Now let's move on to bowler's performance to take stakes. Again, we first used the number of runs considered, the number of balls bowled and the number of wickets taken to measure bowler's performance. Let's run a baseline regression where salary is a function of the number of runs considered. And let's call this rrec_IPL7. The regression results suggest that there is a positive impact of the number of runs considered on the salary. In other words, when the number of runs consider increase, the player's salary will increase as well. This appears to be counterintuitive, as the role of a bowler is to stop the opponent from scoring runs. However, the runs considered may be correlated with the number of matches that a player play or the number of balls that are player bowl. Does this based on regression, may not repeat the whole story. This can also be reflected by the small r square as well. The r square in this regression is only at 0.023. Next, let's add the number of balls bowl into the regression. Now the estimated coefficient on the runs consider is negative. While the estimated coefficient on the balls bowl is positive, this confirms our previous suspicion that it is the number of balls bowled that, positively impacts players salary. Unfortunately, the estimate on the number of runs considered is not statistically significant with a P value equals 0.172. And the estimated coefficient on the number of balls bowl, it's only significant in the 10% level as the P value it's at point 0.096. The r square is still very small, suggesting a poor fit for our data. In the next regression will add the number of wickets taken to the equation. The estimate on the number of runs considered and the number of wickets taken are both negative. This results suggest that the poorer the performance of the bowler, the lower the salary. The balls bowl is positive as 6343.24, which means that bowling one more ball will increase the player's salary by 6343.24. Neither the runs considered nor the wickets taken variable is statistically significant. The number of balls bowl variable is statistically significant at 5% level. This may indicate that the performance of a bowl is not as important a factor compared to the term he played. In the next regression, we'll use our modified bowling average and bowling strike variables to measure a bowler's performance. In this regression, both bowling average and bowling strike as statistically significant, the estimate on bowling averages negative and the estimate on bowling strike is positive. We call it bowling average, is defined as the number of runs considered divided by the number of wickets taken. And the bowling strike is defined as the number of balls bowled, divided by the number of wickets taken. The sign on bowling average makes sense as the know what the bowling average, the better the performance bowler is, the sign on bowling strike. However, it's opposite from what we would expect. Bowling strike measures the effectiveness of bowler taking wickets, the lower the bowling strike, the more effective a bowler is a taking wickets quickly or getting a batman out. Our regression results suggest that the more effective the bowler is the last salary he receives, again. This can be due to the dominant role of the number of balls bowled for a player. Lastly, let's consider incorporating bowl betting statistics and bowling statistics in the same regression to see if both of them together would impact the salary of the player. We'll use the original variables, the number of runs, the number of nuts out, the number of balls phase, number of runs considered, balls bowled and the number of wickets taken in this regression. Compared to the questions 4 and regression 9, the signs of the coefficients are the same. The sciences of their estimates are smaller in the new regression. The number runs change from 2871 to 2089, while the number of not_outs changed from 89,450 to 59,500. The estimated coefficient on the number of balls faced change from -2044 to -354, and the number of runs considered changed from -3049 to -1737. Additionally, the estimate on the number of balls bowl changed from 6243 to 5030. And the estimated coefficients on the wickets taken change from -27,370 to -22,310. From the relative size changes we could see that runs is the most important determinant in batman's salary, while for bowlers, the number of balls bowled and the number of wickets taken are more important. Also notes that in this new regression, the r square is improved to 0.408, which suggest that we obtain a better fit compared to the previous models. Lastly, let's use our modified betting average, betting strike, bowling average as well as bowling strike to measure the player performance and incorporate all four measures in one regression. So we'll compare this regression 12 with regression 6 and regression 10. The estimate co-efficient on betting average changes from 19,000 to 24,000. The estimate co-efficient on betting strike changes from 6,353,000 to -612,000, but it is no longer a statistically significant. The estimated coefficients on bowling average changes from -33,000 to -31,860, and the estimated coefficient on bowling strike changes from 49,140 to 59,410. Again, the r square is now at 0.308, which is higher than the r squaring regression 6 at 0.234. And much higher than the are square in regression 10 at 0.054. With all this analysis, we can see that compared to bowlers, the performance of batman is more important in determining their salary.
