3. Note the Exercises 3/4 data analysis is given in the Appendix: Plant data are analyzed in the Appendix which include photosynthesis rate (Y) and radiation (X) for three levels (Low, Medium and High) of water availability. Since we wish to fit SLR equations to each of the water levels, a dummy variable for the Medium level (called "WLMED") and a dummy variable for the High level (called "WLHIGH") are used in the output. The researcher first wants to know whether a single line can be fit to all three sets of data (versus three separate lines).Perform the relevant composite test below giving all hypotheses in terms of model parameters, etc.

Full Model model function E(Y)=

Indicate the letter(s) of all the Output(s) used for this exercise: A B C D

Null Hypothesis (H₀):

Alternative Hypothesis (H_A):

Calculated Test Statistic (show all work):

Degrees of Freedom:

P-value:

Detailed Findings/Conclusion:

a) Give the estimated regression line for the Low level of water availability, and, using this estimated line, predict the expected photosynthesis rate for low water availability and with radiation equal to 8.0.

b) Give the estimated regression line for the Medium level of water availability, and, using this estimated line, predict the expected photosynthesis rate for medium water availability and with radiation equal to 8.0.

c) Give the estimated regression line for the High level of water availability, and, using this estimated line, predict the expected photosynthesis rate for high water availability and with radiation equal to 8.0.

Exercises 3/4: Minitab Output A Regression Analysis: y versus x The regression equation is y = 247 + 18.8 x Predictor Coef SE Coef T P Constant 247 .32 76. 18 3.25 0 . 006 X 18 . 791 7. 134 2 . 63 0 . 021 S = 126.956 R-Sq = 34.8% R-Sq (adj) = 29.88 Analysis of Variance Source DF SS MS F P Regression 1 111845 111845 6. 94 0 . 021 Residual Error 13 209533 16118 Total 14 321378 Exercises 3/4: Minitab Output B Regression Analysis: y versus WLMED, WLHIGH The regression equation is y = 431 + 32 WLMED - 41 WLHIGH Predictor Coef SE Coef T P Constant 431 . 20 71 . 65 6. 02 0. 000 WLMED 32 . 4 101 .3 0. 32 0 . 755 WLHIGH -40 . 6 101.3 -0. 40 0 . 696 S = 160 .208 R-Sq = 4.28 R-Sq (adj) = 0.08 Analysis of Variance Source DF SS MS F P Regression 2 13379 6689 0. 26 0. 775 Residual Error 12 307999 25667 Total 14 321378Exercises 3/4: Minitab Output C Regression Analysis: y versus WLMED, WLHIGH, x, WLMEDX, WLHIGHX The regression equation is = 158 - 174 WLMED - 63 WLHIGH + 45.2 x + 3. 8 WLMEDX - 22.6 WLHIGHX Predictor Coef SE Coef T P Constant 158 . 31 88.37 1 . 79 0 . 107 WLMED -174.1 130.7 -1.33 0 . 216 WLHIGH -63. 1 134.1 -0. 47 0 . 649 X 45 . 18 13. 59 3.32 0. 009 WLMEDX 3.84 16 . 45 0. 23 0 . 821 WLHIGHX -22 . 63 15 . 42 -1. 47 0. 176 S = 73. 1099 R-Sq = 85 .08 R-Sq(adj) = 76.78 Analysis of Variance Source DF SS MS F P Regression 273272 54654 10.23 0. 002 Residual Error 9 48106 5345 Total 14 321378 Exercises 3/4: Minitab Output D Regression Analysis: y versus x, WLMEDX, WLHIGHX The regression equation is y = 83.6 + 55.9 x - 15.8 WLMEDx - 32.5 WLHIGHX Predictor Coef SE Coef T P Constant 83 . 59 54 . 19 1 .54 0. 151 X 55 . 858 9. 207 6. 07 0. 000 WLMEDX -15. 831 6. 526 -2. 43 0 . 034 WLHIGHX -32 . 515 6. 828 -4. 76 0. 001 S = 72 . 4176 R-Sq = 82.08 R-Sq (adj) = 77.28 Analysis of Variance Source DE SS MS F P Regression 3 263690 87897 16. 76 0. 000 Residual Error 11 57687 5244 Total 14 321378