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Assignment 2: The data set provided below is 1,000 observations for the model Y=alpha+beta X + epsilon. Population parameters are alpha= 1 and beta...

Assignment 2:

The data set provided below is 1,000 observations for the model

Y=alpha+beta X + epsilon.

Population parameters are alpha= 1 and beta =5. Epsilon is distributed normal with zero mean and unitary variance.

1- Split the data into sizes of 5 observations (first 5 observations of (Y,X), next 5 observations of (Y,X), etc.) for a total of 200 different data sets. Calculate the beta hat of these data sets and plot their sampling distribution. Is your estimator biased/unbiased? Calculate the degree of bias by bias = average (beta hats) - beta. What is the mean squared error (MSE)? Calculate the MSE by MSE = var(beta hat) + bias squared (beta hat).

2- Repeat Question (1) by splitting the data into sizes of 20 observations for a total of 50 different data sets.

3- Repeat Question (1) by splitting the data into sizes of 40 observations for a total of 25 different data sets.

4- Repeat Question (1) by splitting the data into sizes of 50 observations for a total of 20 different data sets.

5- Illustrate consistency of beta hat by using your results from (1)-(4) graphically.


You can use Eviews, Stata, Excel or R as software.

The data set is:
Y X
1 2.758351791 -0.04503362
2 2.989603935 0.386025168
3 0.328154451 0.089103784
4 1.236011346 -0.070756065
5 0.70614413 0.249995487
6 -5.77302486 -1.158440409
7 0.896364614 -0.175224152
8 5.524250448 0.989686873
9 9.427908989 1.511941041
10 0.478388708 -0.355520185
11 -2.043636659 -0.369636406
12 6.34462259 1.023429461
13 5.199586138 0.747320217
14 -0.635408807 -0.028578803
15 -4.55264254 -0.843659328
16 5.607798618 1.002961387
17 -1.221680786 -0.531740202
18 -1.587406544 -0.702913944
19 -0.67433359 0.209221816
20 5.524367722 0.759335153
21 1.368280511 0.499685161
22 -6.137309765 -1.282761277
23 8.226436037 1.389327918
24 1.225705458 -0.021933952
25 4.52820334 0.610716998
26 1.886340895 0.298202312
27 -1.815201828 -0.405343775
28 2.695558863 0.17188337
29 -2.696328153 -1.011758419
30 -1.332321159 0.069315382
31 3.208899051 0.452837469
32 7.719018768 1.638555881
33 -0.136696719 -0.00568255
34 5.491174481 0.754087898
35 -2.300798983 -0.516327104
36 -4.114632414 -0.989074248
37 9.805014768 2.020744832
38 -2.64311066 -0.78140069
39 0.475005352 -0.007845276
40 -0.531994471 -0.176800688
41 0.430584625 -0.196977711
42 2.841669546 0.3430673
43 -6.20378778 -1.481843628
44 5.400712585 0.935459527
45 8.273240308 1.577114675
46 5.152835705 0.737552641
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This question was asked on Jan 28, 2013.

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