Question

miguel wrote the predicted and residual values for a data set using the line of best fit ( y = 1.82x - 4.3 ). he left out two of the values. which represents the missing values of a and b? ( a = 1.16 ) and ( b = 0.12 ) ( a = 1.16 ) and ( b = - 0.12 ) ( a = 0.5 ) and ( b = 6.08 ) ( a = 0.5 ) and ( b = - 6.08 )

Explanation:

Step1: Calculate the value of \(a\)

The formula for the residual is \(Residual = Given - Predicted\). Rearranging for \(Predicted\) gives \(Predicted=Given - Residual\).
For \(x = 3\), \(Given = 1.1\) and \(Residual=- 0.06\).
So, \(a=1.1-(-0.06)=1.1 + 0.06=1.16\)

Step2: Calculate the value of \(b\)

Using the formula \(Residual = Given - Predicted\)
For \(x = 4\), \(Given = 3.1\) and \(Predicted = 2.98\)
So, \(b=3.1 - 2.98=0.12\)

Answer:

\(a = 1.16\) and \(b = 0.12\) (First option)