3300 Econometric HW

Problem 2.

Use the data in the “Autocorrelation” tab to test

1. For Autocorrelation using the Durbin Watson Test

2. Graph the Residuals and determine whether they are distributed normally or whether they are biased

****C language****

char lName[][15] = {"Brum","Carroll","Carter","Dodson","Garbus", "Greenwood", "Hilliard", "Lee", "Mann", "Notz", "Pastrana", "Rhon", "Rodriguez", "Wilson", "Zimmerman"};

char fName [][15] = {"Natalie","Cody","Sophia","Dominic","Chandler","Caleb","Sydnee","Peyton","Brianna","Zachery","Kevin","Luke","Juan","Kelci","Adam"};

char middleInitial[15]={'N','L','X','L','O','L','M','B','S','T','J','C','P','D','Z'};

char dob[][11]={"05/27/1935","11/27/1971","10/17/2003","12/08/1990","11/25/1991","10/30/1992","09/22/1993","08/04/1994","07/11/1995","06/18/1996","05/28/1997","04/07/1998","03/12/1999","02/23/2000","01/15/2001"};

How would we make a list ordered by their age, oldest first, Print the patient's full name and then their age.  Left justify the name and right justify the age.

Example:
Johnson, Fred N 80

**Half of the code is provided**

int patientAge[15] = {0};

for(int p = 0; p <15; p++)
{
int year = ((dob[p][6] - '0') * 1000) + ((dob[p][7] - '0') *100) + ((dob[p][8] - '0') * 10) + ((dob[p][9] - '0') * 1);

patientAge[p] = 2019 - year;
printf("%s, %s %c Age: %d\n",lName[p], fName[p], middleInitial[p], patientAge[p]);
}

USING MATLAB:

Using the data from table below fit a fourth-order polynomial to the data, but use a label for the year starting at 1 instead of 1872. Plot the data and the fourth-order polynomial estimate you found, with appropriate labels. What values of coefficients did your program find? What is the LMS loss function value for your model on the data?

The data from Exhibit 3 is also in the Excel file income.xls on the course website. Use Excel, along with this file, to determine Mrs. Bella’s real income for the last fifteen years. Do this by first converting each price index from percent by dividing by 100. Then, divide gross income by your converted (adjusted) price index. Using Excel, find the mean, median, standard deviation, and variance of her past real income. Explain the meaning of these statistics. Can you use mean income to forecast future earnings? Take into account both statistical and non-statistical considerations.

Concert Nation] Concert Nation, INC. is a nationwide promoter of rock concerts. The president of
the company wants to develop a model to estimate the revenue of a major concert event at large venues
(such as Ford Field, Madison Square Gardens) for planning marketing strategies. The company has
collected revenue data of 32 recent large concert events. For each concert, they have also recorded the
attendance, the number of concession stands in the venue, and the Billboard chart of the artist in the
week of each event. This data is available in “Tickets”. They have two potential models that could
explain the revenue. The two competing models are:

Model A: ??????? = ?? + ???????????? + ???????????? + ??????????? + ?0123?

Model B: ??????? = ?? + ???????????? + ??????????? + ?012?

Run regression on both models. Use only the regression outputs of the two models and the original data
to answer questions 1 to 7 below.
1. [1 pt] Let’s consider the model A first. What does the result of F-test indicate?
(a) The p-value of F-test is 100.83. Thus, the model does not significantly explain the revenue.
(b) The p-value of F-test is close to zero. Thus, all independent variables in the regression model are
statistically significant.
(c) The p-value of F-test is close to zero. This indicates that at least some independent variables in the
regression model significantly explain the revenue.
(d) This indicates weak evidence of a linear relationship, because the p-value is very low.
2
2. [1 pt] If we use model A for prediction, what is the point estimate for the revenue of a concert that has
attendance of 50,000 people, 5 concession stands, and the song ranked in no. 15 in the Billboard ranking?
(a) $3.145 M
(b) $2.851 M
(c) $3.252 M
(d) $340K
3. [1 pt] What is an approximate 95% prediction interval for the concert listed in the previous question?
(a) [$2.757M, $3.533M]
(b) [$2.463M, $3.239M]
(c) [$2.368M, $3.922M]
(d) [$2.074M, $3.628M]
4. [1 pt] Which of the following statement is correct?
(a) The estimated slope for the attendance is only $59.2. This means that, when keeping everything
else the same, the revenue does not depend much on the attendance.
(b) The t-statistic associated with the slope for the attendance variable is 16.9. This means that there is
too much noise to determine if the slope is definitely positive.
(c) The p-value for the concession variable is 0.933. This means that the number of concession stands
is not a statistically significant variable to determine the revenue.
(d) The p-value for the concession variable is 0.933. This means that the number of concession stands
is a statistically significant variable to determine the revenue.
5. [1 pt] Is it appropriate to use model A as a final model to estimate the revenue of a concert?
(a) Yes. All independent variables are statistically significant.
(b) Yes, because the analysis indicates a linear relationship between revenue and attendance.
(c) No, because not all independent variables are statistically important. Thus, revision is necessary.
(d) No, because some of the slopes were negative. Thus, revision is necessary.
3
6. [1 pt] Now, consider model B. According to model B, what is a point estimate for a concert that has
attendance of 50000 people, 5 concession stands, and the song ranked in no. 15 in the Billboard ranking?
(a) $3.147M
(b) $2.839M
(c) $7.139M
(d) $13.637M
7. [1 pt] Based on the regression outputs, which model would you consider more suitable for predicting the
revenue between the two models– Model A and Model B?
(a) Model A is more suitable, because it has a higher ?2, lower standard error of the estimates
(??), and lower F-test p-value.
(b) Model A is more suitable because the fraction of SST accounted for by the residuals is higher than
for model B.
(c) Model B is more suitable, because, while both models have similar ?2 and F-test p-value, model B
has lower standard error of the estimates (??) and all independent variables are statistically
significant.
(d) Model B is more suitable, because the slope coefficient is larger in magnitude.

6.    Fred is a teenager who likes to listen to music and to play games on his computer. Suppose that he has an annual entertainment budget of $144 and that each music CD costs $12 and each computer game costs $24.

Quantity Consumed                   Total Utility                    Total Utility

     (per year)                             of Music CDs                of Computer Games

            0                                           0                                     0

            1                                       200                                 160

            2                                       236                                 232

            3                                       268                                 296

            4                                       296                                 352

            5                                       320                                 400

            6                                      340                                 440

            7                                       344                                 472

1. Calculate the marginal utility of each unit of music CDs and computer games.
2. Using the prices mentioned above, calculate the marginal utility per dollar of music CDs and computer games. Round to two decimal places.
3. What much of each good will Fred purchase to maximize satisfaction? (Find the utility-maximizing combination of music CDs and computer games.)
4. What is the total amount of utility that Fred will receive when he consumes the combination computed in Part C, i.e. the total utility from the music CDs plus the total utility from the computer games?
5. Given your answer in C, explain why buying two more music CDs and 1 less computer game makes Fred worse off.

1. Adam works for Marnie. Jessa is injured through Adam's negligence. Marnie may be liable to Jessa if Adam’s conduct occurred

a. in the course and scope of Adam's employment.

b. during normal working hours.

c. outside the parties' employment relationship

d. is Adam had done it before but even if Marnie could not have known it.

2. Allie hires Lon to act as her agent to purchase The Notebook Company. Allie tells Lon to reveal that he is buying the gym on behalf of a third party and to tell the seller who that third party is. Allie is

a. an undisclosed principal.

b. a partially disclosed principal.

c. an apparent principal.

d. a disclosed principal

3. Tito is a editor for Entertainment Comic Books, Inc. Tito has a detailed job description, must work certain hours in his office, and must follow particular rules about how to edit the comics he receives from the artists and authors. Tito most likely is

a. an employee.

b. an independent contractor.

c. a principal.

d. an employer

4. Ryan and Miranda put their agency agreement into a written document that describes the rights and duties of both parties. Ryan, as the agent, has

a. apparent authority.

b. express authority.

c. equal authority.

d. implied authority

The managing director of SleekMode Enterprises, a medium sized firm, are the operators of a number of theme parks in a number a major cities across the country. The theme parks include facilities such as children’s play grounds, cinema halls, roller-coaster rides, restaurants and boat rides, among other attractions. Yeovil Mootooma, the chief marketing officer, has the task of increasing visitor numbers at the company’s theme parks across the country. The company has experienced consistent declines of about 5% in the last three fiscal years. This has led to significant falls in the company’s earnings per share. Yeovil Mootooma has turned to you unearth the possible factors the company needs to addresstoturnaroundthecompany’sfortunes. YourpreliminarymeetingswithYeovilMootooma suggests that the company has no direct competitors in terms of theme parks. However, it seemshouseholdsareattracted to other channels of family entertainment that has turned visitors away from the company’s theme parks. You are also made aware that there is a difference in the patronage of the current services in different parts of the country.

(a) What research questions (decision problems) does Yeovil Mootooma problem present?

(b) Outline a research design you would conduct to provide Yeovil Mootooma with the answers neededtodevelopastrategytochangethecompany’svisitor trend. Your response should provide justification for each action that would be undertaken.