(IPS10-2.8) Blueberries and anthocyanins. Anthocyanins are compounds that appear to have some health benefits for bones, the heart, and the brain. Blueberries are a good source of many different anthocyanins. Researchers at the Piedmont Research Station of North Carolina State University have assembled a database giving the concentrations of 18 different anthocyanins for 267 varieties of blueberries. Four of the anthocyanins measured are delphinidin-3-arabinoside, malvidin-3-arabinoside, cyanidin-3-galactoside, and delphinidin-3-glucoside, all measured in units of mg per 100 g of berries (dry weight). In the data file, we have simplified the names of these anthocyanins to Antho1, Antho2, Antho3, and Antho4. ex02-008berries.csv

(a) Make a scatterplot of the data with Antho4 on the x axis and Antho3 on the y axis.

(b) Describe the form, direction, and strength of the relationship.

(c) Are there any outliers or unusual observations?

(d) Is it useful to add a straight line to your scatterplot? Explain your answer.

(e) If you have access to the appropriate software, explore the use of a scatterplot smoother to understand this relationship. Summarize what you have found using this method.

(f) Blueberries and anthocyanins with logs. Refer to the previous exercise and examine the distributions of Antho3 and Antho4. Transform each of the variables with a log, make a scatterplot, and answer the questions in the previous exercise for the transformed data.

Data:

43 1.9912 2.466 0.6272 0.1097 0.68 88 0.9026 -0.4665 -2.2101 14 1.902 2.7053 0.4925 0.0864 0.6429 0.9952 0.7083 2.4492 45 1.8517 2.2849 0.4382 0.0728 0.6161 0.8263 0.825 2.6197 16 1.1956 1.4892 0.3668 0.0689 0.1787 0.3983 -1.003 2.6751 47 1.4594 1.7634 0.268 0.0488 0.378 0.5672 -1.3169 3.0192 18 1.4295 1.508 2.028 0.0983 0.3573 0.4108 0.707 2.3193 19 1.8364 1.8871 0.8797 0.7764 0.6078 0.635 0.1282 0.2531 50 0.6776 1.2451 0.9478 0.0657 0.3892 0.2192 -0.0536 -2.7224 51 1.7024 1.9273 1.0295 1.0259 0.5321 0.6561 0.0291 0.0256 52 1.8919 1.4713 0.7296 1.3516 0.6376 0.3861 0.3153 0.3013 53 1.7095 1.7977 0.5324 0.7384 0.5362 0.5865 -0.6304 0.3032 54 1.82 25 1.6692 0.8771 1.2116 0.6002 0.5123 0.1312 0.1919 55 1.8437 1.563 0.6719 1.4466 0.6118 0.4466 -0.3976 0.3692 56 2.48 88 1.3397 0.7387 0.6416 0.9118 0.2925 -0.3029 0.4439 57 2.1471 1.7551 0.6638 1.0819 0.7641 0.5625 -0.4098 0.07 88 58 1.2396 1.2453 0.2776 0.5246 0.2147 0.2194 -1.2817 0.6451 59 2.4448 2.3808 1.1688 0.1613 0.8939 0.8674 0.156 1.8243 50 2.1012 1.0443 0.6214 4.2995 0.7425 0.0433 -0.4758 1.4585 61 2.0299 1.2147 0.7254 2.3757 0.708 0.1945 -0.3211 0.8653 3.2373 2.9934 1.8366 0.301 1.1747 1.0964 0.6079 1.2005 63 1.3298 1.8306 0.5767 0.1339 0.285 0.6046 0.5505 -2.0108 54 0.7606 1.3331 0.1907 0.0363 0.2737 0.2875 -1.6572 3.3148 65 0.2157 0.2369 0.0546 0.0209 -1.534 1.4402 2.9071 3.8701 56 1.9446 1.8314 0.5701 0.208 0.665 0.6051 0.562 -1.5702 57 1.8923 1.9794 0.9185 0.1192 0.6378 0.6828 -0.085 2.1268 58 1.3897 2.0006 0.5641 0.0962 0.3291 0.6934 0.5724 2.3414 69 1.7121 1.8928 0.7703 0.1921 0.5377 0.6381 -0.261 -1.65 70 2.1665 1.8379 0.9559 0.2332 0.7731 0.6086 -0.0451 1.4557 71 1.9118 1.9916 0.422 0.0705 0.648 0.6889 0.8628 2.6518 72 1.2104 1.1866 0.3564 0.0752 0.1909 0.1711 -1.0318 2.5882 73 0.5263 0.7603 0.2241 BEO'O 0.642 0.2741 1.4957 3.2691 74 1.8507 1.8034 0.8916 0.1191 0.6156 0.5897 -0.1147 2.1279 75 1.4197 1.1971 0.659 0.1068 0.3504 0.1799 0.417 2.2367 76 1.3805 2.1963 0.4912 0.0858 0.3225 0.7868 0.7109 2.4557 77 1.8119 1.7519 0.7201 0.2013 0.5944 0.5607 -0.3284 -1.6029 78 0.6263 0.7138 0.2083 0.0482 0.4679 0.3372 1.5689 3.0328 79 1.1019 1.2578 0.467 0.0571 0.0971 0.2294 0.7613 2.8633 80 0.8982 0.7286 0.3444 0.1374 0.1073 -0.3166 -1.066 1.985 81 1.6206 2.2185 0.5088 0.1033 0.4828 0.7968 0.6757 -2.2703 82 1.1637 0.7856 0.4038 0.1002 0.1516 -0.2413 -0.9069 2.3004 83 0.207 0.1825 0.0628 0.0243 -1.5749 -1.6991 2.7671 3.7193 84 2.4112 2.6039 1.8659 0.2177 0.8801 0.957 0.6237 1.5248 85 2.0756 2.9914 2.6699 0.199 0.7303 1.0957 0.9821 -1.6143ID Antho1 Antho2 Antho3 Antho4 LAntho1 LAntho2 LAntho3 LAntho4 1 1.8249 1.3049 0.4306 0.0878 0.6015 0.2662 -0.8425 -2.4325 1.708 1.8887 0.5093 0.3107 0.5353 0.6359 0.6748 -1.1688 3 2.2612 2.3272 1.0364 1.9937 0.8159 0.8447 0.0358 -0.0064 4 1.4566 1.4782 0.9475 1.5592 0.3761 0.3908 0.054 0.4441 5 1.1866 1.7263 1.8749 0.0924 0.1711 0.546 0.6285 -2.3814 6 1.6313 2.0016 0.4624 0.0841 0.4894 0.694 0.7712 -2.4753 7 1.3214 1.5729 0.2806 0.0471 0.2787 0.4529 -1.2708 3.0563 1.1604 1.6177 1.1105 0.7085 0.1488 0.481 0.1048 -0.3446 1.9479 2.8627 2.1338 2.3667 0.6667 1.0518 0.7579 0.8615 10 1.672 1.8367 1.6296 0.9621 0.514 0.608 0.4883 -0.0387 11 1.8639 2.0833 0.9797 0.2456 0.6227 0.734 -0.0205 -1.4041 12 1.2805 1.1564 0.9835 0.069 0.2472 0.1453 -0.0167 -2.6743 13 1.4198 1.1465 1.0384 1.7067 0.3505 0.1367 0.0377 0.5345 14 1.6068 2.068 0.7696 1.0001 0.4743 0.7266 -0.2619 0.0001 15 1.591 1.5491 0.6041 0.9227 0.4643 0.4377 -0.5041 -0.0804 16 1.803 2.0591 1.0721 1.5586 0.5895 0.7223 0.0697 0.4438 17 0.957 1.3827 0.5719 0.2377 0.044 0.324 -0.5588 -1.4367 18 1.1861 1.5205 0.3334 0.049 0.1706 0.419 -1.0985 3.0155 19 1.3816 1.2787 0.7506 0.264 0.3233 0.2459 -0.2869 -1.3319 20 1.0795 0.6727 0.4278 0.8404 0.07 65 0.3964 -0.849 0.1739 21 1.5017 1.3051 0.9093 1.0132 0.4066 0.2663 0.0951 0.0131 22 3.03 2.5652 1.1119 2.2473 1.1086 0.942 0.1061 0.8097 23 1.686 1.9895 0.54 0.0759 0.5223 0.6879 0.6163 2.5784 24 1.8367 1.6981 0.8591 0.5193 0.608 0.5295 -0.1519 0.6552 25 1.8292 2.3505 0.4243 0.0809 0.6039 0.8546 0.8573 2.514 26 1.9061 1.3669 1.0756 2.2906 0.6451 0.3126 0.0729 0.8288 27 1.6165 1.8809 0.5812 0.0642 0.4802 0.6318 0.5426 -2.7461 28 2.2002 0.8899 1.2715 0.1031 0.7885 0.1167 0.2402 2.2723 29 2.2239 2.2849 1.1012 0.1339 0.7992 0.8263 0.0964 -2.0106 30 2.0084 2.034 0.749 0.1146 0.6973 0.71 -0.289 -2.1663 31 2.2576 1.8397 0.7639 0.114 0.8143 0.6096 0.2693 2.1717 32 1.4435 2.4365 0.5351 0.0433 0.3671 0.8906 0.6253 3.1387 33 1.4882 1.5609 0.4445 0.0664 0.3976 0.4453 0.8108 -2.7118 34 1.727 2.5159 0.5741 0.0656 0.5464 0.9226 0.5549 -2.7243 35 1.7055 2.4097 0.3775 0.0778 0.5335 0.8795 0.9742 -2.5532 36 2.4653 2.7433 0.8173 0.1102 0.9023 1.0092 0.2018 2.2052 37 2.3509 1.881 0.7036 0.1265 0.8548 0.6318 0.3515 -2.0674 38 1.8069 2.5152 0.58 0.0786 0.5916 0.9224 0.5447 2.5428 39 2.0474 1.1867 0.6781 0.1348 0.7166 0.1712 0.38 84 -2.0042 40 1.7394 2.236 0.334 0.0767 0.5535 0.8047 -1.0966 2.5684 41 2.2887 2.4714 0.5929 0.0714 0.828 0.9048 -0.52 28 2.6399 42 2.3427 2.1203 0.8571 0.0984 0.8513 0.7515 -0.1542 -2.319