# Risk Assessment using Scatter Diagrams & Regression Analysis

2. You are given the following set of data:

Historical Rates of Return

Year NYSE Stock Y

1 4.0% 3.0%

2 14.3 18.2

3 19.0 9.1

4 (14.7) (6.0)

5 (26.5) (15.3)

6 37.2 33.1

7 23.8 6.1

8 (7.2) 3.2

9 6.6 14.8

10 20.5 24.1

11 30.6 18.0

Mean = 9.8% 9.8%

σ = 19.6% 13.8%

a. Construct a scatter diagram showing the relationship between returns on

Stock Y and the market, and then draw a freehand approximation of the

regression line. What is the approximate value of the beta coefficient? If you

have a calculator with a linear regression function or a spreadsheet, check

the approximate value of beta obtained from the graph.

b. Give a verbal interpretation of what the regression line and the beta

coefficient show about Stock Y's volatility and relative riskiness as compared

with those of other stocks.

c. Suppose the scatter of points had been more spread out, but the regression

line was exactly where your present graph shows it. How would this effect

(1) the firm's risk if the stock is held in a one-asset portfolio and (2) the actual

risk premium on the stock if the CAPM holds exactly?

d. Suppose the regression line had been downward sloping and the beta

coefficient had been negative. What would this imply about (1) Stock Y's

relative riskiness, (2) its correlation with the market, and (3) its probable risk

premium?

e. Construct an illustrative probability distribution graph of returns on

portfolios consisting of (1) only Stock Y, (2) 1% each of 100 stocks with beta

coefficients similar to that of Stock Y, and (3) all stocks (i.e. the distribution

of returns on the market). Use as the expected rate of return the arithmetic

mean as given previously for both Stock Y and the market and assume that

the distributions are normal. Are the expected returns "reasonable"; that is,

is it reasonable that % 8 . 9 ? ? = = M Y k k ?

https://brainmass.com/statistics/regression-analysis/132160

#### Solution Preview

Hello

a. Construct a scatter diagram showing the relationship between returns on

Stock Y and the market, and then draw a freehand approximation of the

regression line. What is the approximate value of the beta coefficient? If you

have a calculator with a linear regression function or a spreadsheet, check

the approximate value of beta obtained from the graph.

Approximate Value of Beta is 0.6 - please see the attached excel sheets for calculations and scatter diagram

b. Give a verbal interpretation of what the regression line and the beta

coefficient show about Stock Y's volatility and relative riskiness as compared

with those of other stocks.

The Beta Coefficient is a measure of risk, it shows how volatile stock Y is with respect to the NYSE index. A Beta Value of 0.6 means ...

#### Solution Summary

The solution contains a word document and an excel file that answer the questions posted. Questions are about drawing a scatter diagram, assessing the risk of a stock when held alone and within a portfolio.

Statistics.

Confidence Interval Estimation

2. Compute a 95% confidence interval for the population mean, based on the sample 15, 17, 13, 14, 15, 14, and 59. Change the number from 59 to 14 and recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme value on the confidence interval.

Hypothesis Testing

3. The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that X (bar) = $330.4 and s = $45.20.

a. a. Using the 0.10 level of significance, is there evidence that the population mean is above $300?

b. b. What is your answer in (a) if s = $90 and the 0.05 level of significance is used?

c. c. What is your answer in (a) if X (bar) = $305.10 and s = $45.20?

d. d. Based on the information in part (a), what decision should the director make about the books used for the courses if the goal is to keep the cost below $300?

4. A large hat manufacturer, MALLORY HATS, is concerned that the mean weight of their signature Kentucky Derby hat is not greater than 2.5 pounds. It can be assumed that the population standard deviation is .5 pounds based on past experience. A sample of 196 hats is selected and the sample mean is 2.55 pounds. Using a level of significance of .10, is there evidence that the population mean weight of the hats is greater than 2.5 pounds? Fully explain your answer.

Problem Set #3

Hypothesis Testing

1. The MBA department is concerned that dual degree students may be receiving lower grades than the regular MBA students. Two independent random samples have been selected 150 observations from population 1 (dual degree students) and 200 from population 2 (MBA students). The sample means obtained are X1(bar)=86 and X2(bar)=88. It is known from previous studies that the population variances are 4.8 and 5.2 respectively. Using a level of significance of .10, is there evidence that the dual degree students are receiving lower grades? Fully explain your answer.

Simple Regression

2. A CEO of a large pharmaceutical company would like to determine if he should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling diabetes. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called DIB and the number of orders received. The manufacturing process of this drug is very difficult and requires stability so the CEO would prefer to generate a stable number of orders. The cost of advertising is always an important consideration in the phase I roll-out of a new drug. Data that have been collected over the past 20 months indicate the amount of money spent of television advertising and the number of orders received.

The use of linear regression is a critical tool for a manager's decision-making ability. Please carefully read the example below and try to answer the questions in terms of the problem context. The results are as follows:

Month

Advertising Cost (thousands of dollars)

Number of Orders

1

$68.93

3,902,000

2

72.62

3,893,000

3

79.58

5,299,000

4

58.67

4,130,000

5

69.18

4,367,000

6

70.14

3,111,000

7

93.37

3,923,000

8

68.88

4,935,000

9

82.99

5,276,000

10

75.23

4,654,000

11

91.38

4,598,000

12

52.90

2,967,000

13

61.27

3,999,000

14

79.19

4,345,000

15

90.03

3,934,000

16

78.21

4,653,000

17

83.77

5,625,000

18

62.53

3,978,000

19

98.76

4,999,000

20

72.64

3,834,000

a. Set up a scatter diagram and calculate the associated correlation coefficient. Discuss how strong you think the relationship is between the amounts of money spent on television advertising and the number of orders received. Please use the Correlation procedures within Excel under Tools > Data Analysis. The Scatterplot can more easily be generated using the Chart procedure.

NOTE: If you do not have the Data Analysis option under Tools you must install it. You need to go to Tools select Add-ins and then choose the 2 data toolpak options. The original Excel CD will be required for this installation. It should take about a minute.

b. Assuming there is a statistically significant relationship, use the least squares method to find the regression equation to predict the advertising costs based on the number of orders received. Please use the regression procedure within Excel under Tools > Data Analysis to construct this equation.

c. Interpret the meaning of the slope, b1, in the regression equation.

d. Predict the monthly advertising cost when the number of orders is 5,100,000. (Hint: Be very careful with assigning the dependent variable for this problem)

e. Compute the coefficient of determination, r2, and interpret its meaning.

f. Compute the standard error of estimate, and interpret its meaning.

Hypothesis Testing on Multiple Populations

3. The Course Manager for AMBA 610 wants to use a new tutorial to teach the students about business ethics. As an experiment she randomly selected 15 students and randomly assigned them to one of three groups which include either a PowerPoint presentation created by the faculty, AuthorGen Presentation created by the faculty, or a well known tutorial by the ABC company. After completing their assigned tutorial, the students are given a Business Ethics test. At the .01 significance level, can she conclude that there is a difference between how well the different tutorials work for the students?

Students Grades on the Business Ethics Test following the Tutorial

PowerPoint Tutorial

AuthorGen Tutorial

ABC Tutorial

88

79

65

85

86

83

91

72

78

87

92

86

88

91

81