TABLE 3 Truncated Regression Pooled Data (dependent variable time in seconds) 10
ID: 3375592 • Letter: T
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TABLE 3 Truncated Regression Pooled Data (dependent variable time in seconds) 10 i5 10 Half Kilometer Kilometer Kilometer Kilometer Mile Marathon Maratho Linear specification 05.1 222.5 277.7355.9* 459.3 546.9 1289 (5.917) (5.824) €24.39) 14.020 -3.309 39.06 (0.251) 06 5962) 2.166) 1.043) (0.926 (5.377) 006265 0.7049 09276 2.275 -1.095 0.6053 6.793 (0.267) 06 (872) 2.206 (1.083) 98 5.710) 6.889) 12.53) 18.44) 51.16-122.1 57.71 -27.12 383.2 Prize difference/ ,000 33.14496.424.5481.08107.8-87.27-2203 2.099 2.221 2.462 2.049) 1.612 4.103) p value LR test of race dummies 00410303265 154 0008800000 000000000) 251 104 145 107 526 Quadratic specification Prize difference/1,000-64.78 491.5 71.97 -171.1 398.0 272.6 9083 1.191).546 (2.877 546) (0.807) (1.647)(3.791) Prize di 77.65 7.88 (0612 (0.006) (2014) 3.7919.79259.4 1852 (0.865 1026 180) 2.949) 1,000,000 NOTE: Figures in parentheses are t statistics Next, they include another variable in the regression-1993 points. This variable is a measure of runner ability. Consider the lower panel (with 1993 points), and column 2 (8 kilometer race) only, of the following table: TABLE 4 Truncated Regressions Linear Specification One-TimeRunners With and Without 1993 Points (dependent variable time in seconds) 10 IS Kilometer Kilommter Kilometer Kilometer Mile Mahn Marathon Without 1993 Points Prize difference 31.34 -5026 -18.22 4200 1650)2.097) 433) 1.740)535) 0.368 (3.277 1,000 8483 31.3-26.49 p value LR test of race dummies 0007285 07203 00005 02185 122 100 402 With 1993 points 0004769-002226-001449-0003016 -0.008837-0.05023-0.06393 1.082).2 2507) (0327) (0.687) 2.76) (3.351) 1993 points Prize difference 004 -294.6 (0.028 .480) (0002 (1077) 0.598) .418) 1.837) 0.03186 4646.78 135.9 NOTE: Figures in s are statistics. a. What is the coefficient on the variable (prize difference/1000)? b. Compare this to the coefficient on (prize difference/1000) in the top panel of this table (i.e. in the regression without 1993 points). Is there a difference in the significance eve of these two coefficients? (t statistics in the parentheses) c. Why/why not do you think there's a difference in the coefficients (and their significance levels)? Explain. (Hint: It is related to including a measure of ability in the regression)Explanation / Answer
A) The coefficient on the variable (prize difference/1000) is -294.6. The sign on the coefficient is negative. This can be interpreted as the variable (prize difference/1000) as which means price difference will decrease with increase in time taken and runners ability.
B) The coefficient in the top panel (without 1993) is -502.6.
t value of coefficient with 1993 = 1.480
t value of coefficient without 1993 = 2.097
T statistic of without 1993 is more than with 1993. Thus coefficient of prize difference/1000 has more significance for without 1993 points
c) There is the difference in correlation and their significance because in without 1993 points, they regress the time taken to finish the race on prize difference, however with 1993 points they have included another measure which is the ability of the runner which changes the coefficient because now measure of prize difference is dependent on two factors - time to finish the race and runners ability.
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