Hi, need to submit a 500 words paper on the topic Simple leaner regression. Question In the CAPM model, B0 is the risk free rate of return and its value is expected to be positive (usually the Treasur

Hi, need to submit a 500 words paper on the topic Simple leaner regression. Question In the CAPM model, B0 is the risk free rate of return and its value is expected to be positive (usually the Treasury bill). The slope, B1,is the beta coefficient in CAPM model and measures the volatility of an asset’s return compared to that of the overall market. The benchmark value is 1.0 (perfect slope). The value can be more than 1.0 to show that a stock is more responsive to market changes or simply riskier than the market. The value can be less than 1.0 which indicates that the stock is less responsive to market changes (or is less risky).

Question 2

The plotted trajectories of x and y are shown in the chart below. As shown, a positive linear relationship between the two variables is expected.

Question 3

Obs

y

x

y2

χ2

yχ

=0+1χ

ɛ = y -

1

3.32

0.72

11.02

0.52

2.39

1.34

1.98

2

1.40

1.68

1.96

2.82

2.35

2.12

- 0.72

3

0.65

- 0.72

0.42

0.52

- 0.47

0.19

0.46

4

0.93

0.81

0.86

0.66

0.75

1.42

- 0.49

5

- 1.21

- 0.35

1.46

0.12

0.42

0.49

- 1.70

6

- 1.62

- 2.30

2.62

5.29

3.73

- 1.08

- 0.54

7

1.41

0.80

1.99

0.64

1.13

1.41

0.00

8

0.18

0.40

0.03

0.16

0.07

1.09

- 0.91

9

1.88

- 0.65

3.53

0.42

- 1.22

0.24

1.64

10

1.35

0.39

1.82

0.15

0.53

1.08

0.27

Total

8.29

0.78

25.74

11.30

9.68

8.29

-

Completed table

obs

Y

X

SQY

SQX

YX

Y_HAT

E

1

3.32

0.72

11.02240

0.518400

2.390400

1.355465

1.964535

2

1.40

1.68

1.960000

2.822400

2.352000

2.091122

-0.691122

3

0.65

-0.72

0.422500

0.518400

-0.468000

0.251979

0.398021

4

0.93

0.81

0.864900

0.656100

0.753300

1.424433

-0.494433

5

-1.21

-0.35

1.464100

0.122500

0.423500

0.535513

-1.745513

6

-1.62

-2.30

2.624400

5.290000

3.726000

-0.958791

-0.661209

7

1.41

0.80

1.988100

0.640000

1.128000

1.416770

-0.006770

8

0.18

0.40

0.032400

0.160000

0.072000

1.110246

-0.930246

9

1.88

-0.65

3.534400

0.422500

-1.222000

0.305620

1.574380

10

1.35

0.39

1.822500

0.152100

0.526500

1.102583

0.247417

Eviews Summary Descriptive Results

Y

X

SQX

SQY

YX

Y_HAT

E

&nbsp.Mean

&nbsp.0.829000

&nbsp.0.078000

&nbsp.1.130240

&nbsp.2.573570

&nbsp.0.968170

&nbsp.0.863494

-0.034494

&nbsp.Std. Dev.

&nbsp.1.447730

&nbsp.1.117615

&nbsp.1.659833

&nbsp.3.141602

&nbsp.1.482091

&nbsp.0.856439

&nbsp.1.136141

&nbsp.Sum

&nbsp.8.290000

&nbsp.0.780000

&nbsp.11.30240

&nbsp.25.73570

&nbsp.9.681700

&nbsp.8.634939

-0.344939

&nbsp.Sum Sq. Dev.

&nbsp.18.86329

&nbsp.11.24156

&nbsp.24.79541

&nbsp.88.82698

&nbsp.19.76935

&nbsp.6.601388

&nbsp.11.61734

&nbsp.Observations

&nbsp.10

&nbsp.10

&nbsp.10

&nbsp.10

&nbsp.10

&nbsp.10

&nbsp.10

Question 4

The slope (β0) = (0.620455)(1.45)/(1.12) = 0.804

The intercept (β1) = 0.83 – (1.01)(0.08) = 0.766.

Question 5

SSR = Sum of (Predicted y – population mean of y)^2 = 6.6132

SSR

&nbsp.Mean

&nbsp.0.661329

&nbsp.Median

&nbsp.0.305059

&nbsp.Maximum

&nbsp.3.196195

&nbsp.Minimum

&nbsp.0.074847

&nbsp.Std. Dev.

&nbsp.0.994800

&nbsp.Skewness

&nbsp.1.938750

&nbsp.Kurtosis

&nbsp.5.352234

&nbsp.Jarque-Bera

&nbsp.8.570002

&nbsp.Probability

&nbsp.0.013774

&nbsp.Sum

&nbsp.6.613286

&nbsp.Sum Sq. Dev.

&nbsp.8.906647

&nbsp.Observations

&nbsp.10

Question 6

Variance of returns, σ2 = 2.10

Standard deviation of returns, y, σ = 1.45

Standard deviation, x = 1.12

Question 7

The slope is 0.804 and the p-value is 0.056. At 5% level of significance, the slope is not significantly different from zero. The intercept is 0.766 and the p-value is 0.079. At 5% level, the intercept is not significantly different from zero.

Variable

Coefficient

Std. Error

t-Statistic

Prob.&nbsp.&nbsp.

C

0.766310

0.381844

2.006865

0.0797

X

0.803721

0.359171

2.237714

0.0556

R-squared

0.384964

&nbsp.&nbsp.&nbsp.&nbsp.Mean dependent var

0.829000

Adjusted R-squared

0.308084

&nbsp.&nbsp.&nbsp.&nbsp.S.D. dependent var

1.447730

S.E. of regression

1.204243

&nbsp.&nbsp.&nbsp.&nbsp.Akaike info criterion

3.386435

Sum squared resid

11.60160

&nbsp.&nbsp.&nbsp.&nbsp.Schwarz criterion

3.446952

Log likelihood

-14.93218

&nbsp.&nbsp.&nbsp.&nbsp.Hannan-Quinn criter.

3.320048

F-statistic

5.007366

&nbsp.&nbsp.&nbsp.&nbsp.Durbin-Watson stat

1.877887

Prob(F-statistic)

0.055623

Question 8

Testing whether the slope, 0.804, is bigger or lower than 1 is a one-tailed t-test. Since the calculated t-statistic is below the rejection level, we cannot reject the null hypothesis that the slope is significantly lower than 1. The stock is not more volatile than the market.

Wald Test:

Equation: EQ_CAPM_REG

Test Statistic

Value

df

Probability

t-statistic

-0.612004

&nbsp.8

&nbsp.0.5575

F-statistic

&nbsp.0.374549

(1, 8)

&nbsp.0.5575

Chi-square

&nbsp.0.374549

&nbsp.1

&nbsp.0.5405

Null Hypothesis: C(1) = 1

Null Hypothesis Summary:

Normalized Restriction (= 0)

Value

Std. Err.

-1 + C(1)

-0.233690

&nbsp.0.381844

Restrictions are linear in coefficients.

Question 9

SSE = 11.60

SST = SSE + SSR = 11.60 + 7.26 = 18.86

Question 10

Correlation coefficient = 0.62 (Excel I21)

Coefficient of determination, r2 = 0.622 = 0.38

Question 11

Done and tables pasted in the questions above.