Two-Variable Data: Models and Scatterplots Flashcards

A scatterplot shows data about car speed (x, mph) and fuel efficiency (y, mpg). The line of best fit is y = −0.3x + 55. Predict fuel efficiency at 80 mph.

Answer: 31 mpg

y = −0.3(80)+55 = −24+55 = 31 mpg.

Which of the following correlation coefficients indicates the strongest linear relationship?

Answer: r = −0.97

|−0.97| = 0.97 is the largest absolute value, indicating the strongest linear relationship.

A scatterplot of age of used cars (x, years) vs. value (y, dollars) shows a negative linear trend. Which value of r is most plausible?

Answer: r = −0.82

A negative trend with relatively strong association corresponds to r ≈ −0.82.

A quadratic model y = 2x² − 4x + 3 predicts production cost. What is the cost when x = 5?

Answer: 33

y = 2(25)−4(5)+3 = 50−20+3 = 33.

The line of best fit y = 7x − 14 describes hours of practice (x) and score improvements (y). For what number of hours does the model predict zero improvement?

Answer: 2

Set 0 = 7x−14 → x = 2.

A data table shows: x = 0, 1, 2, 3 and y = 2, 6, 18, 54. Which equation models this data?

Answer: y = 2 · 3^x

Check ratios: 6/2=3, 18/6=3, 54/18=3; constant ratio of 3 confirms y=2·3^x (a=2 at x=0, b=3).

A residual plot shows points in a U-shaped curve (not random scatter). What does this suggest?

Answer: A linear model is not the best fit; a curved model may be more appropriate.

A non-random (U-shaped) residual pattern indicates systematic error, suggesting the model form should be reconsidered.