Virginia SOL Math / Algebra II / Statistics

A2.ST.2

Bivariate Data & Best-Fit Curves

What you'll learn

  • Make and read a scatterplot of bivariate data
  • Choose a linear, quadratic, or exponential model
  • Use a curve of best fit to make predictions

Words to know

Bivariate data —
data with two variables per point
Scatterplot —
a graph of ordered-pair data
Curve of best fit —
a model that follows the data trend
Correlation —
how strongly two variables move together
Prediction —
an estimate read from the model

Why it matters Fitting a curve to data lets us summarize a trend and predict outcomes, such as estimating a value between or beyond the points collected.

Worked examples

Model ItI do

A scatterplot of the data rises then falls. Which model fits best?

A pattern that rises to a peak and then falls is not a straight line, so a linear model does not fit. A quadratic (parabola) rises and then falls, matching the shape, so a quadratic curve of best fit is the best choice.

Try It TogetherWe do

Data increase at a steady rate. Which model fits best?

A steady, constant rate of change matches a straight line, so a linear model is best.

Now YouYou do

Data double at each step. Which model fits best?

Decide whether a constant rate or a constant multiplier fits. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.What graph shows bivariate data as individual points?

  2. 2.Data increase at a steady, constant rate. Which model fits best?

  3. 3.Data double at each step. Which model fits best?

On Level

The core Quick Check from the book.

  1. 1.What graph shows bivariate data as points?

  2. 2.Which model has a straight-line trend?

  3. 3.Which model has a U or upside-down U shape?

  4. 4.Which model grows by a constant multiplier?

  5. 5.What is a line or curve that follows the data called?

Challenge

Stretch your thinking.

  1. 1.A scatterplot rises to a peak and then falls symmetrically. Which model fits best?

  2. 2.A best-fit line is y = 3x + 5. Predict y when x = 10.

  3. 3.Data rise quickly at first, then level off toward a ceiling. Of the Algebra II families, which fits best?