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Learning Math Home
Data Session 7: Notes
 
Session 7 Part A Part B Part C Part D Homework
 
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A B C D
Homework

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Solutions for Session 7: Homework

See solutions for Problems: H1 | H2 | H3 | H4 | H5 | H6


Problem H1

Overall, there is a positive association between forearm length and foot length. On the graph, the points generally go up and to the right.

<< back to Problem H1


 

Problem H2

To find the quadrants, we must use the mean forearm and foot lengths, which we know are 262.1 mm and 255.7 mm, respectively.

Recall that:

 

Quadrant I has points that correspond to people with above-average forearm and foot lengths.

 

Quadrant II has points that correspond to people with below-average forearm lengths and above-average foot lengths.

 

Quadrant III has points that correspond to people with below-average forearm and foot lengths.

 

Quadrant IV has points that correspond to people with above-average forearm lengths and below-average foot lengths.

Here is the scatter plot divided into quadrants:

This table shows which quadrant each point is in:

Forearm Length

Foot Length

Quadrant

287

271

I

243

261

II

237

230

III

227

225

III

247

236

III

264

252

IV

247

243

III

247

247

III

251

238

III

254

274

II

 

Forearm Length

Foot Length

Quadrant

277

256

I

303

305

I

285

273

I

254

234

III

280

290

I

264

265

I

261

241

III

292

292

I

248

228

III

253

252

III

<< back to Problem H2


 

Problem H3

a. 

The contingency table is above.

b. 

Of the eight people with above-average forearm lengths, 87.5% (7 / 8) also have above-average foot lengths.

c. 

Of the eight people with above-average forearm lengths, only 12.5% (1/ 8) have below-average foot lengths.

d. 

Of the 12 people with below-average forearm lengths, 83.3% (10 / 12) also have below-average foot lengths.

e. 

Of the 11 people with below-average forearm lengths, only 16.7% (2 / 12) have above-average foot lengths.

f. 

These percentages say that there is a fairly strong (more than 80%) positive association between forearm length and foot length.

<< back to Problem H3


 

Problem H4

a. Here is the completed table:

Person #

Forearm Length (X)

Foot Length (Y)

YL = X

Error = Y - YL

(Error)2
=
(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.

<< back to Problem H4


 

Problem H5

Here is the completed table:

Person #

Forearm Length (X)

Foot Length (Y)

YL =
X + 4

Error = Y - YL

(Error)2
=
(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.

<< back to Problem H5


 

Problem H6

The first SSE is smaller, which means that the line Foot Length = Forearm Length is a better fit to the data than the line Foot Length = Forearm Length + 4. Here is an illustration of these two lines on top of the data set:

As you can see from the graph, the line Foot Length = Forearm Length is a closer representation of the data than the line Foot Length = Forearm Length + 4.

<< back to Problem H6


 

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