Question

the value of a bicycle was recorded over a period of five years. based on how the plot of the residuals might look, would a linear function that passes through (0,250) and (4,25) be a good fit for the data shown?
yes, the residuals would tend to be one - sided.
no, the residuals would tend to be one - sided.
yes, the residuals would be randomly distributed.
no, the residuals would be randomly distributed.

Explanation:

Step1: Identify linear function points

Given points: $(0,250)$ and $(4,25)$

Step2: Calculate slope of linear function

Slope $m = \frac{25 - 250}{4 - 0} = \frac{-225}{4} = -56.25$
Equation: $y = -56.25x + 250$

Step3: Compare data points to linear fit

Data points: $(1,130)$, $(2,75)$, $(3,40)$, $(4,30)$

• At $x=1$: Predicted $y=-56.25(1)+250=193.75$, Residual $=130-193.75=-63.75$
• At $x=2$: Predicted $y=-56.25(2)+250=137.5$, Residual $=75-137.5=-62.5$
• At $x=3$: Predicted $y=-56.25(3)+250=81.25$, Residual $=40-81.25=-41.25$
• At $x=4$: Predicted $y=-56.25(4)+250=25$, Residual $=30-25=5$

Step4: Analyze residual pattern

All residuals (except $x=4$) are negative; they are one-sided (mostly below the line), not random. A good linear fit requires randomly distributed residuals.

Answer:

No, the residuals would tend to be one-sided.