In a linear regression model, how does the goodness-of-fit measure relate to the interpretation of parameters?

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Seekh · Accepted Answer

The goodness‑of‑fit statistic, such as R², tells you how much of the variation in the outcome is explained by the predictors in the model; a higher value means the predictors together capture more of the true signal. Because each regression coefficient represents the expected change in the outcome for a one‑unit change in its predictor, the magnitude and significance of these coefficients are meaningful only when the overall model actually fits the data well. If R² is low, even a statistically significant coefficient might be misleading because the predictor explains little of the outcome’s variability, making its practical impact questionable. For example, in a simple model predicting test scores from study hours, an R² of 0. 90 means the hours explain 90 % of the score variation, so the slope coefficient (say 2 points per hour) is a reliable estimate of the true effect; if R² were 0.

In a linear regression model, how does the goodness-of-fit measure relate to the interpretation of parameters?

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