which answer is the best estimate of the residual value when x = 5?\n-1.5\n-0.5\n0.5\n1.5
which answer is the best estimate of the residual value when x = 5?\n-1.5\n-0.5\n0.5\n1.5
Answer
Explanation:
Step1: Recall residual formula
Residual = Observed - Predicted.
Step2: Find observed value at x = 5
From the scatter - plot, find the observed y - value at x = 5. Let's assume we can visually estimate the observed y - value at x = 5 to be around 7.
Step3: Find predicted value at x = 5
The line of best - fit passes through points (1, 3) and (7, 9). First, find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{9 - 3}{7 - 1}=\frac{6}{6}=1$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point (1, 3), we have $y-3 = 1\times(x - 1)$, so $y=x + 2$. When $x = 5$, the predicted value $y=5 + 2=7.5$.
Step4: Calculate residual
Residual = Observed - Predicted = $7-7.5=-0.5$.
Answer:
-0.5