# 28.3 - Two Continuous Measurements

28.3 - Two Continuous Measurements

## One Group with Two Continuous Measurements

If we have two continuous measurements, we could consider either of two possible analyses, namely:

• Correlation
• Linear regression

Correlation helps to answer the research question "does a linear relationship exist between two continuous random variables?" Linear regression, on the other hand, helps to answer the research question "what is the linear relationship between a fixed predictor and a random variable?" In Minitab, we use the following commands:

• Stat >> Basic Statistics >> Correlation... to conduct a correlation analysis
• Stat >> Regression >> Regression... to conduct a linear regression analysis

## Example 28-10 Does a (linear) relationship exist between a husband's and wife's height?

Because we are only interested in learning whether a linear relationship exists between husbands' and wives' heights, and not the nature of the relationship, we would want to conduct a correlation analysis. We can use Minitab's Stat >> Basic Statistics >> Correlation... command to test the null hypothesis:

$$H_0 : \rho = 0$$

against the alternative hypothesis:

$$H_A : \rho \ne 0$$

## Example 28-11 If a randomly selected college student goes out to party ten times each month, what kind of grade point average (GPA) can he or she expect?

$$\mu_y=\alpha + \beta x$$