Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 A B C DHomework

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.

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

 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

 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

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.

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.

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.

 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.