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Reading 11- LOS F (Part 2): : Q2

2Rebecca Anderson, CFA, has recently accepted a position as a financial analyst with Eagle Investments. She will be responsible for providing analytical data to Eagle’s portfolio manager for several industries. In addition, she will follow each of the major public corporations within each of those industries. As one of her first assignments, Anderson has been asked to provide a detailed report on one of Eagle’s current investments. She was given the following data on sales for Company XYZ, the maker of toilet tissue, as well as toilet tissue industry sales ($ millions). She has been asked to develop a model to aid in the prediction of future sales levels for Company XYZ. She proceeds by recalling some of the basic concepts of regression analysis she learned while she was preparing for the CFA exam.

Year

Industry Sales (X)

Company Sales (Y)

(X-X)2

1

$3,000

$750

84,100

2

$3,200

$800

8,100

3

$3,400

$850

12,100

4

$3,350

$825

3,600

5

$3,500

$900

44,100

Totals

$16,450

$4,125

152,000

 

Coefficient Estimates

Predictor

Coefficient

Stand. Error of
the Coefficient

t-statistic

Intercept

-94.88

32.97

??

Slope (Industry Sales)

0.2796

0.0363

??

 

Analysis of Variance Table (ANOVA)

Source

df
(Degrees of Freedom)

SS
(Sum of Squares)

Mean Square (SS/df)

F-statistic

Regression

1 (# of independent variables)

11,899.50 (SSR)

11,899.50 (MSR)

59.45

Error

3 (n-2)

600.50 (SSE)

200.17 (MSE)

 

Total

4 (n-1)

12,500 (SS Total)

 

 

 

Abbreviated Two-tailed t-table

df

10%

5%

2

2.920

4.303

3

2.353

3.182

4

2.132

2.776

Which of the following is the correct value of the correlation coefficient between industry sales and company sales?

A)   0.9757.

B)   0.2192.

C)   0.9062.

D)   0.0023.

The correct answer was A)

The R2 = (SST - SSE)/SST = (12,500 - 600.50)/12,500 = 0.952

The correlation coefficient is the square root of the R2 in a simple linear regression, which is the square root of 0.952 = 0.9757.

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