Download the dataset returns.xlsx. This dataset records 83 consecutive monthly returns on the stock of Philip Morris (MO) and on Standard & Poor’s 500 stock index, measured in percent. Investors might be interested to know if the return on MO stock is influenced by the movement of the S&P 500 index. Please be aware that return is defined as new price − old price old price × 100%, so it is always reported as a percentage.
6. Fit a linear regression model for this dataset and verify that the least-squares regression line is ˆy = 0.3537 + 1.1695x. Also record the values of the regression standard error, sample correlation, and coefficient of determination. Interpret the coefficient of determination in context.
7. Calculate a 95% confidence interval for the slope of the regression line. What is the margin of error for this interval? Interpret this interval in context.
8. Perform a hypothesis test to see if there is a linear relationship between the two variables. Be sure to write the null and alternative hypotheses, calculate the test statistic, find the p-value and critical value, and state an appropriate conclusion. Round to 4 decimal places.
9. Calculate a 95% confidence interval for the mean monthly returns on the stock of Philip Morris when the S&P stock index is 3.0. Interpret this interval in context.
10. Calculate a 95% prediction interval for the monthly return on the stock of Philip Morris when the S&P stock index is 3.0. Interpret this interval in context.
| MO | S&P |
| -5.7 | -9 |
| 1.2 | -5.5 |
| 4.1 | -0.4 |
| 3.2 | 6.4 |
| 7.3 | 0.5 |
| 7.5 | 6.5 |
| 18.6 | 7.1 |
| 3.7 | 1.7 |
| -1.8 | 0.9 |
| 2.4 | 4.3 |
| -6.5 | -5 |
| 6.7 | 5.1 |
| 9.4 | 2.3 |
| -2 | -2.1 |
| -2.8 | 1.3 |
| -3.4 | -4 |
| 19.2 | 9.5 |
| -4.8 | -0.2 |
| 0.5 | 1.2 |
| -0.6 | -2.5 |
| 2.8 | 3.5 |
| -0.5 | 0.5 |
| -4.5 | -2.1 |
| 8.7 | 4 |
| 2.7 | -2.1 |
| 4.1 | 0.6 |
| -10.3 | 0.3 |
| 4.8 | 3.4 |
| -2.3 | 0.6 |
| -3.1 | 1.5 |
| -10.2 | 1.4 |
| -3.7 | 1.5 |
| -26.6 | -1.8 |
| 7.2 | 2.7 |
| -2.9 | -0.3 |
| -2.3 | 0.1 |
| 3.5 | 3.8 |
| -4.6 | -1.3 |
| 17.2 | 2.1 |
| 4.2 | -1 |
| 0.5 | 0.2 |
| 8.3 | 4.4 |
| -7.1 | -2.7 |
| -8.4 | -5 |
| 7.7 | 2 |
| -9.6 | 1.6 |
| 6 | -2.9 |
| 6.8 | 3.8 |
| 10.9 | 4.1 |
| 1.6 | -2.9 |
| 0.2 | 2.2 |
| -2.4 | -3.7 |
| -2.4 | 0 |
| 3.9 | 4 |
| 1.7 | 3.9 |
| 9 | 2.5 |
| 3.6 | 3.4 |
| 7.6 | 4 |
| 3.2 | 1.9 |
| -3.7 | 3.3 |
| 4.2 | 0.3 |
| 13.2 | 3.8 |
| 0.9 | 0 |
| 4.2 | 4.4 |
| 4 | 0.7 |
| 2.8 | 3.4 |
| 6.7 | 0.9 |
| -10.4 | 0.5 |
| 2.7 | 1.5 |
| 10.3 | 2.5 |
| 5.7 | 0 |
| 0.6 | -4.4 |
| -14.2 | 2.1 |
| 1.3 | 5.2 |
| 2.9 | 2.8 |
| 11.8 | 7.6 |
| 10.6 | -3.1 |
| 5.2 | 6.2 |
| 13.8 | 0.8 |
| -14.7 | -4.5 |
| 3.5 | 6 |
| 11.7 | 6.1 |
| 1.3 | 5.8 |
In: Statistics and Probability
The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.
1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4
(a) Use a calculator with mean and standard deviation keys to find x bar and s (in percentages). (For each answer, enter a number. Round your answers to two decimal places.) x bar = x bar = % s = %
(b) Compute a 90% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit %
(c) Compute a 99% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. (For each answer, enter a number. Round your answers to two decimal places.) lower limit % upper limit %
(d) The home run percentages for three professional players are below. Player A, 2.5 Player B, 2.2 Player C, 3.8 Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.
We can say Player A falls close to the average, Player B is above average, and Player C is below average.
We can say Player A falls close to the average, Player B is below average, and Player C is above average.
We can say Player A and Player B fall close to the average, while Player C is above average.
We can say Player A and Player B fall close to the average, while Player C is below average.
(e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.
Yes. According to the central limit theorem, when n ≥ 30, the x bar distribution is approximately normal.
Yes. According to the central limit theorem, when n ≤ 30, the x bar distribution is approximately normal.
No. According to the central limit theorem, when n ≥ 30, the x bar distribution is approximately normal.
No. According to the central limit theorem, when n ≤ 30, the x bar distribution is approximately normal.
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Why Programmatic direct is the most popular method (most used) in economics?
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Entropy is one of the most important and most fundamental concepts in thermal dynamics. It is also one of the most frequently misunderstood. In this assignment, you will research entropy and write a 3-5 page informative essay describing what entropy is and how it relates to the 2nd law of Thermodynamics. Your description of entropy should be more than a simple definition; the purpose of the paper is for you to demonstrate your own understanding of this concept and how it is applied in the real world. The second part of the paper should describe what the “heat death” of the Universe refers to, and how this relates to entropy. Your discussion should include a statement of whether or not heat death is inevitable and a description of the reasons why/why not.
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In the UK, most hospitals are owned by the government, whereas in the US, most hospitals are privately owned. What effect would hospital mergers have on the price of care in the US? Could hospital mergers increase quality of care? Explain
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Determine which of the following is:
a) the most concentrated, and
b) the most dilute.
(i) 0.45 mol L-1 NaCl
(ii) 4.2 % m/v NaCl
(iii) 41.6g NaCl L-1
(iv) 39950 ppm NaCl
In: Chemistry
Calcium is the most abundant mineral in the body and also one of the most important.
The recommended daily allowance (RDA) of calcium for adults is 800 milligrams (mg). A random sample of 18 people with incomes below the poverty level gives the following daily calcium intakes:
686, 433, 743, 647, 734, 641, 993, 620, 574, 634, 850, 858, 992, 775, 1113, 672, 879, 609
At the 1% significance level, do the data provides sufficient evidence to conclude that the mean calcium intake of all people with income levels below the poverty level is less than the RDA of 800 mg?
In: Statistics and Probability
the most frequently broken bone in the body is the
what is the most frequent broken bone in the body?
In: Anatomy and Physiology
The most common attributes of a book are the Book Title, and ISBN. The most common functions are to set the Book Title, and ISBN,
Write the code to implement this problem.
1. Write the UML Diagram that represents this class Book
2. Use code blocks editor and in C++
Write a header file Book with these properties.
Write the implementation file for the member functions.
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