1. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone Name: ______________________________
9.3 Inferences for Correlation and Regression Date: ___________
Part 1: Testing and the Standard Error of Estimate
Inferences for Correlation and Regression
In Sections 9.1 and 9.2, we learned how to compute the sample correlation coefficient and the least-
squares line using data from a sample.
o is only a _____________________________________________________________________
o is only a _____________________________________________________________
o What if we used all possible data pairs?
 In theory, if we had the population of all (x, y) pairs, then we could compute the
_________________________________________________________(Greek letter rho)
and we could compute the __________________________________________________
________________________________________________________________________
Note the following:
Sample Statistic Population Parameter




Requirements for Statistical Inference
o To make inferences regarding correlation and linear regression, we need to be sure that
 The set (x, y) of ordered pairs is a random sample from the population of all possible
such (x, y) pairs
 For each fixed value of x, the y values have a normal distribution. All of the y
distributions have the same variance, and, for a given x value, the distribution of y values
has a mean that lies on the least-squares line. We also assume that for a fixed y, each x
has its own normal distribution. In most cases the results are still accurate if the
distributions are simply mound-shaped and symmetric and the y variances are
approximately equal.
o ____________________________________________________________________________________
____________________________________________________________________________________
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2. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
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.
How to Test the population correlation coefficient
Let be the sample correlation coefficient computed using data pair ( )
1. Use the null hypothesis (x and y have _______________________________).
Use the context of the application to state the alternate hypothesis ( ).
State the level of significance .
2. Obtain a sample of data pairs and compute the sample test statistic
with degrees of freedom
3. Use the TI-83 or TI-84 to calculate the _____________________
 _______________________________________________________________________
4. Conclude the test
 If the P-values is , then reject
 If the P-values is , then fail to reject
5. Interpret the results in the context of your application
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3. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Example: Testing
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
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.
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4. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
You Try It!
A medical research team is studying the effect of a new drug on red blood cells. Let x be a random variable
representing milligrams of the drug given to a patient. Let y be a random variable representing red blood cells
per cubic milliliter of whole blood. A random sample of volunteer patients gave the following results.
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
Use a 1% level of significance to test the claim that
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5. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Standard Error of Estimate
Sometimes a scatter diagram clearly ______________________________________________________
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.
o the coefficient of correlation
o the coefficient of determination
o ______________________________________________________
 For the standard error of estimate, we use a measure of spread that is in some ways like the
standard deviation of measurements of a single variable. Let_________________________________
________________________________________________from the least-squares line.
 Then y – is the difference between the y value of the data point (x, y) shown on the scatter diagram
(Figure 9-16) and the value of the point on the least-squares line with the same x value.
 The quantity __________ is known as the ___________________. To avoid the difficulty of having
some positive and some negative values, we square the quantity (y – ).
 Then we sum the squares and, for technical reasons, divide this sum by n – 2. Finally, we take the
square root to obtain the standard error of estimate, denoted by S .
e
 Standard Error of Estimate = ______________________________________________
where and
 Using the TI 83 & TI 84
1. STAT
2. TEST
3. LinRegTTest
The value for is given as
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6. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Example
June and Jim are partners in the chemistry lab. Their assignment is to determine how much copper sulfate
(CuSO ) will dissolve in water at 10, 20, 30, 40, 50, 60, and 70°C.Their lab results are shown in Table 9-12,
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where y is the weight in grams of copper sulfatethat will dissolve in 100 grams of water at x°C. Sketch a scatter
diagram, find the equation of the least-squares line, and compute
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7. AP/H Statistics Guided Notes
Mrs. LeBlanc – Perrone
Summary Questions
1. What does testing the population correlation coefficient show?
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
2. Complete 9.1 – 9.3 Graphing Calculator Exercises (including the “You Try It”)
“HOT” Question:
__________________________________________________________________________________________
__________________________________________________________________________________________
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