Question

computing residuals from an equation and table
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 =
age (years) given value predicted value residual
1 15 a 0.2
2 12 11.9 b
3 9 c 0
4 5 6.1 d
5 4 3.2 0.8

Explanation:

Step1: Calculate \(a\)

The formula for residual is \(Residual = Given\ Value - Predicted\ Value\). When \(x = 1\), the predicted - value \(a\) is calculated using the equation \(y=-2.9x + 17.7\). Substitute \(x = 1\) into the equation: \(y=-2.9\times1+17.7=14.8\).

Step2: Calculate \(b\)

The formula for residual is \(Residual=Given\ Value - Predicted\ Value\). Given \(Given\ Value = 12\) and \(Predicted\ Value = 11.9\), then \(b=12 - 11.9 = 0.1\).

Step3: Calculate \(c\)

Since the residual is \(0\), then \(Given\ Value=Predicted\ Value\). So \(c = 9\).

Step4: Calculate \(d\)

The formula for residual is \(Residual = Given\ Value - Predicted\ Value\). Given \(Given\ Value = 5\) and \(Predicted\ Value = 6.1\), then \(d=5 - 6.1=-1.1\).

Answer:

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