An independent variable, or predictor, is a variable used to account for or predict variation in a target (dependent) variable. In regression, several predictors can be assessed together to estimate how they collectively relate to a continuous outcome; in other models, one predictor can be used to compare groups or predict a binary outcome. section 5.0 section 14.5.2 section 14.6
Choose predictors because they are plausible and informative, not simply because they are available. Correlations help screen continuous candidates: values near +1 or -1 indicate stronger positive or negative associations, while values near 0 add little evidence of association. In wide data, this narrows attention before fitting a model. section 5.6 section 5.6.1
A practical predictor workflow is:
- Inspect data for outliers and non-normal variables before modeling. section 5.0 section 5.9
- Compare candidate predictors with the target, then select promising variables. section 5.6
- Check predictors for multicollinearity; remove a strongly correlated predictor and refit a reduced model when needed. section 5.1 section 5.9
- Fit the model, interpret coefficients and p-values, and inspect diagnostics for assumptions and influential observations. section 5.7.3 section 5.7.5
fit1 <- lm(wins ~ screen_assists_pts + deflections + loose_balls + contested_2pt + contested_shots, data = train)
In R's lm() formula, place the target left of ~ and join independent variables with +. Here, wins is predicted from five hustle statistics. section 5.7.2
Predicting NBA wins from hustle statistics
A multiple linear regression uses points off screens, deflections, loose balls recovered, contested two-point attempts, and total contested shots as predictors of regular-season wins. The fitted coefficients translate each predictor value into a predicted win total. For the 2016–17 Miami Heat, the model predicts 39 wins versus 41 actual wins; increasing loose balls recovered from 7.2 to 8.2 changes the prediction to 44. section 5.7.3
A predictor is not automatically important merely because it appears in a model. Coefficients describe the fitted relationship, while p-values are used here to identify predictors with statistically significant influence on variation in wins. Diagnostics then check whether residual behavior remains acceptable across predictor values and whether any observation has undue leverage. section 5.7.3 section 5.7.5
