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6166 UNIT 4 Section 2 Exercises

Welcome  <  Begin  <  <  Unit 4 Section 2 Exercises  >  Section 3 
You can choose to work some or all of the problems listed below. We recommend that you at least work the problems listed in your major area of interest. Answers to these exercises can be found here (Answers).
General Questions. 


For students in agriculture and environmental fields. 
The data below relate number of plant species (Y) in islands along the California coast to the area of the islands (, square miles), maximun elevation (, feet), and latitude (, degrees North). Y X1 X2 X3 205 134 3950 28.2 163 98 4600 29.0 420 96 2470 34.0 340 84 1560 34.0 392 75 2125 33.3 235 56 1965 32.9 120 22 910 33.2 190 14 830 34.0 42 2.8 490 27.9 40 1.0 635 33.4 62 0.9 470 30.5 4 0.2 130 37.7 40 0.02 60 37.1 39 2.5 660 28.3 70 1.1 930 34.0
3) Using this table, calculate the Fstatistic to test the hypothesis (at a=0.05) that X2 adds to the explanation of Y given that X1 is already in the model (e.g compute the partial sums of squares for X2 given X1 then perform the test.) 4) Using this same table, calculate the Fstatistic to test the hypothesis (at a=0.05) that X13 adds to the explanation of Y given that X2 and X3 are already in the model (e.g compute the partial sums of squares for X1 given X2 and X3 then perform the test.) 5) Using the test in 3 and 4 above, which of the following models would be your final best model? i) X2 alone, ii) X2 + X1 iii) All three explanatory variables.


For students in engineering fields.  
For students in toxicology and health science fields. 
A hospital administrator wished to study the relationship between patient satisfaction (Y) and patient's age (X_{1}, in years), severity of illness (X_{2}, an index), and anxiety level (X_{3}, an index). She randomly selected 15 patients and collected the data presented below. Y X1 X2 X3 57 36 46 2.3 66 40 48 2.2 70 41 44 1.8 89 28 43 1.8 36 49 54 2.9 46 42 54 2.9 54 45 48 2.4 26 52 62 2.9 77 29 50 2.1 89 29 48 2.4 67 43 53 2.4 47 38 55 2.2 51 34 51 2.3 57 53 54 2.2 66 36 49 2.0
3) Using this table, calculate the Fstatistic to test the hypothesis (at a=0.05) that X1 adds to the explanation of Y given that X2 is already in the model (e.g compute the partial sums of squares for X1 given X2 then perform the test.) 4) Using this same table, calculate the Fstatistic to test the hypothesis (at a=0.05) that X3 adds to the explanation of Y given that X1 and X2 are already in the model (e.g compute the partial sums of squares for X3 given X1 and X2 then perform the test.) 5) Using the test in 3 and 4 above, which of the following models would be your final best model? i) X2 alone ii) X2:X1 iii) All three explanatory variables (X1:X2:X3).
