Data Session 7: Homework

Session 7:
Homework

Is there an association between the length of your forearm (elbow to wrist) and the length of your feet?

The following are measurements, in millimeters, for forearm length and right-foot length for 20 people:

N = 20 measurements
Mean forearm length = 262.1
Mean foot length = 255.7

Scatter Plot

Problem H1

Describe the association between forearm length and foot length.


Problem H2
Use the mean forearm length and the mean foot length to determine the quadrants and number of points in each quadrant.

Problem H3

a.
Use the quadrants from Problem H2 to create the contingency table for this data.

b.
What percentage of people with above-average forearm lengths also have above-average foot lengths?

c.
What percentage of people with above-average forearm lengths also have below-average foot lengths?

d.
What percentage of people with below-average forearm lengths also have below-average foot lengths?

e.
What percentage of people with below-average forearm lengths also have above-average foot lengths?

f.
What do these percentages say about the strength of the association between forearm length and foot length?

Problem H4

Consider the line Foot Length = Forearm Length (YL = X).

a.	Complete the table below.
b.	Determine the SSE for this data.

When you click "Show Answers," the filled-in table will appear below the problem. Scroll down the page to see it.

Person #

Forearm (X)

Foot (Y)

YL = X

Error = Y - YL

(Error)
=
(Y - YL)²

1	287	271
2	243	261
3	237	230
4	227	225
5	247	236
6	264	252
7	247	243
8	247	247
9	251	238
10	254	274
11	277	256
12	303	305
13	285	273
14	254	234
15	280	290
16	264	265
17	261	241
18	292	292
19	248	228
20	253	252

Person #

Forearm (X)

Foot (Y)

YL = X

Error = Y - YL

(Error)
=
(Y - YL)²

1	287	271	287	-16	256
2	243	261	243	18	324
3	237	230	237	-7	49
4	227	225	227	-2	4
5	247	236	247	-11	121
6	264	252	264	-12	144
7	247	243	247	-4	16
8	247	247	247	0	0
9	251	238	251	-13	169
10	254	274	254	20	400
11	277	256	277	-21	441
12	303	305	303	2	4
13	285	273	285	-12	144
14	254	234	254	-20	400
15	280	290	280	10	100
16	264	265	264	1	1
17	261	241	261	-20	400
18	292	292	292	0	0
19	248	228	248	-20	400
20	253	252	253	-1	1

b. The SSE, (256 + 324 + ... + 400 + 1), is 3,374.

hide answers

Problem H5

Consider the line Foot Length = Forearm Length + 4 (YL = X + 4).

a.	Complete the table below.
b.	Determine the SSE for this data.

When you click "Show Answers," the filled-in table will appear below the problem. Scroll down the page to see it.

Person #

Forearm (X)

Foot (Y)

YL = X + 4

Error = Y - YL

(Error)
=
(Y - YL)²

1	287	271
2	243	261
3	237	230
4	227	225
5	247	236
6	264	252
7	247	243
8	247	247
9	251	238
10	254	274
11	277	256
12	303	305
13	285	273
14	254	234
15	280	290
16	264	265
17	261	241
18	292	292
19	248	228
20	253	252

Person #

Forearm (X)

Foot (Y)

YL = X + 4

Error = Y - YL

(Error)
=
(Y - YL)²

1	287	271	291	-20	400
2	243	261	247	14	196
3	237	230	241	-11	121
4	227	225	231	-6	36
5	247	236	251	-15	225
6	264	252	268	-16	256
7	247	243	251	-8	64
8	247	247	251	-4	16
9	251	238	255	-17	289
10	254	274	258	16	256
11	277	256	281	-25	625
12	303	305	307	-2	4
13	285	273	289	-16	256
14	254	234	258	-24	576
15	280	290	284	6	36
16	264	265	268	-3	9
17	261	241	265	-24	576
18	292	292	296	-4	16
19	248	228	252	-24	576
20	253	252	257	-5	25

b. The SSE, (400 + 196 +... + 576 + 25), is 4,558.

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Problem H6
Compare the SSE in Problem H4 with the SSE in Problem H5. Which line provides a "better" fit? Explain.

Next > Session 8: Probability

Session 7: Index | Notes | Solutions | Video