List Paragraph Normal . In their paper \"The Rewards to running: Prize structure

Question

List Paragraph Normal . In their paper "The Rewards to running: Prize structure and performance in professional road racing", Lynch and Zax present some evidence that races with large prizes record faster times because they attract faster runners, not because they encourage all runners to run faster (the paper can be found on D2L, but you shouldn't need to read it in order to answer this question). They regress the time taken to finish the race on prize difference (defined as the dollar amount of prize money a runner would lose if he or she finished one place lower than her pre-race ranking relative to other race entrants), and other controls, to see if there is a relationship between prize money at risk, and finishing time. They present the following table (note that the figures in parentheses are t-statistics): TABLE 3 Truncated Regression Pooled Data (dependent variable - time in seconds Ha Marathon Kilometer Kilomia Kilometer Kilometer Mile Marathon Marathon 10 Linear specification 105. 222.5 277 355. 459.3* 5469 1289* (5.917) (5.824) (24.39) -3.309 39.06 Gender (4.020) (6.889) (1253) (18.44) 56-122. 57.71 27.12 3832* (0.251) (1.106) 5.962)2.166) (1.043) (0926) (5.377) -0.7049 09276 2.275 1.095 0.6053 6.793 (0267) (1.106) (5.872) (2.206) (1.083) (1.198) (5.710) Age Prize difference/ 33.14** 496.4 24 54 81.08-1078 87.27 -22.03* (2.099) (2.221) (2.386) 2462) (2.049) (1.612) (4.103) 1,000 p value LR test of 004103 03265 00000 0008 00000 00000 00000 race dummies 154 104 629 145 107 251 526 Quadratic specification Prize difference/ 1,000 -64.78 491.5 Prize difference -71.97**-171.1 398.0-2726 9083 (1.19) (0.546) (2877) (1.546) (0.807) (1.647) (3.791) 1100.00 13.79* 19.79 -259.4 77.65 1852* 17.88 (0612) (0.006) (2.014) (0.865) (1.026) (1.180) (2.949) -8.397 NOTE: Figures in parentheses are t statistics. Consider the linear specification, and the 5 kilometer race (l.e. column 1 only) a. What is the coefficient on the variable (prize difference/1000)? Interpret the sign of this coefficient. Is this coefficient significant at 5% level? why? What does it mean for this coefficient to be (or not to be) significant? (Explain in terms of the given variables.) b. d.

Explanation / Answer

(a)
The coefficient on the variable (prize difference/1000) is -33.14

(b)
The sign on the coefficient is negative. This can be interpreted as the variable (prize difference/1000) increases, time to finish the race decreases.
That is there is negative correlation between the variable (prize difference/1000) and time to finish the race.

(c)
t statistics for the coefficent = 2.099
Degree of freedom = n - k - 1 where k is number of predictors
= 154 - 4 - 1 = 149
P-value for t = 2.099 and DF = 149 is
2 * P[t > 2.099] = 2 * 0.01875 = 0.0375
As, p-value is less than the significance level of 0.05, the coefficient on the variable (prize difference/1000) is significant.

(d)
The coefficient is significant means that the variable prize difference/1000 is a significant variable in predicting time to finish the race in the regression model.

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.