Final answer:
To determine the correlation between two variables in a scatter plot, one must examine the pattern of data points and the correlation coefficient. A positive or negative linear correlation suggests that linear regression could be predictive, while a curved pattern or zero correlation would suggest otherwise. The value of the correlation coefficient, such as r = .55, can indicate the strength of the relationship and whether linear regression is suitable.
Step-by-step explanation:
When analyzing a scatter plot to determine the relationship between two variables, one should look for a pattern in the dispersion of the data points. A positive correlation is indicated when the scatter plot shows an upward trend as one variable increases, so does the other; in this case, 0 < r < 1. Alternatively, a negative correlation is observed when the scatter plot trends downward as one variable increases, the other decreases, denoted by -1 < r < 0. When there is no apparent upward or downward trend, and the data points are widely scattered without any discernible pattern, this indicates a zero correlation, where r = 0.
To determine whether linear regression is an appropriate tool for the data in the scatter plot, one must not only consider the correlation coefficient r but also visually inspect the pattern of the points. A strong, either positive or negative, linear correlation suggests that a linear model could be a good predictor for the relationship between the variables. However, if the pattern of data points suggests a curve rather than a straight line, other methods to fit a curve would be more suitable than linear regression. This decision is based on the principle that while the correlation coefficient is helpful, it should not be the sole indicator of the appropriateness of a linear model.
Therefore, when deciding if X and Y variables are good candidates for linear regression, one should analyze both the pattern in the scatter plot and the value of the correlation coefficient. For example, a correlation coefficient of r = .55 might indicate a moderately strong relationship, which would lead a statistician to consider linear regression as a potential model if the scatter plot pattern supports this assumption.