Back to Assess fit by analyzing residuals — Problem 1 · Task Set 7

Exercises: Assess Fit by Analyzing Residuals

Work through each section in order. A residual is observed minus predicted: positive when the data point is ABOVE the model, negative when below. Keep the sign. When reading a residual plot, remember the key idea: random scatter around zero means a GOOD fit, while a clear pattern (a curve or a fan) means the model is wrong.

Grade 10·20 problems·~35 min·Common Core Math - HS Statistics and Probability·standard·hss-id-b-6b

Work through problems with immediate feedback

Warm-Up: What Is a Residual?

These problems review the residual definition and its sign.

A function is fitted to data. For one data point, the observed value is $14$ and the model's predicted value is $17$ . What is the residual at this point?

$-3$ , because residual = observed $-$ predicted $= 14 - 17$

$3$ , because a residual measures how far off the model is, which cannot be negative

$17 - 14 = 3$ , predicted minus observed

$14 + 17 = 31$