# Why is my coefficient so large?

I have a GLM modeling basketball data where the dependent variable is the proportion of wins for a season. The independent variables are either percentages, or numeric. The family is binomial, and the link is logistic.

Why is the "fgp" coefficient so large? Especially compared to "ftp," since the both have similar relationships with the dependent variable, winp: Here are some diagnostic plots for reference:

Also, I know I'm supposed to model the DV as a proportion of successes over total trials. I read the R command for this is: DV <- cbind(myData$wins, myData$losses). Shouldn't it be: DV <- cbind(myData$wins, myData$totalTrials)

• Your first 2 plots are not going to show anything meaningful about the respective relationships unless you limit each X-axis to a much smaller range. – rolando2 Jan 21 '14 at 22:44

## 1 Answer

I am going to answer this assuming that these are basketball statistics. And without the actual data set, this is only an educated guess. Field goal percentage (fgp) is more significant than free throw percentage (ftp) because the proportion of the total points scored in the game that come from field goals is much higher. There are more field goal attempts than free throw attempts and field goals are worth more than free throws. Although I don't have this data, most likely corr(fgp,winp) >> corr(ftp,winp).

The reason the coefficient for fgp is high relative to other variables like trbg (rebounds), astg (assists), stlg (steals), blkg (blocks), tovg (turnovers) is that the variables are scaled differently. Fgp is a proportion between 0 and 1, while other statistics are expressed in positive integers. So it stands that the coefficient for fgp is larger if the variables are not normalized prior to the coefficient fitting.

• Small point: I'd say a proportion or a fraction between 0 and 1, not a percentage. You have logic on your side, as 100% means 100/100, but nevertheless in practice expressions such as "a percentage between 0 and 1" will sound odd to many readers, even mathematically competent readers. I don't know any software that supports the idea that percentage is just a display format. In practice, you have to multiply by 100 to work with percents, or divide by 100 to work with proportions, and that dominates attitudes. – Nick Cox Jan 19 '14 at 12:00
• @user37464 Yes. These are basketball statistics. So should I normalize the IVs such that mean=0, variance=1? I'm afraid this would make interpretation of the resulting scaled coefficients more difficult to interpret. – user2205916 Jan 19 '14 at 12:19
• @user37464: With regard to comparison between corr(fgp,winp) and corr(ftp,winp), from the first two graphs the difference doesn't seem to be large – Abhimanyu Arora Jan 19 '14 at 12:33
• @AbhimanyuArora That's what I thought too. I added the cor(winp, ftp) cor(winp, fgp) for both at the bottom of my question and I guess it looks larger than the plots depict. – user2205916 Jan 19 '14 at 13:00
• @NickCox Your point is interesting. I was told to use the win proportion for my DV. So is a two-column matrix justified for the DV, or was it meant that the win percentage (or win proportion) should have been used? – user2205916 Jan 19 '14 at 13:25