Question

john estimates the value of his car over time. the equation for the line of best fit is approximated as ( y = -2.9x + 17.7 ), where ( y ) represents the value, in thousands of dollars.
what values complete the residual table?
( a = )
( b = )
( c = )
( d = )

Explanation:

Step1: Calculate the value of \(a\)

The formula for residual is \(Residual = Given\ Value - Predicted\ Value\). We know that when \(x = 1\), \(Residual=0.2\) and \(Given\ Value = 15\). Using the formula \(0.2=15 - a\), we can solve for \(a\) as \(a = 15 - 0.2=14.8\)

Step2: Calculate the value of \(b\)

When \(x = 2\), \(Given\ Value = 12\) and \(Predicted\ Value=11.9\). Using the residual formula \(b=12 - 11.9 = 0.1\)

Step3: Calculate the value of \(c\)

When \(x = 3\), \(Given\ Value = 9\) and \(Residual = 0\). Using the formula \(0=9 - c\), we get \(c = 9\)

Step4: Calculate the value of \(d\)

When \(x = 4\), \(Given\ Value = 5\) and \(Predicted\ Value=6.1\). Using the residual formula \(d=5 - 6.1=- 1.1\)

Answer:

\(a = 14.8\), \(b = 0.1\), \(c = 9\), \(d=-1.1\)