Two-Variable Data: Models and Scatterplots Flashcards

The linear model for height (y, inches) based on age (x, years, ages 2–10) is y = 2.5x + 32. By how much does the model predict height increases per year?

Answer: 2.5 inches

The slope 2.5 means the model predicts a 2.5-inch increase in height per year.

A best-fit line passes through (0, 12) and (4, 28). What is the equation of this line?

Answer: y = 4x + 12

Slope = (28 − 12)/(4 − 0) = 4; y-intercept = 12, giving y = 4x + 12.

A scatterplot shows the following points: (1, 2), (2, 8), (3, 18), (4, 32). Which model best fits these data?

Answer: Quadratic

The second differences are constant (Δ²y = 4), which is the signature of a quadratic model.

What does a residual plot that shows a curved pattern (not random scatter) indicate?

Answer: The chosen model is not an appropriate fit; a different model should be tried

A curved pattern in residuals means the linear model fails to capture a non-linear trend in the data.

A scatterplot of x and y shows r = 0.60. Which statement is most accurate?

Answer: There is a moderate positive linear relationship between x and y

r = 0.60 indicates a moderate positive linear relationship; r is not the slope.

A model y = 2x + 5 predicts production costs. An actual data point is (6, 22). By how much does the model overpredict or underpredict?

Answer: The model overpredicts by 5

Predicted = 2(6) + 5 = 17; actual = 22; residual = 22 − 17 = 5 > 0, so the model underpredicts by 5.

Two scatterplots: Plot A has r = 0.95 and Plot B has r = 0.40. Which plot shows points closer to the line of best fit?

Answer: Plot A

Higher |r| means points cluster more tightly around the line; r = 0.95 is much closer to 1 than r = 0.40.