Two-Variable Data: Models and Scatterplots Flashcards

The model y = 200(0.85)^x represents the number of bacteria (y) after x hours. What type of model is this and what is happening to the population?

Answer: Exponential decay; the population is decreasing

The base 0.85 is between 0 and 1, making this exponential decay — the population decreases by 15% each hour.

A data point at (4, 30) lies above the line of best fit y = 5x + 6. What is the residual?

Answer: 4

Predicted y = 5(4) + 6 = 26; residual = 30 − 26 = 4.

A line of best fit for the data x: 1, 2, 3, 4, 5 and y: 7, 9, 11, 13, 15 is y = mx + b. What is m?

Answer: 2

The y values increase by 2 for every unit increase in x, so the slope m = 2.

Which correlation coefficient indicates the weakest linear relationship?

Answer: r = −0.02

The value closest to 0 (r = −0.02) indicates the weakest linear relationship.

Using a line of best fit to predict y for an x value far outside the range of the data is called extrapolation. Why is this risky?

Answer: The model may not accurately represent the relationship outside the observed range

Extrapolation is unreliable because the pattern established in the data range may not continue outside it.

Data shows years of experience (x) and salary (y, thousands). The line of best fit is y = 3.5x + 42. Predict the salary for someone with 10 years of experience.

Answer: $77,000

y = 3.5(10) + 42 = 35 + 42 = 77, so $77,000.

A scatterplot shows a strong positive correlation between x and y. A student concludes that x causes y. Is this conclusion valid?

Answer: No; correlation does not imply causation

Correlation only shows association — a third variable or coincidence may explain the pattern.