# Explanation of multiple linear regression output

Just looking for some help with the interpretation of my multiple linear model output and also some validation on the methods I used.

I have 1 response - Ball speed and 9 continuous predictors and 1 categorical predictor (the type of club with 4 levels).

I have used forward entry method with condition for entry alpha = 0.05

I get from the output with mini-tab, 4 regression equations one for each club. With only a changing y-intercept but the coefficient for other predictors between the clubs stays the same. Is this correct and can anyone explain why? I was expecting the coefficient for the other predictor variables to change with each club.

## 1 Answer

I don't know Minitab, but that style of output strikes me as strange. Nonetheless, the interpretation is straightforward.

Each of the four equations is a regression for a particular type of club. They could be combined into one equation by taking that one categorical predictor as three binary predictors of 0/1 for club A, 0/1 for club B, 0/1 for club C. Then club D would be (0,0,0).

$$y_i = \beta_{intercept} + \sum_{j=1}^9 \beta_jx_{ij} + \beta_{A}x_{iA} + \beta_{B}x_{iB} + \beta_{C}x_{iC}$$

The $$x_{iA}$$, $$x_{iB}$$, and $$x_{iC}$$ are the binary (0 or 1) indicator variables in row $$i$$ of your data matrix. If you run your regression this way, you should get some familiar-looking numbers from when you ran it the way you did.

If you run the regressions separately for each club, then you should expect different regression coefficients on the continuous predictors, though I recommend against this. It's more parameter estimates, more potential to overfit, and less elegence than one equation.

It would be standard to do three indicator variables for four clubs, as the effect of the fourth club is included in the intercept term (think of it as a reference or control group).