Loading…
Example 12.13 from Statistics, 12.5 Outliers
Outliers: example 12.13
- Draw a scatter plot of the data.
- Calculate the least-squares line. Write the equation in the form ŷ = a + bx.
- Draw the line on a scatter plot.
- Find the correlation coefficient. Is it significant?
- What is the average CPI for the year 1990?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
- See Figure 12.18.
- Using our calculator, ŷ = –3204 + 1.662x is the equation of the line of best fit.
- See Figure 12.18.
- r = 0.8694. The number of data points is n = 14. Use the 95 Percent Critical Values of the Sample Correlation Coefficient table at the end of Chapter 12: In this case, df = 12. The corresponding critical values from the table are ±0.532. Since 0.8694 > 0.532, r is significant. We can use the predicted regression line we found above to make the prediction for x = 1990.
- ŷ = –3204 + 1.662(1990) = 103.4 CPI.
Figure 12.18Discussion
Note
In the example, notice the pattern of the points compared with the line. Although the correlation coefficient is significant, the pattern in the scatter plot indicates that a curve would be a more appropriate model to use than a line. In this example, a statistician would prefer to use other methods to fit a curve to these data, rather than model the data with the line we found. In addition to doing the calculations, it is always important to look at the scatter plot when deciding whether a linear model is appropriate.
If you are interested in seeing more years of data, visit the Bureau of Labor Statistics CPI website (ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt). Our data are taken from the column Annual Avg. (third column from the right). For example, you could add more current years of data. Try adding the more recent years: 2004, CPI = 188.9; 2008, CPI = 215.3; and 2011, CPI = 224.9. See how this affects the model. (Check: ŷ = –4436 + 2.295x; r = 0.9018. Is r significant? Is the fit better with the addition of the new points?)
0 of 2 steps open
How did it go?