Question

a residual plot shown below analyzes the fit of the function representing the gold medal winning times for the women’s 100 - meter freestyle swimming race since 1972 is shown. residual plot chart which conclusion about the fit of the function is supported by the residual plot?
a) the function is an appropriate fit and represents a negative, linear association between years and winning times.
b) the function is an appropriate fit and represents a positive, linear association between year and winning times.
c) the function is an inappropriate fit of the association between year and winning times.
d) there is no association between year and winning times.

Explanation:

Step1: Recall Residual Plot Interpretation

A residual plot shows the difference between observed and predicted values (residuals) against the independent variable (here, year). For a good fit, residuals should be randomly scattered around zero with no pattern. If there's a pattern (like curved or increasing/decreasing), the model is inappropriate.

Step2: Analyze Each Option

• Option a: A negative linear association would mean residuals show a linear trend downward, but the plot here (from description, residuals seem to have a curved pattern? Wait, no—wait, the problem is about the fit. Wait, actually, the key is: if the residual plot has a pattern (non - random), the function is inappropriate. Wait, let's re - read the options. Option c says "The function is an inappropriate fit of the association between year and winning times". Let's think about residual plots: if the residuals have a pattern (like a curve, or a trend that's not random), the model (function) is not a good fit.

• Option a: The function being appropriate with negative linear association—if residuals had a linear negative trend, but the plot (from the image, the residuals are plotted and likely show a pattern that's not random, so the function is inappropriate. Wait, maybe the residual plot here has a curved pattern, indicating that a linear function (if the model was linear) is inappropriate. So option c is correct.

Answer:

c. The function is an inappropriate fit of the association between year and winning times