28) Data for the following regression model are in this file.

Yi=0+1X1i+2X2i+3X3i+uiYi=0+1X1i+2X2i+3X3i+ui

Estimate the model using the OLS method.

1. Using the critical value method and a significance level of 10%, test H0:1=1H0:1=1against H1:1>1H1:1>1.

Show all your working, including the output for the estimated model. For the hypothesis test, in your answer you should state the null and alternative hypotheses, the significance level, the formula for the test statistic, the PDF of the test statistic under the null hypothesis, the value of the test statistic, the critical value and your conclusion.

2. State some assumptions under which your conclusion is valid

Y 1 3.188324 2 0.371512 3 1.209168 4 2.315490 5 4.068481 6 3.599471 7 3.347456 8 4.341477 9 2.422526 10 -0.575377 11 0.332239 12 -0.412307 13 -1.035231 14 3.931719 15 2.034877 16 1.551644 17 -2.053383 18 0.891141 19 1.586812 20 0.175500 21 0.765645 22 1.045009 23 4.200476 24 3.817783 25 1.740418 26 2.454143 27 0.106630 28 4.608884 29 3.871801 30 2.357806 31 1.184598 32 2.454598 33 1.037941 34 4.233936 35 1.967725 36 2.267937 37 -1.988420 38 0.335198 39 7.160587 40 4.429552 41 -0.420576 42 1.367904 43 3.050362 44 -0.268364 45 3.507415 46 1.121353 47 4.507987 48 3.822905 49 -0.639181 50 0.382343 51 -0.324696 52 0.998809 53 -2.359494 54 2.629830 55 -0.226426 56 -0.385571 57 -1.703544 58 2.768706 59 2.029576 60 0.178774 61 4.726472 62 1.377942 63 1.502151 64 0.612790 65 3.050864 66 7.186961 67 3.510465 68 -0.686955 69 0.962295 70 0.508007 71 0.279387 72 3.629327 73 2.705184 74 2.725582 75 3.372900

X1 1 1.322454 2 0.939808 3 -0.946512 4 -1.022129 5 -2.952907 6 0.165687 7 -1.328868 8 -1.011494 9 -1.129836 10 0.535641 11 1.852501 12 0.208367 13 -0.326004 14 -1.983518 15 -0.630793 16 -1.710230 17 1.829660 18 -1.135011 19 -2.512559 20 -0.837957 21 1.602401 22 -1.614359 23 -0.218954 24 -1.281724 25 -0.823561 26 -2.309117 27 0.573218 28 -2.349716 29 -2.464288 30 -2.396990 31 -2.086180 32 -1.312529 33 0.700334 34 -1.914448 35 -0.605695 36 0.337501 37 0.626158 38 -1.119751 39 -3.961736 40 -1.412685 41 1.032742 42 -2.071556 43 -1.113492 44 -1.302117 45 -1.399510 46 0.851181 47 -1.616793 48 -1.658944 49 0.108627 50 -1.118171 51 3.148802 52 1.377338 53 -0.392222 54 -2.032765 55 0.794591 56 2.047970 57 1.590400 58 -3.586018 59 1.166123 60 -0.023247 61 -1.907544 62 -0.647783 63 -2.290432 64 -1.117889 65 -2.350971 66 -3.929681 67 -1.942308 68 0.162462 69 1.500770 70 0.355875 71 -1.317480 72 -0.377026 73 0.337357 74 -0.613352 75 -0.527492

X2 1 2.333763 2 -0.999680 3 -2.478330 4 -0.328361 5 0.520941 6 1.787707 7 -0.687782 8 1.115462 9 -1.174063 10 -0.689368 11 -0.145460 12 -1.802225 13 -2.750379 14 -0.570098 15 -1.416326 16 -2.609330 17 -1.416242 18 -2.540259 19 -2.398356 20 -0.967441 21 0.586145 22 -1.048687 23 1.518677 24 1.230370 25 -0.879870 26 -0.501385 27 -1.761302 28 0.399026 29 -0.007490 30 -0.958512 31 -2.540443 32 -1.004945 33 -0.923020 34 1.197898 35 -0.944775 36 -0.890890 37 -2.127700 38 -1.179069 39 0.928948 40 1.400552 41 -0.327217 42 -1.455402 43 0.325727 44 -3.048746 45 -0.021157 46 -0.159752 47 2.161093 48 2.275850 49 -0.800668 50 -0.552711 51 2.867991 52 0.735515 53 -2.933562 54 1.144794 55 -2.413588 56 0.433340 57 -1.542651 58 -1.950156 59 1.356934 60 -1.998068 61 2.029093 62 -2.681211 63 -0.070836 64 -1.461325 65 0.227150 66 0.808231 67 0.655817 68 -2.468598 69 -0.471368 70 -0.661483 71 -0.480598 72 0.558504 73 0.294050 74 -0.006872 75 -0.534887

X3 1 -0.368837 2 -3.003301 3 0.031888 4 -1.397803 5 -1.308268 6 -0.337566 7 0.562434 8 -0.828164 9 -0.810105 10 0.049823 11 0.089743 12 0.161335 13 -0.701465 14 -0.038987 15 0.107068 16 0.528042 17 -1.012182 18 -0.768308 19 0.156025 20 -0.226693 21 -0.348865 22 1.895559 23 -0.999042 24 -0.962295 25 1.110824 26 0.872157 27 -0.317950 28 -1.610361 29 -2.091458 30 -2.876573 31 -2.474159 32 -0.380350 33 0.953440 34 -0.563835 35 -2.620852 36 -3.224796 37 1.694669 38 -0.773184 39 -1.019215 40 -1.902129 41 -0.186114 42 0.035934 43 -1.653982 44 0.688719 45 -0.498563 46 1.281866 47 -0.988105 48 0.119426 49 1.704033 50 -0.996311 51 -0.464769 52 -0.947597 53 0.730791 54 -0.671521 55 -1.986113 56 0.424360 57 0.034711 58 -1.031691 59 -0.221364 60 -0.053877 61 -1.264877 62 -3.350637 63 3.267020 64 0.072986 65 0.587031 66 -2.839215 67 -2.065998 68 -0.486812 69 -0.876140 70 0.652056 71 0.409053 72 -2.907804 73 -1.996151 74 -0.248731 75 -0.824805