Transcript AP Statistics Chapter 27 Notes

AP Statistics
Chapter 27 Notes
“Inference for Regression”
Scatter plots Review

To enter the data –
 STAT, EDIT, X’s in L1, Y’s in L2

To see the picture –
 2nd, Y=, Turn on plot 1, Set it on scatter plot for L1 and L2, Zoom, #9 ZoomStat

To find the equation –
 STAT, CALC, #8 LinReg (a + bx) L1, L2

To look at a residuals plot –
 2nd, Y=, Change L2 to RESID (which is in 2nd, STAT after you calculate the
regression equation)
NOTE: Go into the catalog (2nd, 0) and turn Diagnostics On to get the r and r2
values.
Scatter plots Review
 1. Make a scatter plot. Label
the axes and at least two
points.
 2. Find the regression
equation.
 3. Find r. What does it tell
you?
 4. Find
you?
r2 .
What does it tell
 5. Look at the residuals plot.
What does it tell you?
GPA
ACT score
3.25
24
2.87
21
2.66
18
3.33
22
2.87
22
3.21
22
2.76
18
3.91
28
3.55
29
2.55
18
2.44
20
3.22
24
3.01
21
3.44
24
3.22
25
Inference for Regression
 Different samples will give different
regression equations and thus, different
slope and y-intercept values.
 We will use the slope from our sample to:
 1. Check for a significant relationship between x
and y
 2. Make a confidence interval for the true slope
for the entire population
Hypothesis Testing for the Slope
of the Regression Line
 If there is a relationship between x and y, the slope
of the regression line would not be zero.
 Thus, Ho:
 0
No relationship exists
between x and y
Ha:
  0,   0
or
B0
A relationship exists
between x and y
 The hypothesis test to test the null hypothesis is a ttest with n – 2 degrees of freedom.
Example
 The given data is a
random sample of GPAs
and ACT scores for
students at a certain
high school as collected
by a school counselor.
Based on this sample, is
there evidence of a
linear relationship
between GPA and ACT
scores for students at
this high school?
GPA
ACT
score
3.25
24
2.87
21
2.66
18
3.33
22
2.87
22
3.21
22
2.76
18
3.91
28
3.55
29
2.55
18
2.44
20
3.22
24
3.01
21
3.44
24
3.22
25
The Solution Process

1. State the hypotheses.
Ho: slope is 0
(there is no relationship between x and y)
Ha: slope is not 0 (there is a relationship between x and y)

2. Check the conditions.
- The scatter plot of the data should look linear
- The residual plot should show random scatter with no pattern
- The data should be randomly selected
- The histogram of the residuals should be unimodal and roughly
symmetric or the Normal probability plot should look fairly straight

3. Test the hypotheses and state your conclusion. (STAT, TESTS, F)

4. Create and interpret a 95% confidence interval for the slope of the
regression line. (STAT, TESTS, G)