Regression and Correlation Analysis & ANOVA
tututt
Week6-SimpleRegression-Correlation1.xlsxRegression-Residuals
| Regression Model: Predicted y = b0 x + b1 | x | Observed y | Predicted y | Residual=Observed - Predicted | Residual=Observed - Predicted | Bin | Frequency | Normal Probability Plot of Residuals | Residual=Observed - Predicted | Standardized Residual | ranks i | (i - 0.5) / n | Standard Z values | |||||||||
| χ2 | 16 | 37.1 | 38.2 | -1.1 | Residuals have to be: | -1.1 | -3.03 | 1 | -3.0 | -2.80 | 1 | 0.0078125 | -2.42 | |||||||||
| 14 | 33.5 | 33.1 | 0.4 | 1. Normally distributed | For Homoscedasticity, plot the resiuals | For independency, plot the residuals vs | 0.4 | -2.38 | 1 | -2.5 | -2.31 | 2 | 0.0234375 | -1.99 | ||||||||
| 13 | 30.3 | 30.6 | -0.3 | 2. Have a zero mean | vs the predicted Y values. | the independent variable (or vs time if possible). | -0.3 | -1.74 | 2 | -2.3 | -2.15 | 3 | 0.0390625 | -1.76 | ||||||||
| SLOPE | 2.53 | 19 | 46.7 | 45.8 | 0.9 | 3. Have a constant variance | There should not exist and pattern in the plot | There should be any distinguishing pattern | 0.9 | -1.10 | 4 | Standardizing: | -2.2 | -2.06 | 4 | 0.0546875 | -1.60 | |||||
| INTERCEPT | -2.26 | 9 | 20.2 | 20.5 | -0.3 | they are Homoscedastic | -0.3 | -0.45 | 12 | Z = (x - mean(s))/ (SD(x)) | -1.6 | -1.46 | 5 | 0.0703125 | -1.47 | |||||||
| Correlation R | 0.9953 | 9 | 20.3 | 20.5 | -0.2 | 4. Are independent | -0.2 | 0.19 | 14 | -1.5 | -1.40 | 6 | 0.0859375 | -1.37 | ||||||||
| Determination R2 | 0.9907 | 17 | 40.1 | 40.7 | -0.6 | -0.6 | 0.84 | 16 | -1.1 | -1.02 | 7 | 0.1015625 | -1.27 | |||||||||
| 16 | 38 | 38.2 | -0.2 | -0.2 | 1.48 | 11 | -1.1 | -1.02 | 8 | 0.1171875 | -1.19 | |||||||||||
| 16 | 38.7 | 38.2 | 0.5 | 0.5 | More | 3 | -1.0 | -0.96 | 9 | 0.1328125 | -1.11 | |||||||||||
| Residual Mean | 0.00 | 8 | 18.4 | 18.0 | 0.4 | 0.4 | -1.0 | -0.95 | 10 | 0.1484375 | -1.04 | |||||||||||
| Residual standard dev | 1.08 | 15 | 35.3 | 35.7 | -0.4 | -0.4 | -1.0 | -0.94 | 11 | 0.1640625 | -0.98 | |||||||||||
| 11 | 26.3 | 25.6 | 0.7 | 0.7 | -1.0 | -0.92 | 12 | 0.1796875 | -0.92 | |||||||||||||
| 3 | 5.93 | 5.3 | 0.6 | 0.6 | -0.8 | -0.75 | 13 | 0.1953125 | -0.86 | |||||||||||||
| 5 | 8.81 | 10.4 | -1.6 | -1.6 | -0.7 | -0.68 | 14 | 0.2109375 | -0.80 | |||||||||||||
| 15 | 36.1 | 35.7 | 0.4 | 0.4 | -0.7 | -0.63 | 15 | 0.2265625 | -0.75 | |||||||||||||
| 11 | 25.5 | 25.6 | -0.1 | -0.1 | -0.7 | -0.61 | 16 | 0.2421875 | -0.70 | |||||||||||||
| 14 | 33 | 33.1 | -0.1 | -0.1 | -0.6 | -0.59 | 17 | 0.2578125 | -0.65 | |||||||||||||
| 8 | 17.5 | 18.0 | -0.5 | -0.5 | -0.6 | -0.58 | 18 | 0.2734375 | -0.60 | |||||||||||||
| 17 | 40.5 | 40.7 | -0.2 | -0.2 | -0.6 | -0.58 | 19 | 0.2890625 | -0.56 | |||||||||||||
| 15 | 35.3 | 35.7 | -0.4 | -0.4 | -0.5 | -0.44 | 20 | 0.3046875 | -0.51 | |||||||||||||
| 6 | 13.2 | 12.9 | 0.3 | 0.3 | -0.4 | -0.34 | 21 | 0.3203125 | -0.47 | |||||||||||||
| 6 | 14.1 | 12.9 | 1.2 | 1.2 | -0.4 | -0.34 | 22 | 0.3359375 | -0.42 | |||||||||||||
| 10 | 24.3 | 23.0 | 1.3 | 1.3 | -0.3 | -0.31 | 23 | 0.3515625 | -0.38 | |||||||||||||
| 4 | 7.12 | 7.9 | -0.7 | -0.7 | -0.3 | -0.29 | 24 | 0.3671875 | -0.34 | |||||||||||||
| 17 | 40.1 | 40.7 | -0.6 | -0.6 | -0.3 | -0.28 | 25 | 0.3828125 | -0.30 | |||||||||||||
| 4 | 9.33 | 7.9 | 1.5 | 1.5 | -0.2 | -0.21 | 26 | 0.3984375 | -0.26 | |||||||||||||
| 9 | 18 | 20.5 | -2.5 | -2.5 | -0.2 | -0.19 | 27 | 0.4140625 | -0.22 | |||||||||||||
| 10 | 20.7 | 23.0 | -2.3 | -2.3 | -0.2 | -0.19 | 28 | 0.4296875 | -0.18 | |||||||||||||
| 12 | 28.3 | 28.1 | 0.2 | 0.2 | -0.1 | -0.13 | 29 | 0.4453125 | -0.14 | |||||||||||||
| 8 | 19 | 18.0 | 1.0 | 1.0 | -0.1 | -0.05 | 30 | 0.4609375 | -0.10 | |||||||||||||
| 17 | 39.7 | 40.7 | -1.0 | -1.0 | 0.0 | 0.03 | 31 | 0.4765625 | -0.06 | |||||||||||||
| 19 | 46.6 | 45.8 | 0.8 | 0.8 | 0.0 | 0.03 | 32 | 0.4921875 | -0.02 | |||||||||||||
| 14 | 32.1 | 33.1 | -1.0 | -1.0 | 0.1 | 0.05 | 33 | 0.5078125 | 0.02 | |||||||||||||
| 14 | 33.9 | 33.1 | 0.8 | 0.8 | 0.1 | 0.07 | 34 | 0.5234375 | 0.06 | |||||||||||||
| 5 | 11.3 | 10.4 | 0.9 | 0.9 | 0.2 | 0.20 | 35 | 0.5390625 | 0.10 | |||||||||||||
| 16 | 39.3 | 38.2 | 1.1 | 1.1 | 0.3 | 0.26 | 36 | 0.5546875 | 0.14 | |||||||||||||
| 14 | 33.2 | 33.1 | 0.1 | 0.1 | 0.3 | 0.28 | 37 | 0.5703125 | 0.18 | |||||||||||||
| 8 | 18 | 18.0 | 0.0 | 0.0 | 0.4 | 0.33 | 38 | 0.5859375 | 0.22 | |||||||||||||
| 12 | 27.4 | 28.1 | -0.7 | -0.7 | 0.4 | 0.34 | 39 | 0.6015625 | 0.26 | |||||||||||||
| 8 | 18 | 18.0 | 0.0 | 0.0 | 0.4 | 0.40 | 40 | 0.6171875 | 0.30 | |||||||||||||
| 16 | 39.1 | 38.2 | 0.9 | 0.9 | 0.4 | 0.40 | 41 | 0.6328125 | 0.34 | |||||||||||||
| 10 | 20.8 | 23.0 | -2.2 | -2.2 | 0.4 | 0.40 | 42 | 0.6484375 | 0.38 | |||||||||||||
| 13 | 29.6 | 30.6 | -1.0 | -1.0 | 0.5 | 0.46 | 43 | 0.6640625 | 0.42 | |||||||||||||
| 15 | 36.1 | 35.7 | 0.4 | 0.4 | 0.5 | 0.47 | 44 | 0.6796875 | 0.47 | |||||||||||||
| 13 | 29.1 | 30.6 | -1.5 | -1.5 | 0.6 | 0.55 | 45 | 0.6953125 | 0.51 | |||||||||||||
| 19 | 46.3 | 45.8 | 0.5 | 0.5 | 0.6 | 0.58 | 46 | 0.7109375 | 0.56 | |||||||||||||
| 10 | 24.5 | 23.0 | 1.5 | 1.5 | 0.7 | 0.66 | 47 | 0.7265625 | 0.60 | |||||||||||||
| 19 | 46.5 | 45.8 | 0.7 | 0.7 | 0.7 | 0.69 | 48 | 0.7421875 | 0.65 | |||||||||||||
| 9 | 19.5 | 20.5 | -1.0 | -1.0 | 0.8 | 0.70 | 49 | 0.7578125 | 0.70 | |||||||||||||
| 17 | 40.8 | 40.7 | 0.1 | 0.1 | 0.8 | 0.75 | 50 | 0.7734375 | 0.75 | |||||||||||||
| 9 | 20.8 | 20.5 | 0.3 | 0.3 | 0.9 | 0.83 | 51 | 0.7890625 | 0.80 | |||||||||||||
| 10 | 20 | 23.0 | -3.0 | -3.0 | 0.9 | 0.84 | 52 | 0.8046875 | 0.86 | |||||||||||||
| 6 | 12.1 | 12.9 | -0.8 | -0.8 | 0.9 | 0.84 | 53 | 0.8203125 | 0.92 | |||||||||||||
| 4 | 9.32 | 7.9 | 1.5 | 1.5 | 1.0 | 0.95 | 54 | 0.8359375 | 0.98 | |||||||||||||
| 14 | 32.5 | 33.1 | -0.6 | -0.6 | 1.1 | 1.02 | 55 | 0.8515625 | 1.04 | |||||||||||||
| 8 | 20.1 | 18.0 | 2.1 | 2.1 | 1.2 | 1.09 | 56 | 0.8671875 | 1.11 | |||||||||||||
| 9 | 19.4 | 20.5 | -1.1 | -1.1 | 1.3 | 1.17 | 57 | 0.8828125 | 1.19 | |||||||||||||
| 11 | 27 | 25.6 | 1.4 | 1.4 | 1.4 | 1.33 | 58 | 0.8984375 | 1.27 | |||||||||||||
| 11 | 24.9 | 25.6 | -0.7 | -0.7 | 1.5 | 1.35 | 59 | 0.9140625 | 1.37 | |||||||||||||
| 17 | 42.5 | 40.7 | 1.8 | 1.8 | 1.5 | 1.36 | 60 | 0.9296875 | 1.47 | |||||||||||||
| 15 | 36.3 | 35.7 | 0.6 | 0.6 | 1.5 | 1.36 | 61 | 0.9453125 | 1.60 | |||||||||||||
| 7 | 17.4 | 15.4 | 2.0 | 2.0 | 1.8 | 1.63 | 62 | 0.9609375 | 1.76 | |||||||||||||
| 10 | 23.4 | 23.0 | 0.4 | 0.4 | 2.0 | 1.81 | 63 | 0.9765625 | 1.99 | |||||||||||||
| 4 | 7.52 | 7.9 | -0.3 | -0.3 | 2.1 | 1.96 | 64 | 0.9921875 | 2.42 |
y = 2.5286 x - 2.2566 R² = 0.9907
16 14 13 19 9 9 17 16 16 8 15 11 3 5 15 11 14 8 17 15 6 6 10 4 17 4 9 10 12 8 17 19 14 14 5 16 14 8 12 8 16 10 13 15 13 19 10 19 9 17 9 10 6 4 14 8 9 11 11 17 15 7 10 4 37.1 33.5 30.3 46.7 20.2 20.3 40.1 38 38.700000000000003 18.399999999999999 35.299999999999997 26.3 5.93 8.81 36.1 25.5 33 17.5 40.5 35.299999999999997 13.2 14.1 24.3 7.12 40.1 9.33 18 20.7 28.3 19 39.700000000000003 46.6 32.1 33.9 11.3 39.299999999999997 33.200000000000003 18 27.4 18 39.1 20.8 29.6 36.1 29.1 46.3 24.5 46.5 19.5 40.799999999999997 20.8 20 12.1 9.32 32.5 20.100000000000001 19.399999999999999 27 24.9 42.5 36.299999999999997 17.399999999999999 23.4 7.52
Residuals vs Predicted Y for Homoscedasticity
38.200751471483656 33.143581794195242 30.614996955551042 45.78650598741627 20.500657600974218 20.500657600974218 40.729336310127863 38.200751471483656 38.200751471483656 17.972072762330011 35.672166632839449 25.557827278262629 5.3291485691089839 10.386318246397394 35.672166632839449 25.557827278262629 33.143581794195242 17.972072762330011 40.729336310127863 35.672166632839449 12.914903085041601 12.914903085041601 23.029242439618422 7.8577334077531891 40.729336310127863 7.8577334077531891 20.500657600974218 23.029242439618422 28.086412116906835 17.972072762330011 40.729336310127863 45.78650598741627 33.143581794195242 33.143581794195242 10.386318246397394 38.200751471483656 33.143581794195242 17.972072762330011 28.086412116906835 17.972072762330011 38.200751471483656 23.029242439618422 30.614996955551042 35.672166632839449 30.614996955551042 45.78650598741627 23.029242439618422 45.78650598741627 20.500657600974218 40.729336310127863 20.500657600974218 23.029242439618422 12.914903085041601 7.8577334077531891 33.143581794195242 17.972072762330011 20.500657600974218 25.557827278262629 25.557827278262629 40.729336310127863 35.672166632839449 15.443487923685804 23.029242439618422 7.8577334077531891 -1.1007514714836546 0.3564182058047578 -0.31499695555104168 0.91349401258373319 -0.30065760097421901 -0.20065760097421759 -0.62933631012786151 -0.20075147148365602 0.49924852851634682 0.42792723766998719 -0.37216663283945195 0.74217272173737214 0.60085143089101578 -1.5763182463973937 0.42783336716055231 -5.7827278262628568E-2 -0.1435817941952422 -0.47207276233001139 -0.22933631012786293 -0.37216663283945195 0.28509691495839817 1.1850969149583985 1.2707575603815791 -0.73773340775318896 -0.62933631012786151 1.472266592246811 -2.5006576009742183 -2.3292424396184224 0.21358788309316523 1.0279272376699886 -1.0293363101278601 0.81349401258373177 -1.0435817941952408 0.75641820580475638 0.91368175360260651 1.0992485285163411 5.6418205804760646E-2 2.7927237669988614E-2 -0.6864121169068369 2.7927237669988614E-2 0.8992485285163454 -2.2292424396184209 -1.014996955551041 0.42783336716055231 -1.514996955551041 0.51349401258372751 1.4707575603815783 0.71349401258373035 -1.0006576009742183 7.0663689872134228E-2 0.29934239902578241 -3.0292424396184217 -0.81490308504160147 1.4622665922468112 -0.6435817941952422 2.12792723766999 -1.1006576009742197 1.4421727217373714 -0.65782727826262999 1.7706636898721371 0.62783336716054805 1.9565120763141941 0.37075756038157692 -0.3377334077531895
Residuals vs x for Independency
16 14 13 19 9 9 17 16 16 8 15 11 3 5 15 11 14 8 17 15 6 6 10 4 17 4 9 10 12 8 17 19 14 14 5 16 14 8 12 8 16 10 13 15 13 19 10 19 9 17 9 10 6 4 14 8 9 11 11 17 15 7 10 4 -1.1007514714836546 0.3564182058047578 -0.31499695555104168 0.91349401258373319 -0.30065760097421901 -0.20065760097421759 -0.62933631012786151 -0.20075147148365602 0.49924852851634682 0.42792723766998719 -0.37216663283945195 0.74217272173737214 0.60085143089101578 -1.5763182463973937 0.42783336716055231 -5.7827278262628568E-2 -0.1435817941952422 -0.47207276233001139 -0.22933631012786293 -0.37216663283945195 0.28509691495839817 1.1850969149583985 1.2707575603815791 -0.73773340775318896 -0.62933631012786151 1.472266592246811 -2.5006576009742183 -2.3292424396184224 0.21358788309316523 1.0279272376699886 -1.0293363101278601 0.81349401258373177 -1.0435817941952408 0.75641820580475638 0.91368175360260651 1.0992485285163411 5.6418205804760646E-2 2.7927237669988614E-2 -0.6864121169068369 2.7927237669988614E-2 0.8992485285163454 -2.2292424396184209 -1.014996955551041 0.42783336716055231 -1.514996955551041 0.51349401258372751 1.4707575603815783 0.71349401258373035 -1.0006576009742183 7.0663689872134228E-2 0.29934239902578241 -3.0292424396184217 -0.81490308504160147 1.4622665922468112 -0.6435817941952422 2.12792723766999 -1.1006576009742197 1.4421727217373714 -0.65782727826262999 1.7706636898721371 0.62783336716054805 1.9565120763141941 0.37075756038157692 -0.3377334077531895
Distribution of Residuals
-3.03 -2.38 -1.74 -1.10 -0.45 0.19 0.84 1.48 More 1 1 2 4 12 14 16 11 3
Normal Probability Plot of Residuals
-2.4175590162365048 -1.9874278859298957 -1.7616704103630663 -1.6010086648860757 -1.4734675779471014 -1.3662038163720986 -1.2726986411905357 -1.1891643501993372 -1.1131942771609289 -1.043158263318454 -0.97789754394054018 -0.91655666753311338 -0.85848447414183249 -0.8031725655979175 -0.75021537546794015 -0.69928330238321956 -0.65010407064799569 -0.60244945316442367 -0.55612559361869141 -0.51096580673824743 -0.4668251228525897 -0.42357608420119958 -0.38110545476355656 -0.33931160653881726 -0.29810241293048689 -0.25739352610093835 -0.21710694721012977 -0.17716982099173983 -0.13751340214433597 -9.807215248866108E-2 -5.8782936068943067E-2 -1.9584285230126924E-2 1.9584285230126924E-2 5.8782936068943067E-2 9.807215248866108E-2 0.13751340214433597 0.17716982099173983 0.21710694721012977 0.25739352610093835 0.29810241293048689 0.33931160653881726 0.38110545476355656 0.42357608420119958 0.4668251228525897 0.51096580673824743 0.55612559361869141 0.60244945316442367 0.65010407064799569 0.69928330238321956 0.75021537546794015 0.8031725655979175 0.85848447414183249 0.91655666753311338 0.97789754394054018 1.043158263318454 1.1131942771609289 1.1891643501993372 1.2726986411905357 1.3662038163720986 1.4734675779471014 1.6010086648860757 1.7616704103630663 1.9874278859298957 2.4175590162365048 -2.7971021827827709 -2.3090244420840711 -2.1507453569505772 -2.0584086675459767 -1. 4555200832039918 -1.3988980333363044 -1.0163974673404232 -1.016310790419684 -0.9636088799890089 -0.95045507161152998 -0.93721458631330834 -0.92397410101508337 -0.75245453058336631 -0.68119860535103327 -0.63381022442380619 -0.60741593074809908 -0.59426212237061349 -0.58110831399313456 -0.58110831399313456 -0.43589636031638029 -0.34364634783252573 -0.34364634783252573 -0.31185184773263702 -0.29085776048111467 -0.27761727518288976 -0.21176155637473909 -0.18536726269903192 -0.18528058577828924 -0.13257867534761755 -5.3395794320502586E-2 2.5787086706615663E-2 2.5787086706615663E-2 5.2094703461583444E-2 6.5248511839055848E-2 0.19721998021758846 0.26324905286722444 0.2764028612447067 0.32910477167537838 0.34234525697360002 0.3950471674042717 0.3950471674042717 0.39513384432501109 0.46098956313316503 0.47414337151064401 0.55480631952492121 0.57972054621346614 0.65881675031984499 0.6852977209162916 0.69845152929377385 0.75115343972444548 0.8303363207515605 0.84349012912904597 0.84366348297052807 0.9491539807526076 1.0150096995607549 1.0942792575086175 1.1733754616149947 1.3316545467484853 1.3502085615501491 1.3580488404241924 1.3594422304906086 1.6349722317172446 1.8065784790697061 1.9648575642032002 -2.4175590162365048 -1.9874278859298957 -1.7616704103630663 -1.6010086648860757 -1.4734675779471014 -1.3662038163720986 -1.2726986411905357 -1.1891643501993372 -1.1131942771609289 -1.043158263318454 -0.97789754394054018 -0.91655666753311338 -0.85848447414183249 -0.8031725655979175 -0.75021537546794015 -0.69928330238321956 -0.65010407064799569 -0.60244945316442367 -0.55612559361869141 -0.51096580673824743 -0.4668251228525897 -0.42357608420119958 -0.38110545476355656 -0.33931160653881726 -0.29810241293048689 -0.25739352610093835 -0.21710694721012977 -0.17716982099173983 -0.13751340214433597 -9.807215248866108E-2 -5.8782936068943067E-2 -1.9584285230126924E-2 1.9584285230126924E-2 5.8782936068943067E-2 9.807215248866108E-2 0.13751340214433597 0.17716982099173983 0.21710694721012977 0.25739352610093835 0.29810241293048689 0.33931160653881726 0.38110545476355656 0.42357608420119958 0.4668251228525 897 0.51096580673824743 0.55612559361869141 0.60244945316442367 0.65010407064799569 0.69928330238321956 0.75021537546794015 0.8031725655979175 0.85848447414183249 0.91655666753311338 0.97789754394054018 1.043158263318454 1.1131942771609289 1.1891643501993372 1.2726986411905357 1.3662038163720986 1.4734675779471014 1.6010086648860757 1.7616704103630663 1.9874278859298957 2.4175590162365048 -2.4175590162365048 -1.9874278859298957 -1.7616704103630663 -1.6010086648860757 -1.4734675779471014 -1.3662038163720986 -1.2726986411905357 -1.1891643501993372 -1.1131942771609289 -1.043158263318454 -0.97789754394054018 -0.91655666753311338 -0.85848447414183249 -0.8031725655979175 -0.75021537546794015 -0.69928330238321956 -0.65010407064799569 -0.60244945316442367 -0.55612559361869141 -0.51096580673824743 -0.4668251228525897 -0.42357608420119958 -0.38110545476355656 -0.33931160653881726 -0.29810241293048689 -0.25739352610093835 -0.21710694721012977 -0.17716982099173983 -0.13751340214433597 -9.807215248866108E-2 -5.8782936068943067E-2 -1.9584285230126924E-2 1.9584285230126924E-2 5.8782936068943067E-2 9.807215248866108E-2 0.13751340214433597 0.17716982099173983 0.21710694721012977 0.25739352610093835 0.29810241293048689 0.33931160653881726 0.38110545476355656 0.42357608420119958 0.4668251228525897 0.51096580673824743 0.55612559361869141 0.60244945316442367 0.65010407064799569 0.69928330238321956 0.75021537546794015 0.8031725655979175 0.85848447414183249 0.91655666753311338 0.97789754394054018 1.043158263318454 1.1131942771609289 1.1891643501993372 1.2726986411905357 1.3662038163720986 1.4734675779471014 1.6010086648860757 1.7616704103630663 1.9874278859298957 2.4175590162365048
