Two-Variable Data: Models and Scatterplots Flashcards

The line of best fit for data relating study time (x, hours) to GPA (y) is y = 0.3x + 2.1. A student studies 5 hours. What GPA does the model predict?

Answer: 3.6

y = 0.3(5) + 2.1 = 1.5 + 2.1 = 3.6.

A scatterplot shows data points tightly clustered around a line sloping upward from left to right. What can be concluded?

Answer: There is a strong positive linear correlation

Points tightly clustered around an upward-sloping line indicate a strong positive linear correlation.

The linear model y = 6x + 15 predicts the cost (y, dollars) of renting x hours of equipment. By how much does cost increase for each additional hour of rental?

Answer: $6

The slope is 6, meaning each additional hour increases cost by $6.

Which scatterplot characteristic suggests an exponential model is more appropriate than a linear model?

Answer: The data curves upward with increasing steepness

Exponential growth produces a curve that steepens continuously, unlike the U-shape of quadratic or the straight line of linear models.

In a scatterplot, an outlier is a point that lies far from the line of best fit. If a point is an outlier, what happens to the residual for that point?

Answer: The residual has a large absolute value

A residual = actual − predicted; a point far from the line has a large difference, so the residual's absolute value is large.

A line of best fit passes through the points (2, 10) and (6, 18). What is the slope of this line?

Answer: 2

Slope = (18 − 10)/(6 − 2) = 8/4 = 2.

A quadratic model y = x² − 4x + 7 is fitted to data. What is the predicted value when x = 3?

Answer: 4

y = (3)² − 4(3) + 7 = 9 − 12 + 7 = 4.