Linear Regression and Residuals

Learn and apply linear regression and residuals using equations, examples, and interpretation.

Lesson 2 of 53 parts Practice Flashcards

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Best-Fit Line

Objective: Explain and use best-fit line in an Algebra 1 problem.

A regression line summarizes a linear association, often by minimizing squared vertical residuals; it does not have to hit every point. No, it describes association.

Worked examples

Try itExample 1.1: A fitted line is y=2x+15. Predict y when x=5.Show answer

25. Substitute the stated input into the fitted rule. The answer is 25.

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Best-Fit Line

Objective: Explain and use best-fit line in an Algebra 1 problem.

A regression line summarizes a linear association, often by minimizing squared vertical residuals; it does not have to hit every point. No, it describes association.

Worked examples

Try itExample 1.1: A fitted line is y=2x+15. Predict y when x=5.Show answer

25. Substitute the stated input into the fitted rule. The answer is 25.

Residual Calculation

Objective: Explain and use residual calculation in an Algebra 1 problem.

A residual equals observed y minus predicted y; plotting residuals against x can reveal curvature or changing spread. The observation falls below the prediction.

Worked examples

Try itExample 2.1: A model predicts 49 and the observed value is 51. Find observed minus predicted.Show answer

2. Subtract predicted output from observed output. The answer is 2.

Interpreting Slope

Objective: Explain and use interpreting slope in an Algebra 1 problem.

Regression slope expresses predicted change in output per unit input, with units and a meaningful observed range. The association can change outside observed inputs.

Worked examples

Try itExample 3.1: Find the slope through (0,35) and (11,79).Show answer

4. Divide the change in y by the change in x. The answer is 4.

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