Edex limited is a renowned agricultural chemical manufacturer in Australia. They conduct many research and development in the field of Agri and Horticulture. Company wanted to examine the effect of temperature on farming of their selected range of products.
Company has produced following results based on their data gathering.
15 C
35
24
36
39
32
25 C
30
31
34
23
27
35 C
23
28
28
30
31
You are required to answer following questions;
1.State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the perception among three groups.
2.State the decision rule at 5% significance level.
3.Calculate the test statistic.
4.Based on the calculated test statistics, decide whether there are any significant differences between the yield based on the given temperature levels.
Note: No excel ANOVA output allowed in question3. Students need to show all the steps in calculations.
Cumulative Standard Normal Distribution Table Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -0.00 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.10 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.20 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.30 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.40 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.50 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.60 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.70 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.80 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.90 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -1.00 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.10 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.20 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.30 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.40 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.50 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 4 0.0582 0.0571 0.0559 -1.60 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.70 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.80 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.90 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -2.00 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.10 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.20 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.30 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.40 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.50 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.60 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.70 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.80 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.90 0.0019 0.0018 0.0018 0.0017 0 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -3.00 0.0013 0.0013 0.0013 0.0012 2 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.10 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.20 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.30 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.40 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.50 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 -3.60 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.70 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.80 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 1 0.0001 0.0001 *Note: z-values less than -3.89 produce a probability of zero.Cumulative Standard Normal Distribution Table Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.00 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.10 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.20 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.30 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.40 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.50 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.60 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.70 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.80 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.90 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.00 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.10 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.20 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.30 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.40 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.50 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.60 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.70 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.80 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.90 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.00 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.10 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.20 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.30 0.9893 0.9896 0.9898 0.9901 0 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.40 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.50 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.60 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.70 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.80 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.90 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.00 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.10 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.20 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.30 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.40 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.50 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 3.60 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.70 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.80 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 *Note: z-values greater than 3.89 produce a probability of one.Sheet1 Critical values from the t distribution ta Values of a for one-tailed test and a/2 for two-tailed test dfit 0.100 0.050 0.025 0.010 0.005 0.001 3.078 6.314 12.706 31.821 63.657 318.309 1.886 2.920 4.303 6.965 9.925 22.327 On AWN - 1.638 2.353 3.182 4.541 5.841 10.215 1.533 2.132 2.776 3.747 4.604 7.173 1.476 2.015 2.571 3.365 4.032 5.893 1.440 1.943 2.447 3.143 3.707 5.208 1.415 1.895 2.365 2.998 3.499 4.785 1.397 1.860 2.306 2.896 3.355 4.501 1.383 1.833 2.262 2.821 3.250 4.297 1.372 1.812 2.228 2.764 3.169 4.144 11 1.363 1.796 2.201 2.718 3.106 4.025 12 1.356 1.782 2.179 2.681 3.055 3.930 13 1.350 1.771 2.160 2.650 3.012 3.852 14 1.345 1.761 2.145 2.624 2.977 3.787 15 1.341 1.753 2.131 2.602 2.947 3.733 16 1.337 1.746 2.120 2.583 2.921 3.686 17 1.333 1.740 2.110 2.567 2.898 3.646 18 1.330 1.734 2.101 2.552 2.878 3.610 19 1.328 1.729 2.093 2.539 2.861 3.579 20 1.325 1.725 2.086 2.528 2.845 3.552 21 1.323 1.721 2.080 2.518 2.831 3.527 22 1.321 1.717 2.074 2.508 2.819 3.505 23 1.319 1.714 2.069 2.500 2.807 3.485 24 1.318 1.711 2.064 2.492 2.797 3.467 25 1.316 1.708 2.060 2.485 2.787 3.450 26 1.315 1.706 2.056 2.479 2.779 3.435 27 1.314 1.703 2.052 2.473 2.771 3.421 28 1.313 1.701 2.048 2.467 2.763 3.408 29 1.311 1.699 2.045 2.462 2.756 3.396 30 1.310 1.697 2.042 2.457 2.750 3.385 40 1.303 1.684 2.021 2.423 2.704 3.307 50 1.299 1.676 2.009 2.403 2.678 3.261 60 1.296 1.671 2.000 2.390 2.660 3.232 70 1.294 1.667 1.994 2.381 2.648 3.211 80 1.292 1.664 1.990 2.374 2.639 3.195 90 1.291 1.662 1.987 2.368 2.632 3.183 100 1.290 1.660 1.984 2.364 2.626 3.174 150 1.287 1.655 1.976 2.351 2.609 3.145 200 1.286 1.653 1.972 2.345 2.601 3.131 10000 1.282 1.645 1.960 2.327 2.576 3.091 Page 1Area or probability Entries in the table give F. values, where a is the area or probability in the upper tail of the F distribution. For example, with 4 numerator degrees of freedom, 8 denominator degrees of freedom, and a .05 area in the upper tail, Fos = 3.84. Denominattor Area in Numerator Degrees of Freedom Degrees Upper 9 15 20 25 S Tall 60 100 100 of Freedom 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59,44 59.8 60.19 61.22 61.74 62.05 62.26 62.53 62.79 63.01 63.30 .05 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 245.95 248.02 249.26 250.10 251.14 252.20 253.04 254.19 .025 647.79 799.48 864.15 899.60 921.83 937.11 948.20 956.64 963.28 968.63 984.87 993.08 998.09 1001.40 1005.60 1009.79 1013.16 1017.76 F distribution .01 4052.18 4999.34 5 5403.53 5624.26 5763.96 5858.95 5928.33 5980.95 6022.40 6055.93 6156.97 6208.66 6239.86 6260.35 6286.43 6312.97 6333.92 6362.80 .10 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39 9.42 9.44 9.45 9.46 9.47 9.47 9.48 9.49 .05 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.43 19.45 19.46 19.46 19.47 19.48 19.49 19.45 .025 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.43 39.45 39.46 19.46 39.47 39.48 39.49 39.50 98.50 99.00 99.16 99.25 99.30 99.33 99.36 99.38 99.39 99.40 99.43 99.4 99.46 99.47 99.48 99.48 99.49 99.50 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23 5.20 5.18 5.17 5.17 5.16 5.15 5.14 5.13 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.70 8.66 8.63 8.62 8.59 8.57 8.55 8.53 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.25 14.17 14.12 14.08 14.04 13.99 13.96 13.91 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.34 27.23 26.87 26.69 26.58 26.50 26.41 26.32 26.24 26.14 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92 3.87 3.84 3.83 3.83 3.80 3.79 3.78 3.76 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.63 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.66 8.56 8.50 8.46 8.41 8.36 8.32 8.26 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.20 14.02 13.91 13.84 13.75 13.65 13.58 13.47 4.06 3.62 3.52 3.45 3.40 3.37 3.34 3.32 3.324 3.21 3.19 3.17 3.16 3.14 3.13 3.11 5.41 5.19 5.05 4.82 4.52 4.50 4.46 4.43 4.41 4.37 10 01 7.76 7.39 7.15 6.98 6.76 6,33 6.27 6.23 6.18 6.12 6.08 6.02 12.06 11.39 10.97 10.67 10.46 10.29 10.16 9.55 9.45 9.38 9.29 9.20 9.13 9.03Denominator Area in Degrees Upper Numerator Degrees of Freedom of Freedom Tail M 10 60 .10 100 3.78 1000 3.46 .05 3.29 5.99 3.18 5.14 3.11 3.05 4.76 3.01 4.53 2.98 2.96 2.94 2.87 2.84 025 8.81 4.39 7.26 4.28 6.60 4.21 6.23 4.15 2.81 5.99 4.10 2.80 2.78 2.76 5.82 4.06 3.94 5.70 5.60 3.87 2.75 3.83 2.72 13.75 10.92 9.78 5.52 5.46 3.81 5.27 3.77 3.74 9.15 3.71 8.47 8.26 8.10 5.17 3.67 7.98 7.87 5.11 7.56 5.07 5.01 4.96 7.40 4.92 4.86 3.59 3.26 3.07 2.96 7.30 7.23 7.14 7.06 5.59 4.74 2.88 2.83 4.35 2.78 6.99 2.75 6.89 2.72 2.70 2.63 2.59 8.07 4.12 3.97 3.87 2.57 6.54 2.56 2.54 5.89 2.51 2.50 12.25 9.55 5.52 5.29 3.79 3.73 3.68 3.64 3.51 3.44 3.40 3.38 2.47 3.34 8.45 5.12 4.99 4.90 3.30 7.46 7.19 4.82 4.76 4.57 3.27 3.23 6.72 4.47 4.40 6.62 4.36 3.46 6.31 6.16 4.25 4.15 2.92 6.06 4.31 5.99 4.21 5.91 5.82 5.75 5.66 5.32 2.81 4.07 3.84 2.62 2.56 2.54 2.46 2.42 2.40 7.57 6.06 2.38 5.42 2.36 5.05 3.39 3.35 3.22 3.15 2.34 3.11 2.30 11.26 3.08 2.32 7.59 3.04 7.01 4.30 4.10 4.00 3.89 3.01 2.93 3.84 3.36 5.81 3.94 2.97 3.01 5.52 2.81 5.36 2.61 5.26 3.78 3.74 3.68 2.69 5.20 5.12 5.03 4.96 4.87 5.12 3.86 3.48 2.42 2.34 2.30 5.08 4.48 3.14 2.27 2.25 EES 3.01 2.94 2.89 2.21 2.19 2.86 2.16 10.5 6.99 6.06 3.96 3.60 3355 2.79 2.76 2.71 5.26 4.96 3.45 3.34 2.52 4.48 2.38 2.35 4.32 2.32 3.07 2.24 2.20 3.02 2.98 2.16 10.04 3.78 2.77 3.72 2.73 2.70 2.11 2.09 2.66 2.06 3.42 2.62 3.31 2.54 5.06 4.94 3.20 3.09 2.66 4.41 4.25 3.92 2.30 2.27 2.25 3.01 2.95 2.90 2.17 2.12 2.85 2.08 2.05 3.76 3.66 2.72 3.59 2.65 3.53 2.60 2.57 2.01 1.98 3.23 3.12 2.46 2.41 1583 E 4.54 4.10 3.00 2.96 2.89 2.33 2.28 3.78 2.24 3.00 2.91 2.21 2.85 2.19 3.61 2.06 2.03 2.01 1.96 3.73 2.80 1.91 3.61 2.75 5.06 3.51 4.64 3.44 3.37 2.54 2.50 3.07 2.47 2.43 2.38 2.35 2.30 4.30 2.96 2.91 2.43 2.35 3.70 2.80 2.73 3.18 2.28 2.23 3.62 3.54 3.47 3.37 3.03 2.92 2.20 2.16 4.00 2.83 3.77 3.60 2.77 2.14 2.71 2.05 2.01 2.67 2.53 1.98 1.96 2.46 1.90 2.38 1.88 2.34 1.85 5.74 2.41 5.21 2.30 2.26 4.44 4.30 3.25 3.05 2.95 4.10 2.88 2.84 2.78 2.21 2.72 2.67 2.60 2.39 3.66 3.57 2.31 3.51 2.15 3.43 3.27 2.10 3.18 2358 6585 8958 3.11 2.01 1.96 3.89 2.70 2.12 2.60 1.93 2.46 2.39 1.99 2.34 1.89 1.86 2.31 1.83 1.80 5.04 3.29 3.15 2.95 2.84 2.27 2.78 2.22 2.73 2.67 2.19 2.14 E 2.49 3.66 3.51 2.36 3.41 2.61 3.35 2.56 2.50 3.18 2.09 3.02 1.97 1.92 1.89 1.87 9388 2.33 2.28 1.82 2.25 1.79 1.76 2.76 2.16 2.07 R-O 2.40 2.98F TABLE 4 F DISTRIBUTION (Continued) Denominator Area in Numerator Degrees of Freedom Degrees Upper of Freedom Tail 100 1000 -10 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03 1.94 1.89 1.86 1.84 1.81 1.78 1.76 1.72 .05 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.35 2.28 2.23 2.19 2.15 211 2.07 2.02 025 6.12 4.69 4.08 3.73 3.50 3.12 3.05 2.99 2.79 2.68 2.61 2.57 2.51 2.45 2.40 2.32 8.53 6.23 5.29 4.77 3.89 3.78 3.69 3.41 3.26 3.16 3.10 3.02 2.93 2.86 2.76 3.03 2.31 2.06 2.03 2.00 1.91 1.86 1.78 1.75 1.73 1.69 2.96 2.49 2.45 2.06 2.02 1.97 2.38 2.33 2.26 2.83 2.66 S 2.20 2.25 4.30 589 2.94Denominator Area In Degrees Upper Numerator Degrees of Freedom of Freedom Tall m 100 1000 2.92 2.53 2.32 2.18 2.09 2.02 1.97 4.24 3.39 1.93 1.89 1.87 2.99 2.76 2.60 2.49 177 1.72 2.40 2.34 1.59 1.56 1.52 025 5.69 2.28 4.29 2.24 3.69 2.09 3.35 2.01 3.13 2.97 2.85 2.75 2.61 1.87 1.82 7.77 2.68 1.78 1.72 241 15 S 4.18 3.85 3.63 3.46 2.30 2.12 2.05 3.22 3.13 2.85 2.00 1.91 2.70 2.45 2.36 2.29 2.18 2.91 2.31 2.17 2.08 2.01 2.98 2.74 1.76 2.59 2.47 1.55 3.67 3.10 2.94 2.07 3828 2.07 $895 8335 2.02 100 5685 9359 3956 2938 1000 B- 11Za/2 P q n = B2 Time Series Regression~ b, = Et(t - D)(yt - y)] En(t - 7) bo = Y - bite Tt = bot bite ANOVAL SSTR SSE MSTR = = MSE = K - 1 nT - k nj SSTR = SST = > > (xu -2)- 7=1 SSE = (n; -1)s/2 4 F = MSTR / MSE- Simple Linear Regression:~ D = bot bix bo =y - bix~ b1 E(xi - x(yi - y) SST = SSR + SSE E(x1 - x)2 SSE = E(vi - pi)2 SST = E(Vi - 7)+ SSR= E(Di - DY+ Coefficient of determination ~ R2= SSR/SST- Correlation coefficient~ E(x-D( V- 7) EXY- Ex Er r= or 1= N R2 = (rxy )2+ Fry = (sign of bj )Coefficient of DeterminationTesting for Significance ~ + 2 25 = MSE = SSE/{n 0 2) S = VMSE = SSE n-2 S D1 ( * - X) t= F = MSTR / MSE MSR = SSR/k-1+ MSE = SSE-k~ Confidence Interval for it b1 + ta/25b, Multiple Regression 2 2 y=B+Bx+Bx+...+ Bx+& y=b +bx+bx+...+bxe 1 1 22 P n - 1 Ra= =1 - (1 - R2) n- p - 1 R2 = SSR/SSTFORMULA SHEET~ K = 1 + 3.3 log10 ne Summary Measures(n - sample size; N - Population size)~ N p = n = 21=1(x1 -x)2 Or s2 -[()=1x7) -nx2]- Or s2 = 1 n 02 = =EN-1(X; - M)2 Or oz = [(IN1 x7) - nu2]- S~ Range CV = - cv = = Location of the pth percentile: ~ Lp= P (n+1) IQR = Q3- Q14 Expected value of a discrete random variable E ( x ) = 1 => x *f (x)
