Bluebook SAT Test Two-Variable Data: Models and Scatterplots 5

Question 1

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?

Accepted Answer

Exponential decay; the population is decreasing

Answer

Exponential growth; the population is increasing

Answer

Linear decay; the population is decreasing at a constant rate

Answer

Quadratic; the population decreases then increases

Question 2

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

Accepted Answer

4

Answer

−4

Answer

2

Answer

−2

Question 3

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?

Accepted Answer

2

Answer

5

Answer

7

Answer

1

Question 4

Which correlation coefficient indicates the weakest linear relationship?

Accepted Answer

r = −0.02

Answer

r = −0.85

Answer

r = 0.72

Answer

r = 0.91

Question 5

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?

Accepted Answer

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

Answer

The slope may be negative

Answer

The y-intercept may be positive

Answer

Extrapolation always overestimates the true value

Question 6

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.

Accepted Answer

$77,000

Answer

$74,500

Answer

$80,000

Answer

$42,000

Question 7

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

Accepted Answer

No; correlation does not imply causation

Answer

Yes; a strong correlation proves causation

Answer

Only if the correlation coefficient is above 0.9

Answer

Yes, if the data comes from an experiment