# 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?

### Answer

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?

### Answer

If *x* denotes the number of times a randomly selected college student goes out to party in one month, and *y* = the student's grade point average, then we'd be interested in estimating the slope and intercept parameters in the linear regression equation:

\(\mu_y=\alpha + \beta x\)

Of course, that's assuming that the relationship is indeed a linear relationship, but that could be verified when doing the analysis. We could use Minitab's `Stat` >> `Regression` >> `Regression...` command to help complete the analysis.