Quality Quiz from Professor Cleary
"B" is correct.
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Polly has used the correct words, but somehow has them backwards. The dependent variable, y, is a random variable, and x, the independent variable, is a parameter.
A simple classroom exercise that I have used in my university classes involves collecting student data related to the distance to their workplaces (in miles), and the amount of time it takes for them to reach these destinations (in minutes). Creating a scattergram of that data, a pattern such as the following appears:
The relationship is lower-left-to-upper-right, and clearly illustrates the concept that distance from work is a parameter (a number that remains the same for some period of time), while the time to get to work is not the same each day, so it becomes a random variable.
A random variable, of course, has a mean, a measure of variability, and a shape. With the scattergram above, it is clear that a straight line—the regression line--reflects the relationship of the data. Another assumption that can be made is that the observations around the line form a normal distribution for all values of x. This assumption is important, since it helps predict the value of y, given a specific value of x. For example, if someone lives 50 miles from work, one can predict that it will take about 45 minutes to get to work:
This is what is known as a point estimate. Next month, we will begin to build a confidence interval around this estimate.
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