first read through the requirements then bid, Do not vast your time and my as well

The solution need to be in R not in excel. Also I need proper documentation in the code itself to explain the solution.

Above every solution paste the question as well.

Overview: Regression and Beta

According to the famous CAPM, the returns of a stock are linearly correlated with its market returns. Usually, we consider the relationship of the excess stock returns versus the excess market returns.

Where,

· Ri is the return from the ith stock

· Rf is the risk-free rate of return

· β represents exposure to broad market risk

· α(alpha) is the excess returns generated by the stock when compared to the broad market return

· Rmkt is the return obtained from broader market

Considering only excess returns over and above the risk-free rate, the preceding equation could be rewritten as follows:

1. Download data for last 1 year for the DJIA (Dow Jones Industrial Average) and all its 30 constituent stocks. Download data from an appropriate financial website such as Google Finance, Yahoo Finance, Quandl, CityFALCON, or another similar source.

2. Calculate daily returns of the DJIA index and the downloaded stocks over the period under study

3. Considering the equation form provided above and matching the Index returns vs. the returns of one of its constituent stocks at a time, perform linear regression fits and calculate α(alpha) and β values for each stock

4. Graphically represent the distribution of α(alpha) and β values for the constituents of DJIA

I – 25 QUESTIONS

1. If p = 0.25 and n = 1000, considering the binomial probability distribution, what is the mean?

4

250

500

750

2. If p = 0.25 and n = 1000, considering the binomial probability distribution, what is the standard deviation?

1000*0.25*(1-0.25)

1000*0.25

√(1000*0.25(1-0.25))

1000*(1-0.25)

3. A particular process has a uniform probability distribution between 10 and 20. What is the probability that the process is between 15 and 20?

(20-15)/(20-10)

(20-10)/(20-15)

15/20

10/20

4. What does the following equation equal?

∫[e^x] dx

x(e^x)-x + C

x(e^x)-1 + C

x + C

e^x + C

5. If X has a uniform distribution from a to b, then what is the expected value of X?

b - a

a + b

(a + b) / 2

(b – a) / 2

6.

What is the expected value of the following partial probability distribution for X? x--- p(x)

0 --- 1/5

1 ---1/10

2 --- 1/10

3 ---2/5

E(X) = 0 + 1 + 2 + 3

E(X) = 0*(1/5) + 1*(1/10) + 2*(1/10) + 3*(2/5)

E(X) = (1/5) + (1/10) + (1/10) + (2/5)

E(X) = (0*(1/5) + 1*(1/10) + 2*(1/10) + 3*(2/5))/(0 + 1 + 2 + 3)

7. A probability experiment is a binomial experiment if which of the following is true?

The experiment is performed n dependent times. Each repetition is called a trial.

Probability of success is different for each trial

There are two mutually exclusive outcomes: success or failure

image28.jpg

Probability of success is the same for each trial

8. Which of the following is the standard form distribution?

μ = σ = 0

μ = 1 and σ = 0

μ = 0 and σ = 1

μ = 0 and σ = 2

9. What is the equation for standardizing a normal random variable?

Z = (X + μ) / σ

Z = 2X / σ

Z = (X - μ) / σ

Z = μ / σ

10. What is the Normal Probability Density Function when μ=0 and σ=1?

f(x)=e(-x^2)/√(2π)

f(x)=e(-(2x)2/2)/√(2π)

f(x)=e(-x)/√(2π)

f(x)=e(-x2/2)/√(2π)

11. Poisson distribution a=3 and t=20. What is the mean (λ) and standard deviation (σ)?

λ=mean=a*t=3*20=60; σ=√λ=√60

λ=mean=a*t=3*20=60; σ=λ=60

λ=mean=t/a=20/3; σ=√λ=√(20/3)

λ=mean=t/a=20/3; σ=t/a=20/3

12. a=1, t=2. Considering the Poisson distribution, what does P(X=1) equal?

P(X=1) = (1 / 2 * e-2)/1!

P(X=1) = (2 * e-2)/1!

P(X=1) = 2 /e-2

P(X=1) = e-2/1!

13. Which of the following about the probability histogram is true?

Has probabilities on the vertical scale

1≤P(x)≤2

∑P(x) = 0

Is only used for imaginary numbers

14. Given 50 test scores with a mean of 100 and a standard deviation of 10, the value that separates the top 10% is

______________, where z=1.28.

1.28 * 10 / √(50) + 100

1.28 * 1 / √(50) + 100

1.28 * 100 / √(50)

None of the above

15. For samples of size n smaller than 30, distribution of the sample means can be approximated by a _______________

distribution if the original data is fairly close to _______________.

t Student; t Student

F; F

normal; normal

uniform; uniform

16. Which of the following consists of an interval of numbers based on a point estimate?

Confidence interval

Point estimate

Regression

Correlation coefficient

17.

Given a survey of 1,000 people, it was found that 200 invest in securities. Based on this sample, what is the point estimate?

1000/200

200*1000

1000

200/1000

18. What is the value of a statistic that estimates the value of a parameter?

Confidence interval

Point Estimate

Trend line

Error

19. Which of the following are characteristics of a Chi-Square Distribution? (Choose all that apply)

It is symmetric

The shape of the chi-square distribution depends on the degrees of freedom, just like Student’s t-distribution

As the number of degrees of freedom increases, the chi-square distribution becomes more nearly symmetric

image76.jpg

The values of X2 are negative

20. Which of the following statements for problems involving chi-square are correct?

If I have 90% degree of confidence, I would have 5% in each tail

For the right tail critical value, I would look at the area to the right of the 90% in the middle, in this case it would be 5% or 0.05

For the left tail critical value, I would look at the area to the right of the 5% on the left side, in this case it it would be 95% or 0.95

21. Which of the following statements are correct?

Dependent samples are often referred to as matched pairs. It is possible for an individual to be matched against him or herself.

A sampling method is independent when the individuals selected for one sample do not dictate which individuals are to be in a second sample

A sampling method is dependent when the individuals selected to be in one sample are used to determine the individuals in the second sample

22. Given a survey of 1,000 investment companies, it was found that 700 invest in derivatives. Based on this sample, what is the point estimate?

700/1000

1000/700

exp(700/1000)

ln(700/1000)

23. We wish to estimate the mean age of traders in London with 95% confidence within 0.5 years, how many traders should we sample assuming the sample standard deviation from last year was 1.5 where z = 1.96?

1.96/0.5

((1.96*1.5)/0.5)

((1.96*1.5)/0.5)2

(1.96)2

24. The _______________ is the probability, assuming that H0 is true, of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed.

z test statistic

normal distribution

null hypothesis

p-value

25. Which of the following statements for a hypothesis test for a population mean with sigma known are correct?

The sample has no outliers, and the population from which the sample is drawn is normally distributed or the sample size, n, is large (n≥30)

The sampled values are independent of each other

The sample is obtained using simple random sampling or from a randomized experiment

Final Check Save You have used 0 of 1 submissions

II – Read and answer the highlighted question

Dangers of a Little Bit of Statistics Knowledge

It has always been a huge issue with administration at the college where I teach mathematics on how to lower the DWF rate in developmental math (percent of students who get a D, W, or F in a course). Administration pushed for acceleration of these courses. A typical pathway through developmental math at the college was Pre-Algebra -> Elementary Algebra -> Intermediate Algebra -> College Algebra.

Administration decided that all of our developmental math should be accelerated. They wanted data to justify this change. At that time no research provided data to back up this decision yet administration was insistent on having this data so I pulled all the data from three semesters for developmental math and performed a hypothesis test that is described below.

“The DWF% for these three semesters was 49.9%. The breakdown per semester is:

Semester	DWF%
Fall 2012	52.19%
Spring 2013	51.8%
Fall 2013	45.9%

{I have taken out the actual data that I presented to administration including the total number of students, total that received an A, B, or C and the total that received a D, F, or W.}

In testing the claim that the percent of students that succeeded in fall 2013 was greater than fall 2012 at significance level of .01 shows that the percent was significantly greater with p = 0.0096. Assuming we can compare one set of students from one semester to another semester then the major change that was made was the addition of the accelerated course: EBM4404 Elementary Algebra with Review. While it had a huge spike (anomaly?) in spring 2013, the DWF% in Fall 2013 dropped to record lows. Our own data supports the following idea:

Acceleration in math increases success so our regular development math courses need to be transitioned into an accelerated format.”

Administration was very pleased with my results. One vice president sent the results to her “statistics person” and they verified that I was correct on my statistics (which I was on the mechanics of the calculations). The other statistics instructor commented on one problem but not the main problems. I was very wrong in many ways on this claim though. After reading the material in the book and watching the videos, explain why administration should have questioned the above and perhaps why my results should have been discarded. This is another example of how a little bit of knowledge of statistics can be dangerous. Why do you think administration accepted my conclusion?

III - Do the following

1. Pick two separate corporations and from www.nasdaq.com, pick the “historical quote” option and randomly select 30 opening stock prices for the last two years. Place the data into an Excel spreadsheet and outline your sampling method in the main Word document for the project.

2. Determine a claim (prior to analyzing the descriptive statistics) based on two population means/samples.

3. Calculate the descriptive statistics for the two separate corporations. The distribution shape should be analyzed to determine the appropriate descriptive statistics to use (mean/standard deviation versus median/IQR). The graph should be included in the main Word document for the project. Find the appropriate descriptive statistics and place this in the Word document noting any outliers or any irregularities discovered.

4. Conduct the hypothesis test based on the claim from item 2. Outline all the specifics in the Word document describing your conclusion. Note any possible reasons for the results. This might include some research on the corporations chose in item 1.