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. 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 )

Explanation:

Step1: Recall the formula for residual

Residual = Given - Predicted.

Step2: Calculate the value of \(a\)

For \(x = 3\), Given \(=4.1\), Predicted \(=4.5\).
Residual \(a=4.1 - 4.5=- 0.4\).

Step3: Calculate the value of \(b\)

For \(x = 4\), Given \(=7.2\), Predicted \(=7.05\).
Residual \(b=7.2-7.05 = 0.15\).

Answer:

\(a=-0.4\) and \(b = 0.15\), so the answer is \(a=-0.4\) and \(b = 0.15\) (the second option).