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 Residual Formula

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

Step2: Calculate \( a \)

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

Step3: Calculate \( b \)

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

Answer:

\( a = -0.4 \) and \( b = 0.15 \) (corresponding to the option: \( a = -0.4 \) and \( b = 0.15 \))