28.3 - Two Continuous Measurements28.3 - Two Continuous Measurements
One Group with Two Continuous Measurements
If we have two continuous measurements, we could consider either of two possible analyses, namely:
- 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
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:
\(H_A : \rho \ne 0\)
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?
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.