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Learning Math Home
Patterns, Functions, and Algebra
 
Session 7 Part A Part B Part C Part D Homework
 
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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:

Person #

Forearm

Right Foot

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

 

Person #

Forearm

Right Foot

11

277

256

12

303

305

13

285

273

14

254

234

15

280

261

16

264

265

17

261

241

18

292

292

19

248

228

20

253

252

 
   

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

Scatter Plot

Problem H1

Solution  

Describe the association between forearm length and foot length.


 

Problem H2

Solution  

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


 

Problem H3

Solution  

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

show answers  

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

show answers  

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.

hide answers


 

Problem H6

Solution  

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


Next > Session 8: Probability

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