CCSS.Math.Content.HSS-ID.B.6b
The standard
Informally assess the fit of a function by plotting and analyzing residuals.
Common Core State Standards for Mathematics · Summarize, represent, and interpret data on two categorical and quantitative variables
What this standard means
Students need to compare a data set to a chosen model by looking at residuals. They should calculate actual minus predicted values, plot those residuals against the x-values, and decide whether the model is doing a reasonable job.
Mastery looks like noticing patterns, not just saying points are close. A good fit has residuals scattered randomly around zero. A curved pattern, fan shape, or clusters suggest the model is missing something. Students often mix up residuals with y-values, forget the sign, or treat one large residual as proof the whole model is bad.
Ways to teach it
- Give pairs a scatterplot, line of fit, and table, then have them compute residuals with sticky notes and build a residual plot.
- Ask students to write: What would a residual plot look like if a linear model is a poor choice, and why?
- Show three residual plots and have students label each as random scatter, curved pattern, or fan shape, with one sentence of evidence.
- Use school commute time and distance data, fit a line, then check whether the residuals suggest distance alone predicts commute time well.
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Related standards
- CCSS.Math.Content.HSF-IF.C.7a
Graph linear and quadratic functions and show intercepts, maxima, and minima.
- CCSS.Math.Content.HSS-ID.B.6c
Fit a linear function for a scatter plot that suggests a linear association.
- CCSS.Math.Content.HSS-ID.B.6a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
- CCSS.Math.Content.8.F.A
Define, evaluate, and compare functions.