SAT Math: Two-variable data and models

Two-variable data: scatterplots, lines of best fit and models.

Problem-Solving and Data Analysis · Two-variable data: models and scatterplots
Both modules
12 practice questions · 3 with free solutions
Calculator allowed (Desmos)

Practise two-variable data and models →Adaptive SAT module

What the test covers

Line of best fit, predicted vs actual
Linear vs exponential model choice

Key ideas

Predicted value: substitute $x$ into the line of best fit. Residual = actual $-$ predicted.
Constant differences mean a linear model; constant ratios mean an exponential model.
The slope of a line of best fit is the predicted change in $y$ per unit increase in $x$ .

Common mistakes

A residual is actual minus predicted, not the other way round.
'Increasing by 25%' means multiplying by 1.25 each step.

Do it in Desmos

Enter the data in a table and fit y1 ~ mx1 + b or y1 ~ ab^x1 to compare models.

IB link: IB SL 4.4.

Worked example

The line of best fit for a scatterplot is $y = 2.4 x + 15$ . One data point is $(10, 42)$ . How much greater is the actual $y$ -value of this point than the value predicted by the line of best fit?

$3$
$39$
$- 3$
$42$

Answer: A: $3$

Predicted: $2.4 (10) + 15 = 39$ . Actual minus predicted: $42 - 39 = 3$ .

Practice questions

Try each question before opening the solution. Desmos or your own calculator is allowed on every SAT Math question. Solutions to the first 2 are open to everyone; the rest need only a free account. Every answer here was checked independently before it was published.

Question 1

The line of best fit for a scatterplot is $y = 2.4 x + 15$ . One data point is $(25, 77)$ . How much greater is the actual $y$ -value of this point than the value predicted by the line of best fit?

$75$
$- 2$
$77$
$2$

Show the answer and solution

Answer: D: $2$

Predicted: $2.4 (25) + 15 = 75$ . Actual minus predicted: $77 - 75 = 2$ .

Question 2

A quantity $Q$ takes the values 80, 120, 180 and 270 at times $t = 0, 1, 2, 3$ . Which best describes the relationship between $Q$ and $t$ ?

Exponential, increasing by 40% per unit of time
Exponential, increasing by 50% per unit of time
Linear, increasing by 40 per unit of time
Linear, increasing by 50 per unit of time

Show the answer and solution

Answer: B: Exponential, increasing by 50% per unit of time

The differences $40, 60, 90$ are not constant, so it is not linear. The ratios $\frac{120}{80} = \frac{180}{120} = \frac{270}{180} = 1.5$ are constant: exponential growth of 50% per unit of time.

Question 3

The line of best fit for a scatterplot is $y = 0.8 x + 15$ . One data point is $(20, 34)$ . How much greater is the actual $y$ -value of this point than the value predicted by the line of best fit?

$31$
$3$
$- 3$
$34$