Question: Use the data below in solving for the questions. For each question, please explain your answers, and provide the formulas and the R Function codes

Use the data below in solving for the questions.

For each question, please explain your answers, and provide the formulas and the R Function codes used.

We will work with two of the dataset variables: CT and bmi. CT, a complex method for determining body fat, is the outcome variable. The explanatory variable is called bmi.

y CT = percent body fat

X BMI = kg/m3

1. Generate a scatterplot of the CT and bmi values in the dataset. Be sure to include the fitted line. Paste your code and output (scatterplot) here.

2. Discuss the overall pattern of association and any unusual points in the scatterplot. Be sure to address the nature of the relationship (positive or negative) as well as the distribution of the points in different areas of the plot. Any exceptional/influential points?

3. Calculate the averages and standard deviations for the CT and bmi variables. Paste your code and output here.

4. Find the Pearson correlation with the cor function in R. Paste your code and output here. What does the Pearson correlation tell us about the CT and bmi values?(hint you should get 0.7447979)

5. Generate the bmi and CT fitted regression using the lm function in R. Paste your code and output (fitted regression) here.

6. Write out the equation for the fitted regression line.

Body Fat Data

CT age weight height htcm wtkg htm bmi
12.3 23 154.25 67.75 172.085 69.96662 1.72085 23.62679
6.1 22 173.25 72.25 183.515 78.58488 1.83515 23.33436
25.3 22 154 66.25 168.275 69.85323 1.68275 24.66876
10.4 26 184.75 72.25 183.515 83.80119 1.83515 24.88325
28.7 24 184.25 71.25 180.975 83.57439 1.80975 25.51738
20.9 24 210.25 74.75 189.865 95.3678 1.89865 26.45525
19.2 26 181 69.75 177.165 82.10022 1.77165 26.15703
12.4 25 176 72.5 184.15 79.83226 1.8415 23.54155
4.1 25 191 74 187.96 86.63614 1.8796 24.5227
11.7 23 198.25 73.5 186.69 89.92469 1.8669 25.80102
7.1 26 186.25 74.5 189.23 84.48158 1.8923 23.59294
7.8 27 216 76 193.04 97.97595 1.9304 26.29208
20.8 32 180.5 69.5 176.53 81.87342 1.7653 26.27277
21.2 30 205.25 71.25 180.975 93.09983 1.80975 28.42573
22.1 35 187.75 69.5 176.53 85.16196 1.7653 27.32805
20.9 35 162.75 66 167.64 73.82216 1.6764 26.26827
29 34 195.75 71 180.34 88.7907 1.8034 27.3013
22.9 32 209.25 71 180.34 94.9142 1.8034 29.18415
16 28 183.75 67.75 172.085 83.3476 1.72085 28.14537
16.5 33 211.75 73.5 186.69 96.04819 1.8669 27.55796
19.1 28 179 68 172.72 81.19303 1.7272 27.21658
15.2 28 200.5 69.75 177.165 90.94527 1.77165 28.97505
15.6 31 140.25 68.25 173.355 63.61633 1.73355 21.16878
17.7 32 148.75 70 177.8 67.47186 1.778 21.34318
14 28 151.25 67.75 172.085 68.60584 1.72085 23.16728
3.7 27 159.25 71.5 181.61 72.23459 1.8161 21.90109
7.9 34 131.5 67.5 171.45 59.6474 1.7145 20.29161
22.9 31 148 67.5 171.45 67.13167 1.7145 22.83771
3.7 27 133.25 64.75 164.465 60.44118 1.64465 22.34529
8.8 29 160.75 69 175.26 72.91497 1.7526 23.73838
11.9 32 182 73.75 187.325 82.55381 1.87325 23.52587
5.7 29 160.25 71.25 180.975 72.68818 1.80975 22.19354
11.8 27 168 71.25 180.975 76.20352 1.80975 23.26686
21.3 41 218.5 71 180.34 99.10993 1.8034 30.47425
32.3 41 247.25 73.5 186.69 112.1507 1.8669 32.17807
40.1 49 191.75 65 165.1 86.97633 1.651 31.90854
24.2 40 202.25 70 177.8 91.73906 1.778 29.01956
28.4 50 196.75 68.25 173.355 89.2443 1.73355 29.69667
32.6 50 203 67 170.18 92.07925 1.7018 31.79397
34.5 45 262.75 68.75 174.625 119.1814 1.74625 39.08369
31.6 48 217 70 177.8 98.42954 1.778 31.13594
32 41 212 71.5 181.61 96.16158 1.8161 29.15561
7.7 39 125.25 68 172.72 56.81244 1.7272 19.044
13.9 43 164.25 73.25 186.055 74.50255 1.86055 21.52229
10.8 40 133.5 67.5 171.45 60.55458 1.7145 20.60023
5.6 39 148.5 71.25 180.975 67.35847 1.80975 20.56624
13.6 45 135.75 68.5 173.99 61.57516 1.7399 20.34028
4 47 127.5 66.75 169.545 57.83303 1.69545 20.11898
10.2 47 158.25 72.25 183.515 71.78099 1.83515 21.31407
6.6 40 139.25 69 175.26 63.16274 1.7526 20.56342
8 51 137.25 67.75 172.085 62.25555 1.72085 21.02287
6.3 49 152.75 73.5 186.69 69.28623 1.8669 19.87947
3.9 42 136.25 67.5 171.45 61.80196 1.7145 21.02458
22.6 54 198 72 182.88 89.81129 1.8288 26.85335
20.4 58 181.5 68 172.72 82.32702 1.7272 27.5967
28 62 201.25 69.5 176.53 91.28546 1.7653 29.29305
31.5 54 202.5 70.75 179.705 91.85246 1.79705 28.44267
24.6 61 179.75 65.75 167.005 81.53323 1.67005 29.23315
26.1 62 216 73.25 186.055 97.97595 1.86055 28.30328
29.8 56 178.75 68.5 173.99 81.07964 1.7399 26.78324
30.7 54 193.25 70.25 178.435 87.65672 1.78435 27.5312
25.8 61 178 67 170.18 80.73944 1.7018 27.87846
32.3 57 205.5 70 177.8 93.21323 1.778 29.48588
30 55 183.5 67.5 171.45 83.2342 1.7145 28.31567
21.5 54 151.5 70.75 179.705 68.71925 1.79705 21.27934
13.8 55 154.75 71.5 181.61 70.19342 1.8161 21.28222
6.3 54 155.25 69.25 175.895 70.42021 1.75895 22.76095
12.9 55 156.75 71.5 181.61 71.1006 1.8161 21.55727
24.3 62 167.5 71.5 181.61 75.97672 1.8161 23.03568
8.8 55 146.75 68.75 174.625 66.56468 1.74625 21.82886
8.5 56 160.75 73.75 187.325 72.91497 1.87325 20.77903
13.5 55 125 64 162.56 56.69905 1.6256 21.45598
11.8 61 143 65.75 167.005 64.86371 1.67005 23.25642
18.5 61 148.25 67.5 171.45 67.24507 1.7145 22.87629
8.8 57 162.5 69.5 176.53 73.70876 1.7653 23.65277
22.2 69 177.75 68.5 173.99 80.62605 1.7399 26.63341
21.5 81 161.25 70.25 178.435 73.14177 1.78435 22.97235
18.8 66 171.25 69.25 175.895 77.6777 1.75895 25.10668
31.4 67 163.75 67.75 172.085 74.27575 1.72085 25.08193
26.8 64 150.25 67.25 170.815 68.15225 1.70815 23.3576
18.4 64 190.25 72.75 184.785 86.29595 1.84785 25.27301
27 70 170.75 70 177.8 77.4509 1.778 24.49982
27 72 168 69.25 175.895 76.20352 1.75895 24.63021
26.6 67 167 67.5 171.45 75.74992 1.7145 25.76958
14.9 72 157.75 67.25 170.815 71.5542 1.70815 24.52354
23.1 64 160 65.75 167.005 72.57478 1.67005 26.02117
8.3 46 176.75 72.5 184.15 80.17245 1.8415 23.64187
14.1 48 176 73 185.42 79.83226 1.8542 23.22016
20.5 46 177 70 177.8 80.28585 1.778 25.3966
18.2 44 179.75 69.5 176.53 81.53323 1.7653 26.1636
8.5 47 165.25 70.5 179.07 74.95614 1.7907 23.37553
24.9 46 192.5 71.75 182.245 87.31653 1.82245 26.28968
9 47 184.25 74.5 189.23 83.57439 1.8923 23.33959
17.4 53 224.5 77.75 197.485 101.8315 1.97485 26.11042
9.6 38 188.75 73.25 186.055 85.61556 1.86055 24.73262
11.3 50 162.5 66.5 168.91 73.70876 1.6891 25.835
17.8 46 156.5 68.25 173.355 70.98721 1.73355 23.62149
22.2 47 197 72 182.88 89.3577 1.8288 26.71773
21.2 49 198.5 73.5 186.69 90.03809 1.8669 25.83355
20.4 48 173.75 72 182.88 78.81168 1.8288 23.56449
20.1 41 172.75 71.25 180.975 78.35809 1.80975 23.92471
22.3 49 196.75 73.75 187.325 89.2443 1.87325 25.4325
25.4 43 177 69.25 175.895 80.28585 1.75895 25.94968
18 43 165.5 68.5 173.99 75.06953 1.7399 24.79791
19.3 43 200.25 73.5 186.69 90.83187 1.8669 26.06131
18.3 52 203.25 74.25 188.595 92.19265 1.88595 25.92006
17.3 43 194 75.5 191.77 87.99692 1.9177 23.92798
21.4 40 168.5 69.25 175.895 76.43031 1.75895 24.70351
19.7 43 170.75 68.5 173.99 77.4509 1.7399 25.58455
28 43 183.25 70 177.8 83.1208 1.778 26.29337
22.1 47 178.25 70 177.8 80.85284 1.778 25.57595
21.3 42 163 70.25 178.435 73.93555 1.78435 23.22166
26.7 48 175.25 71.75 182.245 79.49207 1.82245 23.93385
16.7 40 158 69.25 175.895 71.66759 1.75895 23.16412
20.1 48 177.25 72.75 184.785 80.39925 1.84785 23.54607
13.9 51 179 72 182.88 81.19303 1.8288 24.27651
25.8 40 191 74 187.96 86.63614 1.8796 24.5227
18.1 44 187.5 72.25 183.515 85.04857 1.83515 25.25363
27.9 52 206.5 74.5 189.23 93.66682 1.8923 26.15808
25.3 44 185.25 71.5 181.61 84.02798 1.8161 25.47677
14.7 40 160.25 68.75 174.625 72.68818 1.74625 23.83696
16 47 151.5 66.75 169.545 68.71925 1.69545 23.90608
13.8 50 161 66.5 168.91 73.02837 1.6891 25.59652
17.5 46 167 67 170.18 75.74992 1.7018 26.15563
27.2 42 177.5 68.75 174.625 80.51264 1.74625 26.40288
17.4 43 152.25 67.75 172.085 69.05944 1.72085 23.32045
20.8 40 192.25 73.25 186.055 87.20313 1.86055 25.19123
14.9 42 165.25 69.75 177.165 74.95614 1.77165 23.88094
18.1 49 171.75 71.5 181.61 77.90449 1.8161 23.62017
22.7 40 171.25 70.5 179.07 77.6777 1.7907 24.22427
23.6 47 197 73.25 186.055 89.3577 1.86055 25.81364
26.1 50 157 66.75 169.545 71.214 1.69545 24.77396
24.4 41 168.25 69.5 176.53 76.31692 1.7653 24.48972
27.1 44 186 69.75 177.165 84.36818 1.77165 26.8796
21.8 39 166.75 70.75 179.705 75.63653 1.79705 23.42131
29.4 43 187.75 74 187.96 85.16196 1.8796 24.10542
22.4 40 168.25 71.25 180.975 76.31692 1.80975 23.30149
20.4 49 212.75 75 190.5 96.50178 1.905 26.59166
24.9 40 176.75 71 180.34 80.17245 1.8034 24.65137
18.3 40 173.25 69.5 176.53 78.58488 1.7653 25.21749
23.3 52 167 67.75 172.085 75.74992 1.72085 25.57974
9.4 23 159.75 72.25 183.515 72.46138 1.83515 21.5161
10.3 23 188.15 77.5 196.85 85.3434 1.9685 22.02415
14.2 24 156 70.75 179.705 70.76041 1.79705 21.91139
19.2 24 208.5 72.75 184.785 94.57401 1.84785 27.69736
29.6 25 206.5 69.75 177.165 93.66682 1.77165 29.84214
5.3 25 143.75 72.5 184.15 65.2039 1.8415 19.22783
25.2 26 223 70.25 178.435 101.1511 1.78435 31.76951
9.4 26 152.25 69 175.26 69.05944 1.7526 22.48317
19.6 26 241.75 74.5 189.23 109.656 1.8923 30.62332
10.1 27 146 72.25 183.515 66.22449 1.83515 19.66416
16.5 27 156.75 67.25 170.815 71.1006 1.70815 24.36808
21 27 200.25 73.5 186.69 90.83187 1.8669 26.06131
17.3 28 171.5 75.25 191.135 77.79109 1.91135 21.29362
31.2 28 205.75 69 175.26 93.32663 1.7526 30.38365
10 28 182.5 72.25 183.515 82.78061 1.83515 24.5802
12.5 30 136.5 68.75 174.625 61.91536 1.74625 20.30418
22.5 31 177.25 71.5 181.61 80.39925 1.8161 24.37656
9.4 31 151.25 72.25 183.515 68.60584 1.83515 20.37126
14.6 33 196 73 185.42 88.90411 1.8542 25.85882
13 33 184.25 68.75 174.625 83.57439 1.74625 27.40693
15.1 34 140 70.5 179.07 63.50293 1.7907 19.80378
27.3 34 218.75 72 182.88 99.22333 1.8288 29.66753
19.2 35 217 73.75 187.325 98.42954 1.87325 28.05007
21.8 35 166.25 68 172.72 75.40973 1.7272 25.27797
20.3 35 224.75 72.25 183.515 101.9449 1.83515 30.27069
34.3 35 228.25 69.5 176.53 103.5325 1.7653 33.22305
16.5 35 172.75 69.5 176.53 78.35809 1.7653 25.14472
3 35 152.25 67.75 172.085 69.05944 1.72085 23.32045
0.7 35 125.75 65.5 166.37 57.03924 1.6637 20.60742
20.5 35 177.25 71 180.34 80.39925 1.8034 24.72111
16.9 36 176.25 71.5 181.61 79.94566 1.8161 24.23904
25.3 36 226.75 71.75 182.245 102.8521 1.82245 30.96719
9.9 37 145.25 69.25 175.895 65.88429 1.75895 21.29486
13.1 37 151 67 170.18 68.49245 1.7018 23.6497
29.9 37 241.25 71.5 181.61 109.4292 1.8161 33.17826
22.5 38 187.25 69.25 175.895 84.93517 1.75895 27.45242
16.9 39 234.75 74.5 189.23 106.4808 1.8923 29.7366
26.6 39 219.25 74.25 188.595 99.45013 1.88595 27.9605
0 40 118.5 68 172.72 53.75069 1.7272 18.01768
11.5 40 145.75 67.25 170.815 66.11109 1.70815 22.65804
12.1 40 159.25 69.75 177.165 72.23459 1.77165 23.01385
17.5 40 170.5 74.25 188.595 77.3375 1.88595 21.74352
8.6 40 167.5 71.5 181.61 75.97672 1.8161 23.03568
23.6 41 232.75 74.25 188.595 105.5736 1.88595 29.68213
20.4 41 210.5 72 182.88 95.48119 1.8288 28.54864
20.5 41 202.25 72.5 184.15 91.73906 1.8415 27.05272
24.4 41 185 68.25 173.355 83.91459 1.73355 27.92317
11.4 41 153 69.25 175.895 69.39964 1.75895 22.43108
38.1 42 244.25 76 193.04 110.7899 1.9304 29.73074
15.9 42 193.5 70.5 179.07 87.77013 1.7907 27.37165
24.7 42 224.75 74.75 189.865 101.9449 1.89865 28.27975
22.8 42 162.75 72.75 184.785 73.82216 1.84785 21.61988
25.5 42 180 68.25 173.355 81.64663 1.73355 27.16849
22 42 156.25 69 175.26 70.87381 1.7526 23.07386
17.7 42 168 71.5 181.61 76.20352 1.8161 23.10444
6.6 42 167.25 72.75 184.785 75.86333 1.84785 22.21766
23.6 43 170.75 67.5 171.45 77.4509 1.7145 26.34823
12.2 43 178.25 70.25 178.435 80.85284 1.78435 25.39424
22.1 43 150 69.25 175.895 68.03886 1.75895 21.99125
28.7 43 200.5 71.5 181.61 90.94527 1.8161 27.57405
6 44 184 74 187.96 83.461 1.8796 23.62396
34.8 44 223 69.75 177.165 101.1511 1.77165 32.22662
16.6 44 208.75 73 185.42 94.68741 1.8542 27.54096
32.9 44 166 65.5 166.37 75.29633 1.6637 27.20344
32.8 47 195 72.5 184.15 88.45052 1.8415 26.08297
9.6 47 160.5 70.25 178.435 72.80157 1.78435 22.8655
10.8 47 159.75 70.75 179.705 72.46138 1.79705 22.43811
7.1 49 140.5 68 172.72 63.72973 1.7272 21.36273
27.2 49 216.25 74.5 189.23 98.08935 1.8923 27.39314
19.5 49 168.25 71.75 182.245 76.31692 1.82245 22.97786
18.7 50 194.75 70.75 179.705 88.33711 1.79705 27.35413
19.5 50 172.75 73 185.42 78.35809 1.8542 22.79138
47.5 51 219 64 162.56 99.33673 1.6256 37.59088
13.6 51 149.25 69.75 177.165 67.69866 1.77165 21.56871
7.5 51 154.5 70 177.8 70.08002 1.778 22.16821
24.5 52 199.25 71.75 182.245 90.37828 1.82245 27.21152
15 53 154.5 69.25 175.895 70.08002 1.75895 22.65099
12.4 54 153.25 70.5 179.07 69.51303 1.7907 21.67807
26 54 230 72.25 183.515 104.3262 1.83515 30.97779
11.5 54 161.75 67.5 171.45 73.36857 1.7145 24.95946
5.2 55 142.25 67.25 170.815 64.52351 1.70815 22.11393
10.9 55 179.75 68.75 174.625 81.53323 1.74625 26.73756
12.5 55 126.5 66.75 169.545 57.37944 1.69545 19.96119
14.8 55 169.5 68.25 173.355 76.8839 1.73355 25.58366
25.2 55 198.5 74.25 188.595 90.03809 1.88595 25.3143
14.9 56 174.5 69.5 176.53 79.15187 1.7653 25.39944
17 56 167.75 68.5 173.99 76.09012 1.7399 25.13504
10.6 57 147.75 65.75 167.005 67.01827 1.67005 24.02892
16.1 57 182.25 71.75 182.245 82.66721 1.82245 24.88984
15.4 58 175.5 71.5 181.61 79.60546 1.8161 24.13589
26.7 58 161.75 67.25 170.815 73.36857 1.70815 25.14537
25.8 60 157.75 67.5 171.45 71.5542 1.7145 24.34222
18.6 62 168.75 67.5 171.45 76.54371 1.7145 26.03961
24.8 62 191.5 72.25 183.515 86.86294 1.83515 25.79238
27.3 63 219.15 69.5 176.53 99.40476 1.7653 31.89849
12.4 64 155.25 69.5 176.53 70.42021 1.7653 22.59749
29.9 65 189.75 65.75 167.005 86.06915 1.67005 30.85948
17 65 127.5 65.75 167.005 57.83303 1.67005 20.73562
35 65 224.5 68.25 173.355 101.8315 1.73355 33.88515
30.4 66 234.25 72 182.88 106.254 1.8288 31.76968
32.6 67 227.75 72.75 184.785 103.3057 1.84785 30.25455
29 67 199.5 68.5 173.99 90.49168 1.7399 29.89235
15.2 68 155.5 69.25 175.895 70.53362 1.75895 22.7976
30.2 69 215.5 70.5 179.07 97.74915 1.7907 30.48367
11 70 134.25 67 170.18 60.89478 1.7018 21.02631
33.6 72 201 69.75 177.165 91.17207 1.77165 29.04731
29.3 72 186.75 66 167.64 84.70837 1.6764 30.14193
26 72 190.75 70.5 179.07 86.52274 1.7907 26.98265
31.9 74 207.5 70 177.8 94.12041 1.778 29.77284

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!