Consider the following regression model

=0+11+22+33+44+

Data for the relevant variables is below. Estimate the model using the OLS method.

Use an F-test with the critical value method and a significance level of 5% to test 0:4+1=0 against 1:4+10.

Show all your working. Your answer should include the relevant output for your estimated regression models and details of their derivation. Also, 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.

Y X1 X2 X3 X4

1 -1.55757 3.196078 -0.342765 0.018655 2.033993 2 -3.43568 1.246111 0.149751 -0.925430 2.635189 3 -4.33865 2.335591 0.048578 -0.599928 3.048100 4 -1.02724 4.050652 -1.079806 0.072504 1.544375 5 1.42478 1.408761 -0.663876 0.317222 0.692687 6 -3.54946 2.134224 -0.667072 -2.251570 1.653776 7 -7.06308 2.831927 0.417966 -2.111255 3.710991 8 -7.00056 2.920789 -0.073222 -0.808058 5.671206 9 -4.10638 2.691688 -0.490355 0.797481 4.453045 10 -0.93919 2.895561 0.232459 -0.848926 -0.169264 11 -6.07105 1.238335 -0.673288 -2.375508 3.860621 12 -5.07900 1.856391 -0.798890 -1.839320 2.950134 13 -4.16264 2.196279 0.299161 -0.438537 2.727386 14 -3.34233 2.899985 -0.872334 -3.592598 -0.778876 15 -2.60996 2.550706 -0.395080 0.160321 3.288511 16 -6.83191 2.752356 -0.244739 -1.251493 4.809832 17 -3.11653 2.360698 -0.030757 -0.412390 2.367318 18 0.95993 2.592107 -0.072890 -0.523313 -1.648274 19 1.43355 1.488421 0.103615 -0.681799 -2.353307 20 -0.48114 3.313479 -0.230761 -0.634522 -0.439658 21 -5.44387 1.474508 -0.507519 -2.063624 3.693592 22 -0.75450 2.310141 -0.394812 0.914507 1.965909 23 1.46474 3.154360 -0.952995 1.048327 0.438868 24 -1.68406 1.703152 -0.600231 -1.688066 0.360528 25 -6.70366 1.871300 -0.223122 -3.130864 2.968936 26 -10.65580 1.389307 0.133871 -2.126016 7.906376 27 -4.74636 0.701635 -0.577315 -2.950060 2.238672 28 -2.29387 3.461974 0.103267 0.477854 2.058195 29 -4.44726 2.838548 -0.916065 -1.981508 2.325532 30 -3.24845 3.711321 -0.490478 -1.731397 1.125875 31 -2.14303 0.639317 -0.023654 -1.626908 0.892438 32 0.11221 0.726426 -0.831449 -0.202692 1.399316 33 -5.50583 1.892093 0.033420 -0.717758 4.042457 34 -0.75851 1.630238 -0.133194 0.066491 1.156744 35 -6.15616 3.420320 -0.157101 -1.947947 2.105151 36 -3.86097 2.869119 -0.756418 -0.732155 3.308552 37 0.05922 0.134709 -0.553116 -0.673540 0.947985 38 0.27688 2.989454 -0.644669 -1.663583 -2.592863 39 -4.25852 2.662904 -1.008695 0.187162 5.016339 40 -4.29854 1.407607 0.007251 -1.351998 2.501778 41 -2.61783 2.583664 -0.851047 -0.480465 1.986393 42 -2.88533 2.115909 -0.960826 -1.135678 2.835082 43 -1.54529 3.211138 -1.345540 -1.715902 0.536921 44 -2.51744 2.169211 -0.674343 -1.020529 0.905273 45 -5.69474 2.502625 -0.904643 -2.541603 2.819320 46 -0.59102 2.755547 -0.714928 0.661135 1.281536 47 -2.57479 2.396286 -0.366622 -0.258879 2.561433 48 -8.95561 1.931014 -1.197197 -2.029919 6.959510 49 -3.57935 3.079193 -1.047249 -2.073586 1.752186 50 -2.91897 4.131866 -0.577087 0.061142 2.238370 51 -2.97485 1.478761 -0.391349 0.062869 3.681793 52 -4.23257 2.383460 -0.841827 -1.127867 3.529329 53 1.11007 2.828634 -0.181015 1.218288 0.347059 54 -7.24029 1.969914 -0.249545 -0.367427 6.857498 55 -1.29883 2.753999 -0.677312 -1.414475 -0.307207 56 -2.99129 3.351103 -0.580865 0.119307 2.789154 57 0.57512 0.863960 -1.074557 -0.458227 0.523282 58 2.28110 1.480748 -0.815295 0.165320 -0.511315 59 -2.18306 1.825798 -0.297740 -2.294779 -0.291411