With simple linear regression, you look for a certain type of relationship between two quantitative (numerical) variables (like high-school GPA and college GPA.) This special relationship is a *linear relationship *— one whose pairs of data resemble a straight line.

In this scatter plot, the two variables plotted are quantitative (numerical). The correlation is *r* = 0.75.

## Sample questions

In looking at this scatter plot, which of the following violations of a necessary condition for fitting a regression line is observed?

A. The variables aren't numeric.

B. Their correlation isn't strong enough.

C. Their relationship isn't linear.

D. Choices (B) and (C)

E. None of the above.

**Answer: C.**Their relationship isn't linear.The variables are numeric, and a correlation of 0.75 is sufficient to perform linear regression. However, the relationship of the points in the scatter plot isn't linear. The points initially have a positive relationship but then curve downward into a negative relationship.

The equation for calculating the least-squares regression line is

*y*=*mx*+*b*. If two variables have a negative relationship, which letter is guaranteed to be negative?**Answer:***m*The slope of the equation is

*m.*If two variables have a negative relationship, they will have a negative slope.

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