Reading slope and intercept in context

Interpret fitted slopes and intercepts using quantities and units in context

Problem types

Linear models of a situation
Scatter plots and trend lines
Residuals and correlation · Earlier idea
Residuals and correlation are used to judge a fitted line and to interpret its coefficients.
Average rate of change · Useful idea
The slope of a fitted line is the average rate of change of the response per unit of the explanatory variable.
Linear equations from constraints · Useful idea
A fitted line is a linear model, with slope as a rate and intercept as a starting value.
Comparing functions given in different forms · Useful idea
Comparing a table, a graph and an equation of a fitted model shows how well it represents the data.
A system written as a matrix equation · Useful idea
Fitting a line through data solves a linear system for the slope and intercept.
End behavior of a polynomial · Useful idea
Choosing a polynomial to fit nonlinear data uses its end behavior and number of turns to judge which degree fits.

Association is not causation · Extend the idea
A strong fitted relationship describes association. Whether it shows cause depends on how the data were collected.
Building an exponential model · See it applied
Equal ratios in a table, or a curved residual plot that a line cannot remove, show data that follow an exponential model. Building that model means finding its starting value and growth factor.
Checking a model against evidence · Extend the idea
Residuals from a regression line are used to decide whether the model should be kept or revised.

Comparing center, spread, and shape · Related idea
An outlier changes a mean, and it can also change a fitted line, so both are judged with outliers in mind.
Choosing a periodic model · Related idea
Fitting a sinusoid to data is a nonlinear regression, and a line fit is the linear case.
Rules for an arithmetic sequence · Shared foundations

Open the interactive map to explore lessons and skill connections.