Linear Modeling and Residuals

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

Lesson 5 of 53 parts Practice Flashcards

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Fitting a Line

Objective: Explain and use fitting a line in an Algebra 1 problem.

A linear model approximates a trend in data; scatter and context determine whether a constant rate is reasonable. Usually not; it summarizes a pattern.

Worked examples

Try itExample 1.1: A fitted line is y=2x+13. Predict y when x=5.Show answer

23. Substitute the stated input into the fitted rule. The answer is 23.

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Fitting a Line

Objective: Explain and use fitting a line in an Algebra 1 problem.

A linear model approximates a trend in data; scatter and context determine whether a constant rate is reasonable. Usually not; it summarizes a pattern.

Worked examples

Try itExample 1.1: A fitted line is y=2x+13. Predict y when x=5.Show answer

23. Substitute the stated input into the fitted rule. The answer is 23.

Residuals

Objective: Explain and use residuals in an Algebra 1 problem.

A residual is observed output minus predicted output; signs show which side of the fitted line an observation falls. The observation is above the prediction.

Worked examples

Try itExample 2.1: A model predicts 47 and the observed value is 49. Find observed minus predicted.Show answer

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

Interpolation and Extrapolation

Objective: Explain and use interpolation and extrapolation in an Algebra 1 problem.

Prediction inside the observed input range is interpolation; prediction outside it is extrapolation and needs extra caution. The original trend may not continue.

Worked examples

Try itExample 3.1: A fitted line is y=4x+33. Predict y when x=11.Show answer

77. Substitute the stated input into the fitted rule. The answer is 77.

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