1. A misguided friend says, “I took statistics. My book said that for a normal distribution of scores, the mean is the same value as the mode. Since the mode is the most common score, wouldn’t our ‘best guess’ of the value of our DV be the mean (or the mode)? Why can’t we just use the mean as our predicted value for y? See, you don’t need any of this silly regression stuff.” How would you respond to this?
2. For a class project, your statistics professor provides you with data from his previous classes on final grade percentage and number of classes sessions missed. You calculate a correlation between the two variables and find r = -.85. Those people who miss class tend to do poorly in the class.
3. Next, your misguided friend from problem #1 presents some data. His analysis is on class grades and the number of psychology courses that the student has previously taken. He finds a correlation of r = +.10. Not only does your friend conclude that it is a good idea to take a lot of psychology classes before you take statistics but that attendance is much less important than prior experience with psychology. His argument goes like this:
“My correlation is +.10, that is a lot bigger than -.85. The smallest correlation is -1.0 and your correlation is pretty close to that!”
Again, enlighten your friend as to the error(s) in his thinking.
4. You performed a statistical analysis and found with 25 pairs of scores the correlation between two variables was +.25.In examining a scatterplot of this relationship you find that most of the pairs of scores exhibit a strong positive relationship. One score however follows a different pattern than the others. You verify the accuracy of the score and find that it is not the result of a data entry error. You delete the pair and the correlation between the variables rises to +.82.
A. How would you interpret the first correlation value (.25)?
B. How would you interpret the second correlation value (.82)?
C. Comment on the deletion of the single outlying score – is it appropriate to delete this score? Why or why not?
D. Suggest a strategy for handling outlying scores such as this.
E. Suggest a strategy for reporting the results of the tests above (i.e., What value should you report?).
That’s it! Congratulations on completing the Regression Tutorial!