Simple linear regression is the technique we use to describe the straight-line relationship between one predictor variable (x) and one response variable (y). In engineering practice, this is how you turn a scatter of measured data — load versus deflection, temperature versus reaction rate, flow rate versus pressure drop — into an equation you can use to explain behavior and predict new outcomes. The model has the familiar form y-hat = b0 + b1*x, where b0 is the intercept and b1 is the slope.
The core computational idea is the least squares method: among all possible lines, we choose the one that minimizes the sum of squared vertical distances (residuals) between the observed data points and the line. From that fitted line we then ask three separate questions. First, what do the coefficients mean physically — what does a one-unit change in x do to y, and is the intercept meaningful within the range of the data? Second, how well does the line fit — this is where R-squared, the proportion of variation in y explained by x, comes in. Third, is the relationship statistically real — this is the t-test on the slope (equivalently the F-test for the overall model) and its p-value.
As you watch the videos below, keep a running list of the formulas and what each quantity represents: the slope and intercept estimators, SST/SSR/SSE, R-squared, and the standard error. Pay attention to how each presenter moves from raw data to a fitted equation, and note the warning about extrapolating predictions outside the range of x values actually observed.
These videos were chosen from YouTube on October 2, 2026. Each has captions; the player turns them on. Videos on YouTube can be changed or removed — if one no longer plays, tell your instructor. If a player does not appear, use its Watch on YouTube link.