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my answers in the red boxes are wrong, Part a) The coefficients of the least squ

ID: 3353049 • Letter: M

Question

my answers in the red boxes are wrong,

Part a) The coefficients of the least square regression line are ,-| 0.030247 -0846197 Part b) Suppose we want to get a prediction interval for each of the next 10 months (beginning January 2013; when the SP500 returns are values in the following R vector. xnext-c(0.049198, 0.011, 0.035355, 0.017924, 0.02055, -0.015113, 0.048278, -0.031798, 0.029316, 0.04363) The t critical value for the 95% prediction interval is 2.262 Using the fitted regression equation for January 2009 to December 2012, the lower endpoint of the 95% prediction interval for January 2013 SP500 return 0.049198) is -0.04728733 The upper endpoint of this 95% prediction interval is 0.1910445 The lower endpoint of the 95% prediction interval for October 2013 (SP500 return 0.04363) is 1-0.05179417 The upper endpoint of this 95% prediction interval is 0.1861281 Part c) Get the 10 prediction intervals for January to October 2013 from part (b) of which you were asked to enter two intervals. The actual values of the monthly stock returns for Apple are in the following vector ynext-c(-0.155568, -0.02563, 0.002789, 0.000328, 0.022193, -0.126007, 0.132236,0.080422, -0.021832, 0.092029) How many of these observed values (not used in the regression equation) are contained in the corresponding prediction intervals. (The response here is an integer between 0 and 10; theoretically it is close to 9.)

Explanation / Answer

Result:

Regression Analysis

0.266

n

48

r

0.516

k

1

Std. Error

0.040

Dep. Var.

Y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

0.0262

1  

0.0262

16.66

.0002

Residual

0.0724

46  

0.0016

Total

0.0986

47  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=46)

p-value

95% lower

95% upper

Intercept

0.0078

0.0058

1.339

.1870

-0.0039

0.0196

X

0.4762

0.1167

4.082

.0002

0.2414

0.7110

Predicted values for: Y

95% Confidence Intervals

95% Prediction Intervals

X

Predicted

lower

upper

lower

upper

Leverage

0.0491980

0.0312386

0.0164181

0.0460590

-0.0499734

0.1124506

0.034

0.0110000

0.0130493

0.0015189

0.0245796

-0.0676272

0.0937257

0.021

0.0353550

0.0246468

0.0116222

0.0376713

-0.0562567

0.1055503

0.027

0.0179240

0.0163464

0.0046534

0.0280393

-0.0643535

0.0970462

0.021

0.0205500

0.0175968

0.0057841

0.0294096

-0.0631204

0.0983141

0.022

-0.0151130

0.0006146

-0.0122800

0.0135093

-0.0802681

0.0814973

0.026

0.0482780

0.0308005

0.0161149

0.0454861

-0.0503870

0.1119880

0.034

-0.0317980

-0.0073305

-0.0223948

0.0077338

-0.0885873

0.0739263

0.036

0.0293160

0.0217711

0.0093436

0.0341986

-0.0590385

0.1025806

0.024

0.0436300

0.0285872

0.0145518

0.0426225

-0.0524852

0.1096596

0.031

Part A

bo=0.008

b1=0.476

Part b

t critical value =2.013

95% lower endpoint of 95% prediction for January 2013 = -0.050

95% upper endpoint of 95% prediction for January 2013 = 0.112

95% lower endpoint of 95% prediction for october 2013 = -0.052

95% upper endpoint of 95% prediction for october 2013 = 0.110

Part c

10

Regression Analysis

0.266

n

48

r

0.516

k

1

Std. Error

0.040

Dep. Var.

Y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

0.0262

1  

0.0262

16.66

.0002

Residual

0.0724

46  

0.0016

Total

0.0986

47  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=46)

p-value

95% lower

95% upper

Intercept

0.0078

0.0058

1.339

.1870

-0.0039

0.0196

X

0.4762

0.1167

4.082

.0002

0.2414

0.7110

Predicted values for: Y

95% Confidence Intervals

95% Prediction Intervals

X

Predicted

lower

upper

lower

upper

Leverage

0.0491980

0.0312386

0.0164181

0.0460590

-0.0499734

0.1124506

0.034

0.0110000

0.0130493

0.0015189

0.0245796

-0.0676272

0.0937257

0.021

0.0353550

0.0246468

0.0116222

0.0376713

-0.0562567

0.1055503

0.027

0.0179240

0.0163464

0.0046534

0.0280393

-0.0643535

0.0970462

0.021

0.0205500

0.0175968

0.0057841

0.0294096

-0.0631204

0.0983141

0.022

-0.0151130

0.0006146

-0.0122800

0.0135093

-0.0802681

0.0814973

0.026

0.0482780

0.0308005

0.0161149

0.0454861

-0.0503870

0.1119880

0.034

-0.0317980

-0.0073305

-0.0223948

0.0077338

-0.0885873

0.0739263

0.036

0.0293160

0.0217711

0.0093436

0.0341986

-0.0590385

0.1025806

0.024

0.0436300

0.0285872

0.0145518

0.0426225

-0.0524852

0.1096596

0.031