4.A regression of number of high school seniors who apply for admission to a college over 22 years (1980 - 2002) produced the following results (standard errors in parenthesis):
t = 150 + 180At + 150Tt + 30.0Pt
(90.0)(1.50)(60.0)
R2 = 0.50N=22 (annual)
Where:
t = the number of high school seniors who apply for admission in year t
At = the number of people on the admission staff who visit high schools full time spreading information about the school in year t
Tt = cost of tuition (in dollars) in year t (adjusted for inflation)
Pt = the percent of the faculty in year t that had PhDs in year t
a.Interpret the R2
b.Interpret each of the three coefficient estimates.
Test each parameter estimate for statistical significance at a five percent significance level.
Summary of variables Variable | Obs Mean Std. Dev. Min Max phg4 6,366 2.133993 2. 805748 12 sah days 6, 354 40.1728 13.24659 67 Goll 6, 403 . 1703889 . 3760034 gender 6, 403 . 4162112 . 4929679 RGovid 6,370 23 . 89433 21.53016 100 pdie 6,365 20.39574 25. 07158 100 Table 2. Ordinary Least Squares Estimation Results phq4 | Coef. Std. Err. t P>Itl [954 Conf. Interval] 0096943 . 0025499 3.80 0.000 . 0046957 . 0146929 age -.0360763 . 0022189 -16.26 0.000 -. 0404261 -.0317266 L. 0666597 0903337 -0.74 0. 461 -. 2437445 . 1104252 gender -. 635857 . 0688721 -9.23 0.000 -. 7708697 -. 5008444 pcovid . 0119738 . 0017445 6. 86 0.000 . 008554 . 0153936 odie . 0140246 . 0015344 9.14 0.000 . 0110167 . 0170325 cons 3.277173 . 1674557 19.57 0.000 2.948903 3. 605443 N=6, 324 R-squared=0. 0936 Adjusted R-squared=0. 0927 F Test (6, 6317) Prob > F (0. 0000)Table T Critical Values of the t Distribution One-Tail = .4 .25 .05 025 .01 .005 .0025 001 0005 df Two-Tail = .8 .5 N 1 .05 02 .01 .005 .002 001 0.325 1.000 3.078 6.314 12.706 31.821 63.657 127.32 318.31 636.62 0.289 0.816 1.886 2.920 4.303 6.965 9.925 14.089 22.327 31.598 AWN 0.277 0.765 1.638 2.353 3.182 4.541 5.841 7.453 10.214 12.924 0.271 0.741 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.610 0.267 0.727 1.476 2.015 2.571 3.365 4.032 4.773 5.893 6.869 0.265 0.718 1.440 1.943 2.447 3.143 3.707 4.317 5.208 5.959 0.263 0.711 1.415 1.895 2.365 2.998 3.499 4.029 4.785 5.408 0.262 0.706 1.397 1.860 2.306 2.896 3.355 3.833 4.501 5.041 0.261 0.703 1.383 1.833 2.262 2.821 3.250 3.690 4.297 4.781 10 0.260 0.700 1.372 1.812 2.228 2.764 3.169 3.581 4.144 4.587 11 0.260 0.697 1.363 1.796 2.201 2.718 3.106 3.497 4.025 4.437 12 0.259 0.695 1.356 1.782 2.179 2.681 3.055 3.428 3.930 4.318 13 0.259 0.694 1.350 1.771 2.160 2.650 3.012 3.372 3.852 4.221 14 0.258 0.692 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4.140 15 0.258 0.691 1.341 1.753 2.131 2.602 2.947 3.286 3.733 4.073 16 0.258 0.690 1.337 1.746 2.120 2.583 2.921 3.252 3.686 4.015 17 0.257 0.689 1.333 1.740 2.110 2.567 2.898 3.222 3.646 3.965 18 0.257 0.688 1.330 1.734 2.101 2.552 2.878 3.197 3.610 3.922 19 0.257 0.688 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3.883 20 0.257 0.687 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3.850 21 0.257 0.686 1.323 1.721 2.080 2.518 2.831 3.135 3.527 3.819 22 0.256 0.686 1.321 1.717 2.074 2.508 2.819 3.119 3.505 3.792 23 0.256 0.685 1.319 1.714 2.069 2.500 2.807 3.104 3.485 3.767 24 0.256 0.685 1.318 1.711 2.064 2.492 2.797 3.091 3.467 3.745 25 0.256 0.684 1.316 1.708 2.060 2.485 2.787 3.078 3.450 3.725 26 0.256 0.684 1.315 1.706 2.056 2.479 2.779 3.067 3.435 3.707 27 0.256 0.684 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3.690 28 0.256 0.683 1.313 1.701 2.048 2.467 2.763 3.047 3.408 3.674 29 0.256 0.683 1.311 1.699 2.045 2.462 2.756 3.038 3.396 3.659 30 0.256 0.683 1.310 1.697 2.042 2.457 2.750 3.030 3.385 3.646 0.255 0.681 1.303 1.684 2.021 2.423 2.704 2.971 3.307 3.551 0.254 0.679 1.296 1.671 2.000 2.390 2.660 2.915 3.232 3.460 120 0.254 0.677 1.289 1.658 1.980 2.358 2.617 2.860 3.160 3.373 0.253 0.674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291 Source: From Biometrika Tables for Statisticians, Vol. 1, Third Edition, edited by E. S. Pearson and H. O. Hartley, 1966, p. 146
