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I use two criterion ($w$ and $x$) for predicting the outcome of football matches. Analysis of historical records has provided me with two best fit linear equations. The probability that the team playing at their home ground will win based on criteria w, is $y_1 = 0.02w + 0.38$. A different probability based on $x$ is $y_2 = 0.01x + 0.37$.

What method should be used to combine these two equations to produce a single equation to obtain $y$, or should an entirely different approach be used to arrive at a single equation?

mdewey
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tams
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  • This looks like you've fit two separate regression models with $x$ as the predictor in one model and $w$ as the predictor in the other. Why not fit a single regression model with both $x$ and $w$ as predictors? Was this an ordinary least squares regression (which may be a little odd since the outcome is a proportion) or logistic regression? – Macro Jun 25 '12 at 21:14
  • Yes, least squares regression. So how do you go about fitting a single regression model with two predictors? What's odd and why? – tams Jun 25 '12 at 21:31
  • If the probabilities are not too close to 0 or 1 the least squares fit might be OK, but otherwise it is not well approximated an unbounded continuous variable, which least squares assumes. What software are you using? – Macro Jun 25 '12 at 21:38
  • To calculate the equation, I use Excel. Probabilities rarely get close to 0 or 1. Thanks. – tams Jun 25 '12 at 22:01
  • In line with what Macro suggests i would say that you should try logistic regression with both w and x as predictors even if the probabilities do not get close to 0 or 1 OLS does not constrain the numbers to faal in the interval [0,1] and si projewcted values could easily fall outside the interval.. – Michael R. Chernick Jun 25 '12 at 22:14
  • Okay, I'll look into Logistic regression wit two variables. Thanks – tams Jun 25 '12 at 23:14
  • Check http://stats.stackexchange.com/questions/155817/combining-probabilities-information-from-different-sources/188554#188554 – Tim Aug 25 '16 at 21:14

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