. Use predictor variables of tar and/or carbon monoxide​ (CO). Select the correct choice and fill in the answer boxes to complete your choice.

A. Nicotine = __ + (__) Tar + (__) CO

B. Nicotine = __ + (__) Tar

C. Nicotine = __ + (__) CO

Consider the system modeled by the differential equation

                              dy/dt - y = t    with initial condition y(0) = 1

the exact solution is given by y(t) = 2et − t − 1

Note, the differential equation dy/dt - y =t can be written as

                                              dy/dt = t + y

using Euler’s approximation of dy/dt = (y(t + Dt) – y(t))/ Dt

                              (y(t + Dt) – y(t))/ Dt = (t + y)

                               y(t + Dt) = (t + y)Dt + y(t)

                              New Value = change + current value

1. Using R implement Euler’s method directly to numerically solve the equation and construct a Table as below – list data to four digits past the decimal point. Submit your R session

               time     ∆t = 0.1           ∆t = 0.0001        Exact Value       %Relative                  %Relative

                                                                                                             Error ∆t = 0.1       Error ∆t = 0.0001                    

                  0

                 0.1

                 0.2

                 0.3

                 0.4

                 0.5

                 0.6

                 0.7

                 0.8

                 0.9

                 1.0

(a) Calculate the five-number summary of the land areas of the states in the U.S. Midwest. (If necessary, round your answer to the nearest whole number.)

(b) Explain what the five-number summary in part (a) tells us about the land areas of the states in the midwest.

(c) Calculate the five-number summary of the land areas of the states in the U.S. Northeast. (If necessary, round your answer to the nearest whole number.)

(d) Explain what the five-number summary in part (c) tells us about the land areas of the states in the Northeast.

(d) Contrast the results from parts (b) and (d).

A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean 60 thousand miles and a standard deviation of 11 thousand miles.

How many miles will be traveled by at least 65% of the truck?
The number of miles that will be traveled by at least 65% of the truck is ____ miles

The data in the below portion of a frequency distribution shows the amount of miles run per day by people in a running club. What is the mean of the grouped data?

Miles (per day)            Frequency

1-2                               22

3-4                               30

5-6                               3

7-8                               28

9-10                             5