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

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.

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.