# Mathematics

5.12 You are trying to develop a strategy for

… investing in two different stocks. The anticipated

annual return for a $1,000 investment in each stock under

four different economic conditions has the following probability

distribution:

Returns

Probability Economic Condition Stock X Stock Y

0.1 Recession -100 50

0.3 Slow growth 0 150

0.3 Moderate growth 80 -20

0.3 Fast growth 150 100

Compute the

a. expected return for stock X and for stock Y.

b. standard deviation for stock X and for stock Y.

c. covariance of stock X and stock Y.

d. Would you invest in stock X or stock Y? Explain.

Question 5.13

Suppose that in Problem 5.12 you wanted to create a

portfolio that consists of stock X and stock Y. Compute the

portfolio expected return and portfolio risk for each of the

following percentages invested in stock X:

a.30%

b.50%

c.70%

d. On the basis of the results of (a) through (c), which portfolio

would you recommend? Explain

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

r = 0.543, n = 25

Select one:

a. Critical values: r = ±0.396, no significant linear correlation

b. Critical values: r = ±0.396, significant linear correlation

c. Critical values: r = ±0.487, significant linear correlation

d. Critical values: r = ±0.487, no significant linear correlation

Question 2

The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters):

Temp 62 76 50 51 71 46 51 44 79

Growth 36 39 50 13 33 33 17 6 16

Find the value of the linear correlation coefficient r.

Select one:

a. 0.256

b. 0.196

c. -0.210

d. 0

Question 3

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.738.

Select one:

a. 0.545

b. 0.262

c. 0.455

d. 0.738

Question 4

The equation of the regression line for the paired data below is y = 3x. Find the unexplained variation.

x 2 4 5 6

y 7 11 13 20

Select one:

a. 78.75

b. 10.00

c. 88.75

d. 14.25

Question 5

A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119. Find the coefficient of determination.

Select one:

a. 0.102

b. 1.114

c. 0.114

d. 0.898

Question 6

The equation of the regression line for the paired data below is y = 6.18286 + 4.33937x. Find the explained variation.

x 9 7 2 3 4 22 17

y 43 35 16 21 23 102 81

Select one:

a. 6,544.86

b. 13.479

c. 6,421.83

d. 6,531.37

Question 7

Use the given data to find the equation of the regression line. Round the final answer to three significant digits, if necessary.

x 6 8 20 28 36

y 2 4 13 20 30

Select one:

a. y = -2.79 + 0.897x

b. y = -2.79 + 0.950x

c. y = -3.79 + 0.801x

d. y = -3.79 + 0.897x

Question 8

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.738.

Select one:

a. 0.545

b. 0.262

c. 0.455

d. 0.738

Question 9

Ten pairs of data yield r = 0.003 and the regression equation y = 2 + 3x. Also, y = 5.0. What is the best predicted value of y for x = 2?

Select one:

a. 17.0

b. 5.0

c. 8.0

d. 7.0

Question 10

Question text

The equation of the regression line for the paired data below is y = 3x and the standard error of the estimate is se = 2.2361. Find the 90% prediction interval of y for x = 3.

x 2 4 5 6

y 7 11 13 20

Select one:

a. 6.8 < y < 11.2

b. 1.2 < y < 16.8

c. 4.5 < y < 13.5

d. 7.1 < y < 10.9