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------------------------------------------------ What does the scatter diagram indicate about the relationship between \(x\) and \(y\)?

The scatter diagram indicates that there is a linear relationship between the two variables.

A scatter diagram indicating a linear relationship between x and y shows the variables may be good candidates for linear regression if the points cluster around a line, implying a linear model could predict y from x.

Explanation:

When analyzing a scatter diagram to infer the relationship between two variables, such as x and y, we look for a pattern that suggests how the variables are related. If the scatter plot shows a clear trend where the points roughly form a straight line, this indicates a linear relationship between the variables. A linear relationship suggests that as one variable increases, the other variable tends to also increase (positive correlation) or decrease (negative correlation) in a predictable way.

In order to decide if x and y are good candidates for linear regression, one should ensure that the scatter plot exhibits such a linear pattern without too many outliers. Good candidates for linear regression will show a scatter plot where the points are clustered around a line that could be drawn through them, indicating that a linear model could reasonably predict the value of y given x. If this is the case, then a regression line can be used to model the linear relationship between x and y in the population.