A study of home energy consumption in the Twin Cities resulted in the data found in "energy.csv". a) Fit the simple linear regression of Carbon on Size. Identify "s" and "R2." For now, assume all assumptions are met. b) Fit the multiple linear regression of Carbon on all the other variables, including Size (a total of four explanatory variables). Report the improvement in the "s" and "R2" statistics achieved by including the additional variables beyond just using Size. Again, assume all assumptions are met. c) Comment on the statistical significance of each variable included in the more complete model (t-test on its coefficient) from part c). Comment on how much the estimated coefficient (slope) for Size changed when comparing the models in parts b) and c). What does that tell you? d) A house (in the Twin Cities) currently has two occupants, is 2400 square feet in size, and has a programmable thermostat that set at 68 during the daytime in the winter. Using the more complete model, predict the carbon equivalents of energy usage for the house and generate an 80% prediction interval.
\f1787.628 764 68 UT W 3385.39 1682 64 2844.468 4 899 68 2299.331 986 67 3430.497 4 1329 65 0 4520.676 3 1376 60 3089.582 5 1720 64 5100.422 3 2827 69 2053.305 4 759 68 4024.689 5 1847 68 3116.689 1 2190 68 3817.093 N 2081 62 2492.545 1493 61 oo 2803.003 1093 68 3524.625 1092 68 O J W N WW NB 3955.022 1155 68 5334.444 1805 68 O 4734.059 2098 70 3084.136 2 1663 66 1815.435 1293 62 4434.176 4 1728 70 2374.871 2 745 65 4171.968 2 1719 70 4667.798 2400 68 3366.458 1214 68 3710.834 1013 68 1811.276 837 65 1872.032 4 2359 55 0 3299.578 1100 68 O 2530.15 768 68 2598.017 4 1246 67 3526.698 2 1324 70 1896.244 2557 66 1246.472 1256 65 2399.551 5 1266 62 O 4724.807 1912 68 O 3761.082 1275 70 2940.138 4 1235 65 3152.188 1 2151 68 2555.779 3 1719 67 3490.164 2 2407 68 0 2832.206 2 947 68 3031.708 2 1405 70 0 4395.185 4 2181 64 O 2985.257 4 1798 66 2207.883 1008 68 3504.527 4 1247 68 4623.977 2 1059 70 2339.471 N 972 712504.194 1125 72 2715.234 IN 1036 68 2780.243 N 1932 68 2510.495 2 863 67 O 2508.935 4 1598 68 3325.971 2 1135 73 2503.795 3 2124 68 2954.158 2 959 70 2966.122 2 912 68 3143.551 2 1227 68 4955.448 2 1255 70 O 2271.492 2 1052 68 2339.406 2 2027 69 4206.976 3 2281 68 0 2698.464 5 2545 68 2515.061 2 978 68 0 2921.214 3 946 68 4278.734 2 2173 70 2909.334 2 761 70 3595.362 2 1909 67 3931.739 2 1409 68 0 4230.208 2 1822 70 2607.096 1 1143 68 O 2887.668 2 1045 68 O 3147.181 5 973 64 3023.155 4 1644 68 2860.361 4 1314 62 3432.543 2 1434 69 4020.547 4 2062 68 3799.399 4 1589 68 3574.661 4 2092 69 3357.685 1678 70 2954.387 4 1004 70 2267.353 4 1159 68 2896.324 954 76 2373.396 1340 68 0 3192.28 2 2218 72 0 3063.605 3 1273 68 2425.645 1493 70 2275.34 1341 68 6360.229 2 1987 69 3220.431 3 3059 70 3328.784 2 1515 68 3313.435 4 1532 71 2800.539 3 1588 72 3319.681 3 1112 65 4270.927 2 1677 67 4289.604 2 1127 72 3732.731 4 1891 702783.144 N 1205 68 2902.523 2 1314 65 3164.636 1090 70 2882.222 3 785 72 3863.208 2133 70 O NW 3633.296 2134 74 O 2690.48 2 1692 64 O 3894.593 4 1182 70 2753.163 2459 67 2687.336 1167 73 O 3380.469 ANNAN 2001 65 4440.664 2489 68 4540.625 2839 66 2095.353 2 1834 66 O 2779.788 3 1607 68 4123.845 3 1771 68 3175.241 5 936 70 0 4167.217 2 1853 67 O 5352.985 3 1531 70 O 1698.71 1129 67 O 3229.429 2 1138 65 4362.594 2 1794 71 4275.656 1 1706 68 3927.01 2 1716 72 2827.816 3 1235 68 O 4049.933 4 1732 70 1356.778 2 1010 70 2430.995 1808 66 3948.639 1523 70 5460.764 W NUNN 2052 70 2067.186 1437 60 O 2928.975 1235 63 O 3660.035 4 1281 68 O 2137.09 983 68 3578.691 2 1444 71 1882.808 2 980 66 2964.173 2 1419 69 3035.287 4 1919 67 1290.492 1005 58 0 2980.808 5 995 72 2769.108 5 943 68 3698.596 4 958 68 O 2570.388 2 1216 65 3336.46 2 1094 72 O 1448.531 2 875 65 3852.844 4 2362 69 4116.155 2235 68 5289.246 N NN 2748 70 OOH 3130.909 1387 681946.69 1972 62 0 3204.981 4 1514 71 5622.587 5 2181 70 1648.635 1 699 65 3085.269 6 984 68 O 3927.938 2 808 69 O 2846.591 2 1275 71 2910.457 4 1473 68 OO 2287.588 1 1693 65 2980.618 1 983 68 3259.657 3 1343 67 3058.948 2 766 68 2845.278 4 1387 68 2432.296 2 1068 58 3923.343 2 1758 72 O 3727.386 2 1548 64 2808.94 1 996 68 3653.932 2 1326 72 2441.129 2 1001 71 2499.5 1261 70 0 3014.998 4 1408 70 2401.517 2 1758 68 O 2714.439 1 1051 68 O 2426.546 2 2447 67 2628.795 1320 68 3435.659 1810 70 3909.967 2 2883 66 3830.745 3 2201 68 2564.264 4 1084 66 2380.406 1786 64 3581.306 2 2219 70 6748.389 3 3101 68 2617.797 2 1384 68 2599.161 2 2183 65 4459.692 4 2197 72 2229.659 3 1590 68 5161.25 5 1644 68 4072.23 4 1531 68 3753.829 5 2057 68 2270.81 2 1252 65 3020.267 2 1257 70 3987.398 2 2461 70 3761.013 4 1645 72 2929.967 2 1398 67 3072.383 1977 70 INN 3555.461 3735 70 3825.32 2150 66 W N 2728.288 1458 70 4010.422 4 2953 682255.07 N 979 70 2598.219 1188 68 O 3021.226 2 1270 68 O 4521.35 4 1632 69 2751.748 2 1121 72 3083.396 2 905 70 2642.081 1 1525 72 6430.378 1224 68 2654.083 1839 66 O 2035.508 1005 IN N N WU 68 2959.894 1102 68 4167.699 1850 68 2961.539 2 1005 67 2314.013 3 992 65 1699.341 1026 68 4549.229 4 1965 69 OO 4537.633 2 1238 72 2510.58 2 1142 68 O 1940.133 1488 66 3496.514 3 2093 70 3629.747 2 985 65 2929.368 2 1976 55 3631.169 IN 1864 73 4392.575 4 1431 73 2891.063 2 1965 64 5040.837 2 2605 70 O 4761.021 4 1575 72 2833.869 1059 69 4328.84 1176 72 UI W N N 3778.366 1089 68 3578.184 1948 68 2988.624 4 1955 68 3293.148 3 1517 68 O 5878.672 1 1054 58 2461.096 2 1212 68 6533.465 4 2346 70 3107.675 2 1315 68 0 3527.962 3 1143 70 3495.658 2 1074 72 1593.793 983 65 3216.169 1343 76 2118.302 956 68 O 3135.75 2 810 70 OO 2394.881 2 946 73 3135.974 2 1682 70 3761.541 2 1129 70 3371.865 1087 72 OO 3822.582 5 1282 68 2924.82 2 1465 683393.071 2 979 68 2461.456 2 1011 68 2730.785 2 1269 72 4264.153 4 1001 68 O 1912.879 903 66 O 2917.319 1 1143 70 2807.491 2 912 70 O 1717.048 1 960 68 2479.34 2 1133 70 2303.256 1 957 68 1873.66 2 1041 71 2200.114 3 1034 62 6758.112 5 2591 68 0 2536.028 2 1421 67 0 2606.017 4 1257 66 2088.466 3 837 68 4880.305 2 1317 70 1951.68 IN 1053 70 2096.946 2 985 68 O 2365.684 941 74 3292.316 2 1395 72 2708.482 2 1059 70 2588.907 2 1246 72 O 4348.964 8 2377 70 2374.424 1469 68 J H 3923.647 1513 70 O 2084.206 3 1541 66 3811.347 6 1388 72 1864.97 4 916 68 2628.051 2 1051 68 0 2965.917 1 1053 72 2447.752 3 1063 68 2721.495 2 974 72 0 2794.792 4 1105 68 2605.056 3 1242 68 4905.417 2 1395 70 0 2762.014 2 1076 70 O 5219.159 3 2193 68 3776.963 4 1977 70 O 4789.468 5 1268 68 1982.623 2 1602 63 3208.965 3 1079 70 4161.562 2 1430 68 2886.303 1233 70 4224 W W N 1087 72 0 2472.363 976 67 3184.131 3 1533 70 2862.887 4 1165 68 2790.714 2 1115 682456.639 1071 70 4167.219 6 1488 71 3040.281 932 68 2998.357 2 1395 70 3443.795 5 1276 70 2785.332 1 1196 67 3558.628 4 1232 72 2832.776 2 1809 68 4111.584 2 1746 72 3019.263 2 1804 68 1 2111.626 1358 66
