Question

Miguel wrote the predicted and residual values for a data set using the line of best fit y = 1.82x – 4.3. He left out two of the values.

A 4-column table with 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled given with entries negative 2.3, negative 0.9, 1.1, 3.1. The third column is labeled predicted value with entries negative 2.48, negative 0.66, a, 2.98. The fourth column is labeled residual value with entries 0.18, negative 0.24, negative 0.06, b.
Which represents the missing values of a and b?

a = 1.16 and b = 0.12
a = 1.16 and b = –0.12
a = 0.5 and b = 6.08
a = 0.5 and b = –6.08

Answer 1

Compute predicted: y = 1.82x − 4.3.
- For x=3: y = 1.82(3) − 4.3 = 5.46 − 4.3 = 1.16 → a = 1.16.
Residual = observed − predicted.
- For x=4: residual = 3.1 − 2.98 = 0.12 → b = 0.12.

Answer: a = 1.16 and b = 0.12.