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
r²
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
r²
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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.