Question

Shanti wrote the predicted values for a data set using the line of best fit y = 2.55x – 3.15. She computed two of the residual 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 0.7, 2.3, 4.1, 7.2. The third column is labeled predicted with entries negative 0.6, 1.95, 4.5, 7.02. The fourth column is labeled residual with entries negative 1, 0.35, a, b.
What are the values of a and b?

a = 0.4 and b = –0.15
a = –0.4 and b = 0.15
a = 8.6 and b = 14.25
a = –8.6 and b = –14.25

Answer 1

Residual = observed (given) − predicted.

For x = 3: predicted = 2.55(3) − 3.15 = 4.5, residual = 4.1 − 4.5 = −0.4 (so a = −0.4).

For x = 4: predicted = 2.55(4) − 3.15 = 7.05, residual = 7.2 − 7.05 = 0.15 (so b = 0.15).

Answer: a = −0.4 and b = 0.15.