Stats 100A Quiz 3 Solutions

 

1. Describe the relation in words:

As temperature increases, the ozone level also increases. Although for temperatures between 20 and about 60 degrees, the ozone level remains fairly flat, and then increases more sharply after 60 degrees.

2. The regression line is yhat = -14.9375 + .432571x, where x is temperature and y is ozone.

a) Graph this line on the scatterplot See above.

b) Interpret the regression line. Tell me everything you can about what this regression line tells us about the relationship between temperature and ozone levels.

The regression line tells us that a one degree F increase in temperature is associated with an increase of .432571 ppm in the average ozone level. This confirms our description that ozone and temperature both tend to increase together.

The correlation, 0.78, is fairly high, and so this tells us that if the relationship were linear, then this regression line would do a pretty good job of predicting ozone levels from the temperature. HOWEVER, a glance at the scatterplot shows that your predictions are more likely to be too high in the range of roughly 50 to 70 degrees, and too low outside, which strongly suggests that the relationship is NOT linear. (For example, at 60 degrees, you could be off by as much as about 8ppm too high, but only 2 or 3 ppm too low. And there are many more points below than above the line, so you are more likely to be too high.)

Because the relationship looks non-linear, the regression line is probably not too trustworthy. In fact, the relationship between average ozone levels and temperature is probably more complex than the simple regression line would have it.