AP Statistics
Chapter 3 Examining Relationships
Correlation & Regression
Name: ________________________
Date: _____________
Block: ______
Standard: CB.I.D.
Correlation
Part I. The table below contains data on microwave ovens found at www.target.com.
Price ($)
80
80
50
90
100
90
110
90
75
80
63
Watts
1100
700
700
1200
1200
1200
1200
1000
1000
1000
700
1. Enter the price and watt values into two lists in your calculator.
2. Obtain a scatterplot using Price as the X variable and Watts as the Y variable.
Does the relationship appear to be
Positive OR Negative?
Linear OR Curved?
Are there any unusual observations?
3. Compute the correlation.
r = ________________
4. What does the value of r indicate about the relationship between Price and Watts?
Adapted From Chapter 5
Activities Worksheets
Part II. Match the graphs to the correlations.
r=0
r = + 0.3
r = – 0.5
r = – 0.7
a.
b.
c.
d.
e.
f.
Adapted From Chapter 5
Activities Worksheets
r = + 0.9
r =0
Solution To Correlation
Part I
2. There relationship appears to be positive and somewhat linear, with several unusual points.
Scatterplot of Watts vs Price
1200
Watts
1100
1000
900
800
700
50
60
70
80
Price
90
100
110
3. r = 0.809
4. There is a strong, positive linear relationship between Price and Watts.
Part II
a. r = –0.7
b. r = 0
c. r = +0.3
d. r = +0.9
e. r = 0
f. r = –0.5
Adapted From Chapter 5
Activities Worksheets
Regression
The determination of gestational age is important for pregnancy evaluation. The most reliable method
of estimating gestational age is the date of the last menstrual period. Ultrasonography offers a unique
opportunity in estimating gestational age since this allows direct visualization of the fetus.
Data were collected on 27 normal pregnant women during routine obstetrical ultrasound
examinations. The variables recorded were:
1. menstrual age of the fetus (weeks since last menstrual period),
2. inner orbital diameter (mm), and
3. outer orbital diameter (mm),
where the inner orbital diameter is the distance between the inner (medial) borders of the optical
orbits, and the outer diameter is the distance between the outer (lateral) borders.
A. Describe the scatterplot.
Age = 3.031 + 1.431 Inner
S r2 = 0.879
2.35811
R-Sq
87.9%
R-Sq(adj)
87.4%
35
Age
30
25
20
15
10
5.0
7.5
10.0
12.5
15.0
Inner
17.5
20.0
22.5
B. The regression line is given above the scatterplot. The slope of the line is ______.
This indicates that for every one mm increase in Inner Orbital Diameter, we expect
Menstrual Age to increase/decrease (circle one) by ______ weeks, on average.
C. The r2 value is given next to the scatterplot. The value of r2 is ______.
This indicates that ______% of the variability in _________________________ is explained by
the linear relationship with _________________________.
D. Use the value of r2 to obtain the value of r. Be sure to give the correct sign (positive or
negative) to r. What is the value of the r for this data? ______
E. What Menstrual Age would you predict for a fetus with in Inner Orbital Diameter of 16
mm?
F. There was one fetus in the sample with an inner orbital diameter of 16 mm. The menstrual
age of this fetus was 24.1 weeks. Compute the error of your prediction in part E by taking the
actual menstrual age and subtracting your prediction.
Adapted From Chapter 5
Activities Worksheets
Data from Serafima Yershov,
B.S. Diagnostic Medical Sonography RIT, 1996
Here is the data for Outer
Orbital Diameter and
Menstrual Age.
2. Obtain a scatterplot and describe the graph.
1. Enter the values into two
lists in your calculator.
Outer
16
20
23
29
31
31
30
33
33
36
34
43
38
45
38
45
48
46
52
52
45
47
50
50
54
51
52
Age
13.7
14.6
15.3
18.0
19.6
19.7
20.4
20.6
21.0
21.0
21.1
24.1
24.6
25.0
26.3
27.3
28.3
29.1
29.9
29.9
30.4
31.3
33.3
34.9
34.9
35.0
35.4
3. Perform a regression on your calculator with Outer as
the X variable and Age as the Y variable.
What is the equation of your regression line?
___________________________________
What is the value of r2? ______
What is the value of r? ______
4. What does the value of the slope indicate? (Write a
sentence similar to the one in part B).
5. What does the value of r2 indicate? (Write a sentence
similar to the one in part C).
6. Which regression is “better”, the one using Inner as the
explanatory variable or the one using Outer? EXPLAIN.
Adapted From Chapter 5
Activities Worksheets
Solution to Regression
A. Scatterplot shows a positive, linear, strong relationship
B. slope = 1.431
increase, 1.431
C. r2 = 0.879
87.9%, menstrual age, inner orbital diameter
D. r = + r 2 = 0.879 = 0.938
Because the relationship is positive, use the positive square root!
E. Ŷ = 3.031 + 1.431X  Ŷ = 3.031 + 1.431(16) = 25.927
F. Error = 24.1 – 25.927 = –1.827 This is also called the residual
(Note: The negative error indicates a point below the line)
2.
55
50
45
Outer
40
35
30
25
20
15
15
20
25
30
35
Age
3. Ŷ = 1.867 + 0.5917X, r2 = 0.912, r = 0.955
4. For every one mm increase in Outer Orbital Diameter, we expect Menstrual Age to increase
by 0.5917 weeks, on average.
5. This indicates that 91.2% of the variability in menstrual age is explained by the linear
relationship with outer orbital diameter.
6. The regression with outer orbital diameter is better because it has a larger r2 value!
Adapted From Chapter 5
Activities Worksheets