Fitting a regression line is only half the job. The other half is reading the output: what each coefficient means in the units of the problem, whether a predictor is statistically distinguishable from zero, how much of the variation in the response the model actually explains, and whether the model as a whole is doing anything useful. Statistical software will happily print a table of numbers for any dataset you hand it, so the engineer's value lies in interpretation, not computation.
In this course, regression output is the bridge between data and decisions. A slope coefficient tells you the expected change in the response per one-unit change in a predictor, holding the other predictors fixed; a p-value tells you how strong the evidence is against the hypothesis that the true coefficient is zero; R-squared and Adjusted R-squared describe how closely the fitted values track the observed data; and the F-test asks whether the predictors, taken together, explain more than chance would. Each piece answers a different question, and confusing them is the most common error students make.
As you watch the videos below, keep a blank regression output table in front of you and label the parts: coefficient, standard error, t statistic, p-value, confidence interval, SSR/SSE/SST, degrees of freedom, mean squares, F, R-squared, and standard error of the estimate. Ask yourself after each number: what practical statement about the engineering system could I write using this value, and what statement would be an overreach? Remember throughout that statistical significance is not the same as practical importance, that a high R-squared does not prove causation or guarantee valid assumptions, and that extrapolating beyond the range of your data is risky.
A short walkthrough of the coefficients section of a multiple regression software output, using a worked problem. Based on the title and description, it covers how to interpret each estimated coefficient, how to build and read confidence intervals for the coefficients, and how to carry out hypothesis tests on individual predictors using the reported t statistics and p-values.
It targets the first two subtopics directly, understanding coefficients and assessing statistical significance, and Joshua Emmanuel's worked-problem style is well suited to reading a real output table line by line.
This video works through the ANOVA portion of a multiple regression output for a stated problem involving 40 observations. It is likely to show how sums of squares and degrees of freedom produce the F-statistic for the overall model, and how R-squared and the standard error of the estimate are computed and interpreted from the same table.
It is the natural companion to the coefficients video, covering the overall F-test and model fit measures, and it connects the ANOVA table arithmetic to the summary statistics students must interpret.
A concise treatment of hypothesis testing in the simple linear regression setting, organized by textbook with an accompanying spreadsheet. Expect it to set up the null and alternative hypotheses for the slope, compute the test statistic from the estimate and its standard error, and reach a conclusion about whether the predictor is significant.
LearnChemE produces accurate, engineering-oriented tutorials, and this one grounds significance testing in the single-predictor case before you generalize the same logic to multiple regression output.
Together these videos move from the simple-regression significance test to the full multiple regression output, which is exactly the progression the module outcomes require. The coefficients walkthrough and the simple linear regression hypothesis test support MO2 by showing how to interpret slope estimates, standard errors, confidence intervals, and p-values, and they reinforce MO1 by keeping the fitted equation in view. The ANOVA and F-test video completes MO2 with R-squared, Adjusted R-squared, the standard error of the estimate, and the overall model test, while the contrast between the simple and multiple regression examples supports MO3. Interpreting these numbers in the units of a stated problem is the first step toward MO5, communicating findings as actionable insights, and the cautions raised about significance, fit, and extrapolation point forward to the assumption checking required by MO4.
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.