1. 9.3 Inferences for Correlation
and Regression

2. Inferences for Correlation and Regression


3. Inferences for Correlation and Regression


4. Testing the Correlation Coefficient
 The first topic we want to study is the statistical
significance of the sample correlation coefficient r.
 To do this, we construct a statistical test of  , the
population correlation coefficient.

5. 

6. Do college graduates have an improved chance at a better
income? Is there a trend in the general population to
support the “learn more, earn more” statement? We
suspect the population correlation is positive, let’s test
using a 1% level of significance. Consider the following
variables: x = percentage of the population 25 or older with
at least four years of college and y = percentage growth in
per capita income over the past seven years. A random
sample of six communities in Ohio gave the information
shown
Education and Income Growth Percentages
Table 9.10

7. Solution

Caution: Although we
have shown that x and y
are positively
correlated, we have not
shown that an increase
in education causes an
increase in earnings.

8. You Try It!

x 9.2 10.1 9.0 12.5 8.8 9.1 9.5
y 5.0 4.8 4.5 5.7 5.1 4.6 4.2

9. Solution


10. Standard Error of Estimate
 Sometimes a scatter diagram clearly indicates the
existence of a linear relationship between x and y,
but it can happen that the points are widely scattered
about the least-squares line. We need a method
(besides just looking) for measuring the spread of a
set of points about the least-squares line. There are
three common methods of measuring the spread.
 the coefficient of correlation
 the coefficient of determination
 the standard error of estimate

11. Standard Error of Estimate

The Distance Between Points (x, y) and (x, )
Figure 9.16

12. Standard Error of Estimate


13. Standard Error of Estimate


14. Example
 June and Jim are partners in the chemistry lab. Their
assignment is to determine how much copper sulfate
(CuSO4) will dissolve in water at 10, 20, 30, 40, 50, 60,
and 70C.
 Their lab results are shown in
Table 9-12, where y is the
weight in grams of copper sulfate
that will dissolve in 100 grams of
water at xC. Sketch a scatter
diagram, find the equation of the Lab Results (x = C, y = amount of CuSo4)
Table 9.12
least-squares line, and compute Se.

15. Solution

Scatter Diagram and Least-Squares
Line for Chemistry Experiment
Figure 9.17