Suppose we want to find the relationship of Y with three variables X1, x2 and X3
ID: 3357758 • Letter: S
Question
Suppose we want to find the relationship of Y with three variables X1, x2 and X3. We selected 31 data. The results are shown as follows. Significance F Parameter Significance Adjusted r-square Combination 1: X1,X2 0.0582 All slopes significant 0.9009 Combination 2 X1, X3 Combination 3: X2, X3 Combination 4: x1, X2, X3 0.0089 2 slopes not significant 0.9158 0.0002 1 slopes not significant 0.8998 0.0052 All slopes significant 0.8997 Here is the summary output for combination 4: dard Error 52.125 3.215 22.012 6.021 t statistics 25.253 13.215 58.214 6.248 p-value 0.009 Intercept X1 x2 X3 Coefficient -568.258 15.696 -268.257 35.425 0.009 0.001 0.046 1.) Which is the best model ? Why? 2.) Are the parameters (intercept, X1, X2 and X3) significant ( .05) for combination 4? And explain why. 3.) Given that X1-569.266, x2-12.369, X3-56.780, can you predict the "Y" value using the best model? 3--56.780, can you predict the "Y" value using the best model? 4.) Can you recommend any method to improve your best model? e decrease 0.01, are the parameters (intercept, X1, X2 and X3) significant (:05) for combination 4? And explain why. 6.) If we increase 0.10, which combination will be the best model and explain why?Explanation / Answer
(1) Model 3 is best here. Because
(i) All slopes are significant
(ii) Adjusted R- square is around 0.9 which is high strength for 3 independent varaible.
(iii) F- value significance is best among all combinations.
(2) Yes, the parameters x1, x2 and x3 are significant in nature for combination 4.as the p - value is less than 0.05 for all the paremeters.
(3) X1 = 569.266, X2 = 12.369 ; X3 = -56.780
Y = -568.258 + 15.696 * X1 -268.257 X2 + 35.425 X3
Y = -568.258 + 15.696 * 569.266 - 268.257 * 12.369 - 35.425 * 56.780 = 3037.4388
(4) All slopes are significant here but if we increase sample size. there will be more refined results for coefficient for the given data.
(5) if alpha will be decreased to 0.01, parameters X1 and X2 will remain significant here because there p - value is less than 0.01 but parameter X3 wouldn't be significant here.
(6) If we increase alpha to 0.10 , the combination 4 will be most the best model still because changing alpha level wil not change any model sensitivity.