Final answer:
The residual for the point (5,1) when compared to the line of best fit y = -0.2x + 1.8 is 0.2. This is found by subtracting the predicted y-value (0.8) from the observed y-value (1).
Step-by-step explanation:
The student is asking about the residual for a specific data point in relation to a line of best fit. A residual is the difference between an observed y-value and the predicted y-value (ε = y - ŷ) on the regression line.
To find the residual for the point (5,1), you first calculate the predicted y-value using the equation of the line of best fit, y = -0.2x + 1.8. So when x = 5, the predicted y (ŷ) is -0.2(5) + 1.8 = -1 + 1.8 = 0.8. Then, calculate the residual by subtracting this predicted value from the observed y-value: 1 - 0.8 = 0.2.
Therefore, the residual for the point (5,1) is 0.2, which means option a. 0.2 is the correct answer.