Two-Variable Data: Models and Scatterplots Flashcards

A scatterplot of study hours (x) vs. exam score (y) shows the line y = 8x + 45. A student studies 0 hours. What does the y-intercept tell us about this student?

Answer: The model predicts a score of 45 even with no study time.

The y-intercept (45) is the model's predicted value of y when x = 0, representing the expected baseline score.

The data (1, 3), (3, 7), (5, 11) appear to follow a pattern. Which model fits exactly?

Answer: y = 2x + 1

Slope = (7−3)/(3−1) = 2; using (1,3): 3=2(1)+b → b=1; equation y=2x+1 checks for all points.

Two models are fit to a dataset: Model A (linear) has r² = 0.72; Model B (quadratic) has r² = 0.94. Which model is more appropriate?

Answer: Model B, because it explains more variability in the data.

A higher r² (0.94 vs 0.72) means Model B explains more of the variance in y and is a better fit.

A linear model y = 2.5x + 15 predicts a student's GPA (y) from weekly hours of tutoring (x). What is the predicted GPA increase from 0 to 4 tutoring hours?

Answer: 10 points

Change in y = slope × change in x = 2.5 × 4 = 10.

A scatterplot shows data that follows a U-shaped pattern. Which model best fits this data?

Answer: Quadratic

A U-shaped pattern in a scatterplot is characteristic of a quadratic (parabolic) model.

A scatterplot has a correlation of r = 0.35. Which description best fits?

Answer: Weak positive linear relationship

r = 0.35 is positive and relatively small (far from 1), indicating a weak positive linear relationship.

A researcher uses the model y = 50 − 2x to predict y. At x = 25, what does the model predict?

Answer: 0

y = 50−2(25) = 50−50 = 0.