Two-Variable Data: Models and Scatterplots Flashcards

Data on number of employees (x) and company revenue (y, millions) is modeled by y = 0.05x + 1.2. What does the slope represent?

Answer: Revenue increases by $0.05 million for each additional employee

The slope is the rate of change of y per unit of x: each extra employee is associated with $0.05 million more revenue.

A quadratic model best fits a dataset when the scatterplot looks like which of these?

Answer: A U-shape or inverted U-shape (parabola)

Quadratic models produce parabolic (U or inverted-U) curves, distinct from linear or exponential shapes.

A linear model predicts that a car's value (y, dollars) decreases with age (x, years): y = −1200x + 18000. What was the car's initial value?

Answer: $18,000

Initial value is when x = 0: y = −1200(0) + 18000 = $18,000.

Using the model y = −1200x + 18000, after how many years is the car's predicted value $9,600?

Answer: 7

9600 = −1200x + 18000 → −1200x = −8400 → x = 7.

A researcher fits both a linear and an exponential model to the same dataset. The exponential model has smaller residuals overall. What does this indicate?

Answer: The exponential model is a better fit for the data

Smaller residuals mean the model's predictions are closer to the actual data, indicating a better fit.

A scatterplot of daily high temperature (x, °F) vs. electricity usage (y, kWh) shows points going upward from left to right. The correlation is r = 0.78. How would you describe this relationship?

Answer: Moderate positive linear relationship

r = 0.78 is positive and moderately strong (between 0.5 and 0.9).

A line of best fit has the equation y = 0.8x + 3. Which point lies on this line?

Answer: (5, 7)

y = 0.8(5) + 3 = 4 + 3 = 7, so (5, 7) lies on the line.