Question

The scatterplot represents the total fee for hours renting a bike. The line of best fit for the data is y = 6.855x + 10.215.

A graph shows hours of rental labeled 2 to 6 on the horizontal axis and cost in dollars on the vertical axis. A line increases from 0 to 6.

Which table shows the correct residual values for the data set?

A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries negative 2.12, 1.575, 1.22, 1.315, negative 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries 2.12, negative 1.575, negative 1.22, negative 1.315, 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries 2.12, negative 1.575, 1.22, negative 1.315, 1.99.
A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries negative 2.12, 1.575, negative 1.22, 1.315, negative 1.99.

Answer 1

Residual = observed − predicted, with predicted ŷ = 6.855x + 10.215.

x=1: ŷ = 17.07 → residual = 14.95 − 17.07 = −2.12
x=2: ŷ = 23.925 → residual = 25.50 − 23.925 = 1.575
x=3: ŷ = 30.78 → residual = 32 − 30.78 = 1.22
x=4: ŷ = 37.635 → residual = 38.95 − 37.635 = 1.315
x=5: ŷ = 44.49 → residual = 42.50 − 44.49 = −1.99

These match option A.