Calculate Residual Values Using a Line of Best Fit (8th Grade Math Problem)

Question

The predicted values were computed by using the line of best fit, $y = 3.2x + 2$. Complete the chart by finding the residual values $a$, $b$, $c$, $d$: 
| $x$ | Given | Predicted | Residual |
|-----|-------|-----------|----------|
| 1   | 6.1   | 5.2       | $a$      |
| 2   | 7.4   | 8.4       | $b$      |
| 3   | 11    | 11.6      | $c$      |
| 4   | 15    | 14.8      | $d$      |

Accepted Answer

$a=0.9$, $b=-1.0$, $c=-0.6$, $d=0.2$

Answer

Step 1: Recall the definition of a residual: Residual = Observed (Given) Value - Predicted Value, which measures the difference between actual data and the value predicted by the line of best fit. Step 2: Calculate residual $a$: Substitute the given and predicted values for $x=1$: $a = 6.1 - 5.2 = 0.9$. Step 3: Calculate residual $b$: Substitute the values for $x=2$: $b = 7.4 - 8.4 = -1.0$. Step 4: Calculate residual $c$: Substitute the values for $x=3$: $c = 11 - 11.6 = -0.6$. Step 5: Calculate residual $d$: Substitute the values for $x=4$: $d = 15 - 14.8 = 0.2$.