What does simple linear regression model?

• A. The relationship between two categorical variables.
• B. A nonlinear relationship between a predictor and an outcome.
• C. The correlation coefficient between two variables without prediction.
• D. The relationship between a single predictor and a continuous outcome, estimating a line that best fits the data.

Answer: (D)

Simple linear regression models how one numeric predictor relates to a numeric outcome by fitting a straight line through the data. It yields an equation like y = β0 + β1 x, where the intercept β0 is the predicted outcome when the predictor is zero and the slope β1 is the amount the outcome changes for each unit increase in the predictor. The line is chosen to minimize the differences between observed outcomes and those predicted by the line, using a least-squares criterion, so the model provides both a summary of the association and a way to predict the outcome for new predictor values. For example, you might use hours studied to predict exam score. The key idea is one predictor and a continuous outcome, with the relationship assumed to be linear, so the model estimates a straight-line relationship. The other options don’t fit: relating two categorical variables isn’t about predicting a continuous outcome with a line; nonlinear relationships require a curved line or a different model; a correlation coefficient describes association but doesn’t provide a predictive equation for the outcome.