Estimation and Prediction

Two-Variable Data: Estimation and Prediction

These questions show a scatterplot with a line of best fit drawn through the data. Your job is to use the line (not the individual data points) to predict a value.

The Technique

1. Find the given value on the appropriate axis.
2. Move straight across (or up) to the line of best fit — not to a data point.
3. From where you hit the line, move to the other axis and read the value.
4. Pick the answer choice closest to your reading.

Worked Example 1

A botanist studies the relationship between hours of sunlight and weekly plant growth. The scatterplot shows data for 14 plants, along with a line of best fit. Based on the line, what is the predicted weekly growth for a plant receiving 6 hours of sunlight?

A) 3 cm
B) 6 cm
C) 11 cm
D) 8 cm

SOLUTION

Locate $x = 6$ on the horizontal axis (hours of sunlight). Go straight up until you hit the line of best fit — not any individual dot. From that point on the line, go straight left to the y-axis. The reading is approximately $8.2$ cm.
The closest choice is $8$.
Answer: D) 8 cm

Why the wrong answers are tempting:
A) 3 cm is the predicted growth for about 2 hours of sunlight — a misread on the x-axis.
B) 6 cm might come from confusing the x-value (6 hours) with the y-value.
C) 11 cm is the predicted growth for about 8 hours — reading from the wrong x-value.

Worked Example 2

A dealership compiled data on car resale value vs. age. The scatterplot shows the data with a line of best fit. Based on the line, what is the closest predicted resale value for a car that is 4 years old?

A) $20,000
B) $12,000
C) $8,000
D) $16,000

SOLUTION

Find $x = 4$ (age in years) on the horizontal axis. Go up to the line of best fit. Read across to the y-axis: the line passes through approximately $16$ on the vertical axis. Since the axis is in thousands of dollars, this is $16,000.
Answer: D) $16,000

A) $20,000 is the predicted value at about age 2 — reading from the wrong x-value.
B) $12,000 is the value at about age 6.
C) $8,000 is the value at about age 8.

The Key Gotcha: Line vs. Data Points

The most common mistake is reading an actual data point instead of the line of best fit. Individual data points scatter above and below the line — they represent real observations, not predictions. The line represents the model's prediction.

If you see a dot at $(5, 25)$ but the line passes through $(5, 20)$, the prediction at $x = 5$ is $20$, not $25$.

When the Question Asks "Closest To"

Since you're reading from a graph, your estimate may not be exact. That's why the question says "closest to." If your reading is $8.2$ and the choices are 3, 6, 8, and 11, pick $8$. Don't overthink it — choose the nearest option.

Reverse Predictions

Sometimes the question gives you a y-value and asks for the corresponding x-value. The technique is the same but in reverse:

1. Find the y-value on the vertical axis.
2. Move straight right to the line of best fit.
3. From that point, move straight down to the x-axis and read the value.

What to Do on Test Day

• Always use the line, not a nearby data point. The line is the model; the dots are observations.
• Use grid lines on the graph to read values accurately. If the grid lines are at intervals of 5, each small division is 1.
• Read the axis labels carefully. If the y-axis says "in thousands of dollars," a reading of 16 means $16,000.
• "Closest to" means pick the nearest choice. Don't worry about being off by a small amount.
• These take 20–30 seconds. The only risk is reading from the wrong line or the wrong axis position.