Question

4

A sports analyst is interested in the relationship
between the number of three-point shots players
attempt in a game and the number of points scored
To investigate the relationship, he collects a simple
random sample of 15 games and records the number
of three-point shots attempted and the total number of
points scored. He finds the equation of the least-
squares regression line to be ý=65.7 +0.729x,
where y is points scored and x is the number of three-
point shots attempted. The residual plot is shown.
Residual
20
10
2
3
Based on the residual plot, is the linear model
appropriate?
7
O No, the residuals are relatively large.
O No, there is a clear pattern in the residual plot
OYes, there is no clear pattern in the residual plot
Yes, about half of the residuals are positive and
half are negative.
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Answer 1

Answer: c. Yes, there is no clear pattern in the residual plot.

Answer 2

B. No, there is a clear pattern in the residual plot.

Explanation:

The residual plot shows the differences between the observed values and the predicted values from the linear regression model. In a good model, the residuals should be randomly scattered around the horizontal line at 0, indicating that the model is capturing all the relevant information in the data.

However, in this case, we can see a clear pattern in the residual plot where the residuals are not randomly scattered around 0. Instead, there seems to be a curved pattern, where the residuals are relatively large for small and large values of x, and relatively small for intermediate values of x. This suggests that the linear model may not be the best fit for the data, and that some other type of model, such as a quadratic or cubic model, may be more appropriate. Therefore, the correct answer is B. No, there is a clear pattern in the residual plot.

Hope this helps! Sorry if it's wrong. If you need more help, ask me! :]