Question

the predicted values were computed by using the line of best fit, $y = 3.2x + 2$. what are the residual values needed to complete the chart? $a = $ $b = $ $c = $ $d = $

Explanation:

Step1: Recall residual formula

Residual is calculated as \( \text{Residual} = \text{Given} - \text{Predicted} \).

Step2: Calculate \( a \)

For \( x = 1 \), Given = 6.1, Predicted = 5.2.
\( a = 6.1 - 5.2 = 0.9 \)

Step3: Calculate \( b \)

For \( x = 2 \), Given = 7.4, Predicted = 8.4.
\( b = 7.4 - 8.4 = -1.0 \)

Step4: Calculate \( c \)

For \( x = 3 \), Given = 11, Predicted = 11.6.
\( c = 11 - 11.6 = -0.6 \)

Step5: Calculate \( d \)

For \( x = 4 \), Given = 15, Predicted = 14.8.
\( d = 15 - 14.8 = 0.2 \)

Answer:

\( a = 0.9 \)
\( b = -1.0 \)
\( c = -0.6 \)
\( d = 0.2 \)