Question

Looking at the scatter plot you produced above, is linear regression a good model to use? If so, what features or characteristics make this model reasonable? If not, what features or characteristics make it unreasonable?

a. Yes, the data points form a clear linear pattern, indicating a strong correlation.
b. No, the data points are scattered and do not follow a linear trend.
c. Yes, because the scatter plot shows a perfect straight line.
d. No, as the data points are too closely packed, violating the assumptions of linear regression.

Answer 1

To decide if linear regression is appropriate for a set of data, one must examine the scatter plot for a linear pattern and check if the correlation coefficient is significant. A clear linear trend suggests that linear regression is suitable, while a nonlinear pattern or significant scatter indicates that another model would be better.

Step-by-step explanation:

When assessing whether linear regression is a good model for a dataset, one should look at the scatter plot produced from the data. If the data points form a clear linear pattern, with variation around a central line, and the correlation coefficient is significant (typically above 0.7 for a strong correlation), then linear regression is a reasonable modeling choice. This implies answer choice (a) might be correct if the scatter plot indeed forms a clear linear pattern. If the data are scattered without any discernible linear trend, as described in answer choice (b), then linear regression is not a good model to use. You should avoid linear regression if the relationship in the scatter plot represents a clear curve or is non-linear, which is implied in the NOTE section and would suggest other regression techniques like polynomial or non-linear regression.

Answer choice (c) suggests a perfect straight line of points, which while ideal, rarely occurs in real-world data. Typically, some degree of error or variance is expected, and a perfect correlation is suspect and could be an indication of overfitting. Answer choice (d) states that the data points are too closely packed, which is not a violation of the prerequisites for linear regression; in fact, closely packed data around a line indicates a strong linear relationship.

For the given student question, assuming that the scatter plot shows a pattern aligned with a linear relationship and a significant correlation coefficient, linear regression would be a sensible model to use. On the other hand, if the data indicates a curved relationship or the scatter plot shows a significant number of outliers or a random scatter of points, these are indications that a different modeling approach should be considered.