North Shore Inc. is considering two projects with the following probability of outcome and cash flows.

State of economy        Probability of outcome                Cash flows ($)

                                                                                       A                     B

Strong                                    0.2                                   700                550

Normal                                   0.5                                   400                400

Weak                                      0.3                                    200                300

Compute the expected net present value, standard deviation, and coefficient of variation of each of the project.

R has a number of datasets built in. One such dataset is called mtcars. This data set contains fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973-74 models) as reported in a 1974 issue of Motor Trend Magazine.

We do not have to read in these built-in datasets. We can just attach the variables by using the code

        attach(mtcars)

We can just type in mtcars and see the entire dataset. We can see the variable names by using the command

The variables are defined as follows:

mpg Miles/(US) gallon

cyl Number of cylinders

disp Displacement (cu.in.)

hp Gross horsepower

drat Rear

axle ratio

wt Weight (lb/1000)

qsec 1/4 mile time

vs V/S (“V” engine or “Straight line”) (0 or V, 1 for S)

am Transmission (0 = automatic, 1 = manual)
gear Number of forward gears
carb Number of carburetors

We want to model mpg by some or all of the other 10 variables . Do a complete regression analysis. Be sure to comment for each thing you do.

Suppose a prototype for a car was in development. This car has 6 cylinders, 250 cubic in. engine, 130 horsepower, a rear axle ratio of 3.8, weighs 2750 pounds, has a 1/4 mile time of 15.9 seconds, is a V engine type, has automatic transmission, 5 forward gears, and 6 carburetors. With 90% confidence, what is an interval estimate for the predicted mpg for this car?

A principal has different options of setting wages and the Agent has different levels of work. Consider this model with the following special values:

u(2√w); d_H=15, d_L=0, g=300, m=200, b=100, w_b=wage base=0

e_H results in a probability of profit levels g, m, b as 0.5, 0.3, 0.2

e_L results in a probability of profit levels g, m, b as 0.2, 0.3, 0.5

Assuming the Principal chooses a pure wage scheme, what would be the expected payoffs for the Principal and the Agent?

Assuming the Principal chooses a pure franchise scheme, what would be the maximum franchise fee? What would be the expected payoffs for the Principal and the Agent?

Assuming the Principal chose a wage plus bonus scheme, what is the minimum bonus to induce e_H? What would be the expected payoffs for the Principal and the Agent? Assume the bonus is awarded only for good, not for medium.

In this scenario, what should the Principal choose to do?

Calculate the theoretical yield of this Williamson Ether Synthesis:

Materials:

25 mL Erlenmeyer flask with stir bar

0.8 mL (0.83g) p-cresol

0.7 mL 1-bromopropane

50 mg (0.05g) t-butyl ammonium bromide

-Add all reagents at room temperature, reflux ~1hr at a 3 setting on a hotplate, cool to room temperature

Workup:

- add 5 mL diethyl ether

-etc.

-etc.

-etc....

Suppose that there are two industries, A and B. There are five firms in industry A with sales at $5 million, $2 million, $1 million, $1 million, and $1 million, respectively. There are four firms in industry B with equal sales of $2.5 million for each firm. The four-firm concentration ratio for industry A is:

A. 0.9.
B. 1.0.
C. 0.8.
D. 0.7.

I don't understand why the answer is 0.9 can someone explain to me.

Design and implement an interactive program named trip.c that collects information about the user's car and planned travel, and reports back useful information.

The dialog below shows exactly what data should be collected as input and reported as output.

Some Hints to get started /* Not tested not complete code Just to get you started

*/ #include

/* FUNCTION PROTOTYPES */

void WelcomeMessage();

void AskUserForInput(); /* ask and check whether user wants to continue if wants to continue gather information and calculate the results (optional create more functions) */

void PrintTripSummary(float fuel, float minCost, float maxCost, float travelMiles); /* could call this from AskUserForInput(); In a loop and feed it the user input */

/* MAIN */

int main() {

/* Call the functions */

return 0;

}

You do not need to verify user input data. Presume that the user enters reasonable/correct data.

Although you might want to test the results of entering "interesting data" such as alpha data instead of numeric.

Below is the program output. Black is used to illustrate the output, while regular text shows user Input.

Welcome to the Trip Planner!

So you are ready to take a trip? Let me help you plan for your fuel costs and required stops to fill up your tank. ============================================================

Please provide answers to the prompts below and I will display a summary for you when I have computed the results. ============================================================

Please input your car's average miles per gallon (enter 0 to quit) >> 16

Please tell me the range of fuel costs you expect to pay (per gallon).

The lowest per gallon cost of fuel is >> 4.17

The highest per gallon cost of fuel is >> 5.20

Please tell me how many miles you plan to travel >> 900

=============== Trip Summary ==================

You will need to purchase approximately 56 gallons of fuel.

The approximate cost of fuel for your trip is between $235 and $293

=============== End Trip Summary ==================

Please input your car's average miles per gallon (enter 0 to quit) >> 11

Please tell me the range of fuel costs you expect to pay (per gallon).

The lowest per gallon cost of fuel is >> 4.17

The highest per gallon cost of fuel is >> 5.20

Please tell me how many miles you plan to travel >> 1300

=============== Trip Summary ==================

You will need to purchase approximately 118 gallons of fuel.

The approximate cost of fuel for your trip is between $493 and $615

=============== End Trip Summary ==================

Please input your car's average miles per gallon (enter 0 to quit) >> 0

Thank you, please drive safely and have a nice trip!

In this discussion, you will apply the statistical concepts and techniques covered in this week's reading about correlation coefficient and simple linear regression. A car rental company wants to evaluate the premise that heavier cars are less fuel efficient than lighter cars. In other words, the company expects that fuel efficiency (miles per gallon) and weight of the car (often measured in thousands of pounds) are correlated. Performing this analysis will help the company optimize its business model and charge its customers appropriately.

In this discussion, you will work with a cars data set that includes two variables:

• Miles per gallon (coded as mpg in the data set)
• Weight of the car (coded as wt in the data set)

The random sample will be drawn from a CSV file. This data will be unique to you, and therefore your answers will be unique as well. Run Step 1 in the Python script to generate your unique sample data.

In your initial post, address the following items:

1. You created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. Does the graph show any trend? If yes, is the trend what you expected? Why or why not? See Step 2 in the Python script.
2. What is the coefficient of correlation between miles per gallon and weight? What is the sign of the correlation coefficient? Does the coefficient of correlation indicate a strong correlation, weak correlation, or no correlation between the two variables? How do you know? See Step 3 in the Python script.
3. Write the simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable. How might the car rental company use this model? See Step 4 in the Python script.
4. What is the slope coefficient? Is this coefficient significant at a 5% level of significance (alpha=0.05)? (Hint: Check the P-value, , for weight in the Python output.) See Step 4 in the Python script.

<Figure size 640x480 with 1 Axes>

    mpg        wt
mpg  1.000000 -0.863527
wt  -0.863527  1.000000

 OLS Regression Results                            
==============================================================================
Dep. Variable:                    mpg   R-squared:                       0.746
Model:                            OLS   Adj. R-squared:                  0.737
Method:                 Least Squares   F-statistic:                     82.10
Date:                Fri, 02 Oct 2020   Prob (F-statistic):           8.10e-10
Time:                        12:39:57   Log-Likelihood:                -75.289
No. Observations:                  30   AIC:                             154.6
Df Residuals:                      28   BIC:                             157.4
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     37.1346      1.960     18.944      0.000      33.119      41.150
wt            -5.2638      0.581     -9.061      0.000      -6.454      -4.074
==============================================================================
Omnibus:                        2.644   Durbin-Watson:                   2.405
Prob(Omnibus):                  0.267   Jarque-Bera (JB):                2.104
Skew:                           0.643   Prob(JB):                        0.349
Kurtosis:                       2.832   Cond. No.                         12.7
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Comment on the relationship between 1920s-1940s economics and today's economic conditions. Are there any similarities that you notice? Any key differences?

Estimate the mass of the Sun from the orbital period of the Earth (it’s presumed you know what this is !) and the Earth’s orbital radius of 93 million miles. If the Sun’s radius is 109 times that of the Earth, what is the Sun’s mean density? What is the acceleration due to gravity on the Sun’s surface? Is it sensible to go and measure this at night?