Virginia SOL Math / Algebra I / Statistics

A.ST.1

Scatterplots & Best Fit

What you'll learn

  • Construct scatterplots from bivariate data
  • Describe the association shown in a scatterplot
  • Fit a line or curve of best fit and use it to predict

Words to know

Scatterplot —
a graph of paired (x, y) data points
Bivariate data —
data with two variables per observation
Association —
the trend between the two variables
Line of best fit —
a line that best models the data trend
Correlation —
how closely the points follow a line
Data cycle —
formulate, collect, analyze, and interpret data

Why it matters Scatterplots reveal whether two things rise or fall together, and a line of best fit turns that trend into predictions.

Worked examples

Model ItI do

Describe the association and draw a line of best fit for the data shown.

As x increases, y increases, so the association is positive. A line of best fit rises through the middle of the points.

Try It TogetherWe do

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

Substitute 10 for x: y = 3(10) + 5 = 30 + 5 = 35. The predicted value is 35.

Now YouYou do

If points fall as x increases, is the association positive or negative?

Decide whether y rises or falls as x grows. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.A cloud of points trending downward shows what kind of association?

  2. 2.Using y = 3x + 2, predict y when x = 5.

  3. 3.What do we call the line that best models a scatterplot?

On Level

The core Quick Check from the book.

  1. 1.A cloud of points trending upward shows what kind of association?

  2. 2.Using y = 2x + 1, predict y when x = 4.

  3. 3.What do we call the line that best models a scatterplot?

  4. 4.Points that fall as x rises show what association?

  5. 5.Name the first step of the data cycle.

Challenge

Stretch your thinking.

  1. 1.A best-fit line is y = -2x + 20. Predict y when x = 6.

  2. 2.A best-fit line is y = 4x + 1. For which x does y equal 25?

  3. 3.As study time increases, test scores increase. What type of association is this?