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.

$x$	given	predicted	residual
2	$2.3$	$1.95$	$0.35$
3	$4.1$	$4.5$	$a$
4	$7.2$	$7.05$	$b$

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 $b = -14.25$

Explanation:

Step1: Recall Residual Formula

Residual = Given - Predicted.

Step2: Calculate \( a \)

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

Step3: Calculate \( b \)

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)