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?
( \bigcirc a = 0.4 ) and ( b = - 0.15 )
( \bigcirc a = - 0.4 ) and ( b = 0.15 )
( \bigcirc a = 8.6 ) and ( b = 14.25 )
( \bigcirc 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 \(=4.5\).
\(a=4.1 - 4.5=- 0.4\)

Step3: Calculate the value of \(b\)

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

Answer:

a = -0.4 and b = 0.15 (the second option)