Suppose that you have the following model and data to estimate the following equation;

Nobs

Y

X₂

X₃

1

1

1

3

2

2

2

2

3

4

4

5

4

3

3

4

5

2

5

1

Find the OLS estimators for the parameters using the matrices above.
Transcribed Image Text:95th Percentile Values for the F Distribution 0.95 (vi degrees of freedom in numerator) (v2 degrees of freedom in denominator) 0.05 .95 1 2 3 4 s 6 7 8 9 10 12 15 20 24 30 40 60 120 1 161 200 216 225 230 234 237 239 241 242 244 246 248 249 250 251 252 253 254 18.5 19.0 19.2 | 19.2 | 19.3| 19.3 9.55 9.28 9.12 9.01 8.94 | 8.89 8.85 2 19.4 | 19.4 19.4 | 19.4 | 19.4 19.4 | 19.4 19.5 19.5 19.5 19.5 19.5| 19,5 8.81 8.79 8.74 8.70 |8.66 8.64 | 8.62 8.59 8.57 8.55 8.53 6.00 5.96 5.91 5.86 5.80 5.77 5.75 5.72 3 10.1 7.71 6.94 6.59 6.39 6.26 6.16 6.09 | 6.04 5.69 5.66| 5.63 5 6.61 5.79 5.41 5.19| 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4.37 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 |4.15 4.10 4.06 | 4.00 3.94 | 3.87 3.84 3.81 3.77 3.74 3.70 3.67 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 | 3.64 | 3.57 3.51 3.44 3.41 | 3.38 3.34 3.30 3.27 3.23 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 | 3.28 3.22 3.15 3.12 | 3.08 3.04 3.01 2.97 2.93 9 5.12 4.26 3.86 3.63| 3.48 3.37 3.29 | 3.23 3.18| 3.14 | 3.07 3.01 2.94 | 2.90 | 2.86 2.83 | 2.79 2.75 2.71 10 4.96 4.10 3.71 |3.48 3.33 3.22 3.14 3.07 3.02 2.98 | 2.91 | 2.85| 2.77 2.74 2.70 |2.66 2.62 2.58 2.54 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.40 12 4.75 3.89 3.49 3.26 | 3.11 3.00 2.91 |2.85 2.80 2.75 | 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.30 13 4.67 3.81 3.41 3.18 | 3.03 2.92 2.83 2.77 2.71 2.67 | 2.60 2.53 | 2.46 2.42 | 2.38 2.34 2.30 2.25 2.21 14 4.60 3.74 3.34 3.11 | 2.96 2.85 2.76 2.70 2.65 2.60 | 2.53 2.46 2.39 2.35 2.31 2.27| 2.22 2.18 2.13 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 | 2.54 2.48 2.40 2.33 2.29 2.25 2.20| 2.16 2.11 2.07 4.49 3.63 3.24 3.01 4.45 3.59 3.20 2.96 2.81 2.70 | 2.61 2.55 16 2.85 2.74 2.66 | 2.59 2.54 2.49 | 2.42 2.35 2.28 2.24 | 2.19 | 2.15 2.11 2.06 2.01 17 2.49 2.45 2.38 2.31 2.23 2.19| 2.15 2.10 2.06 2.01 | 1.96 18 4.41 3.55 3.16 2.93 2.77 2.66 | 2.58 2.51 2.46 2.41 2.34 2.27 2.19 | 2.15 | 2.11 2.06 2.02 1.97| 1.92 4.38 3.52 3.13 2.90 | 2.74 2.63 | 2.54 2.48 2.42 2.38 | 2.31| 2.23 2.16 2.11 2.07 2.03 2.39 2.35 2.28 2.20 2.12 2.08 2.04 1.99 19 1.98 1.93 1.88 20 4.35 3.49 3.10 2.87 2.71 2.60 | 2.51 2.45 1.95 1.90 1.84 21 4.32 3.47 3.07 |2.84| 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.10 2.05 2.01| 1.96 | 1.92 1.87 | 1.81 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 | 2.23 2.15 2.07 2.03| 1.98 | 1.94 1.89 1.84 1.78 23 4.28 3.42 3.03 2.80 2.64 2.53 | 2.44 2.37 2.32 2.27 2.20 2.13 2.05 2.01 1.96 | 1.91| 1.86 1.81 1.76 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.18 2.11 2.03| 1.98 | 1.94 | 1.89 1.84 1.79 1.73 3.39 2.99 | 2.76 2.60 | 2.49 2.40 2.34 2.28 2.24 | 2.16 2.09 | 2.01 1.96 1.92 | 1.87 1.82 1.77 1.71 24 25 4.24 26 4.23 3.37 2.98 | 2.74 2.59 2.47 2.39 2.32 2.27 2.22 | 2.15 2.07 1.99 | 1.95 1.90 1.85 1.80 1.75 1.69 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 2.13 2.06 2.56 2.45 2.36 2.29 2.24 2.19 2.12 2.04 27 4.21 1.97 1.93 1.88 | 1.84 | 1.79 1.73 1.67 28 4.20 3.34 2.95 2.71 1.96 1.91| 1.87 1.82| 1.77 1.71|1.65 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 2.10 2.03 | 1.94 1.90 1.85 | 1.81 1.75 1.70 | 1.64 1.93 1.89 1.84 | 1.79 1.74 4.17 3.32 2.92 | 2.69 | 2.53 2.42 | 2.33 2.27 2.21| 2.16 | 2.09 2.01 4.08 3.23 2.84 2.61 30 1.68 | 1.62 2.45 2.34 2.25 2.18 2.12 2.08 | 2.00| 1.92 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.92 1.84 40 1.84 1.79 1.74 1.69 | 1.64 1.58 | 1.51 60 1.75 1.70 1.65 1.59 1.53 1.47 1.39 3.92 3.07 2.68 2.45 2.29 2.18 | 2.09 2.02 1.96 1.91| 1.83 1.75 1.43 1.35 1.25 1.66 1.61| 1.55 1.50 1.57 1.52 1.46 | 1.39 1.32 120 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 | 1.75 1.67 1.22 | 1.00 -
Transcribed Image Text:TABLE D.2 PERCENTAGE POINTS OF THE I DISTRIBUTION Example Pr (t > 2.086) = 0.025 Pr (t > 1.725) = 0.05 for df = 20 0.05 Pr (|t| > 1.725) = 0.10 1.725 Pr df 0.25 0.50 0.005 0.010 0.10 0.05 0.10 0.025 0.05 0.01 0.02 0.001 0.002 0.20 63.657 9.925 1 1.000 3.078 6.314 12.706 31.821 318.31 6.965 4.541 0.816 1.886 2.920 4.303 22.327 0.765 0.741 3 1.638 2.353 3.182 5.841 10.214 4 1.533 2.132 2.776 3.747 4.604 7.173 0.727 1.476 2.015 2.571 3.365 4.032 5.893 3.707 3.499 0.718 1.440 1.943 2.447 3.143 5.208 7 0.711 1.415 1.895 2.365 2.998 4.785 0.706 0.703 8 1.397 1.860 2.306 2.896 3.355 4.501 9 1.383 1.833 2.262 2.821 3.250 4.297 10 0.700 1.372 1.812 2.228 2.764 3.169 4.144 11 0.697 1.363 1.796 2.201 2.718 3.106 4.025 12 0.695 1.356 1.782 2.179 2.681 3.055 3.930 1.350 1.345 13 0.694 1.771 2.160 2.650 3.012 3.852 14 0.692 1.761 2.145 2.624 2.977 3.787 15 0.691 1.341 1.753 2.131 2.602 2.947 3.733 16 0.690 1.337 1.746 2.120 2.583 2.921 3.686 2.898 2.878 2.861 1.740 2.110 2.567 2.552 17 0.689 1.333 3.646 0.688 0.688 1.330 1.328 3.610 3.579 18 1.734 2.101 19 1.729 2.093 2.539 20 0.687 1.325 1.725 1.721 2.086 2.528 2.845 3.552 0.686 0.686 1.323 2.518 2.831 2.819 21 2.080 3.527 22 1.321 1.717 2.074 2.508 3.505 23 0.685 1.319 1.714 2.069 2.500 2.807 3.485 24 0.685 1.318 1.711 2.064 2.492 2.797 3.467 1.316 1.315 25 0.684 1.708 2.485 2.060 2.056 2.787 3.450 3.435 26 0.684 1.706 2.479 2.779 2.473 2.467 27 0.684 1.314 1.703 2.052 2.771 3.421 3.408 3.396 28 0.683 1.313 1.701 2.048 2.763 29 0.683 1.311 1.699 2.045 2.462 2.756 30 0.683 1.310 1.697 2.042 2.457 2.750 3.385 40 0.681 1.303 1.684 2.021 2.423 2.704 3.307 60 0.679 1.296 1.289 1.671 2.000 2.390 2.358 2.660 3.232 1.980 1.960 3.160 3.090 120 0.677 1.658 2.617 0.674 1.282 1.645 2.326 2.576 Note: The smaller probability shown at the head of each column is the area in one tail; the larger probability is the area in both tails. Source: From E. S. Pearson and H. O. Hartley, eds., Biometrika Tables for Statisticians, vol. 1, 3d ed., table 12, Cambridge University Press, New York, 1966. Reproduced by permission of the editors and trustees of Biometrika.

Question

Suppose that you have the following model and data to estimate the following equation;

Find the OLS estimators for the parameters using the matrices above.

Accepted Answer

This is a regression equation:
Y=B0+B1X2+B2X3
Here,
Y-dependent variable
B0-Intercept
B1 and B2- OLS…

Suppose that you have the following model and data to estimate the following equation; Nobs Y X2 X3 1 1 1 3 2 2 2 2 3 4 4 5 4 3 3 4 5 2 5 1 Find the OLS estimators for the parameters using the matrices above.