Question 7. To predict the response variable Y, three related predictor variable
ID: 3325753 • Letter: Q
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Question 7. To predict the response variable Y, three related predictor variables Xi- Xi were chosen. The regression outputs from 12 observations are summarized in the following table Model ModeMode ModeModelMode Model Variable Int:Coefficient 1.50-23.63 14.69-19.17 6.79 26.00 117.08 (SE (3.32) (5.66 (9.10)(8.36)(4.49) (7.00) (99.78) X1: Coeficient0.86 (0.13) 0.22 1.00 4.33 (SE (0.30 (0.13) (3.02) -0.66 (0.05) 2: Coefficient 2.86 0.85 (0.11) (2.58) 0.86 (SE X3: Coefficient 0.20 (0.33) 0.020 0.10 (0.18)(016(1.60) 0.776 0.43 2.19 (SE) R2 0.778 0.786 0.791 We would like to determine the "best" model with the 10% significance level (a) Recommend the best model by evaluating all possible equations (b) Choose the best model based on backward elimination procedure (c) Choose the best model based on stepwise method (d) Discuss why you have arrived the same (or different) best models based on (a). (b) and (c)Explanation / Answer
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(a) By evaluating all possible models the best model g as its R^2 value is 0.791 which is the highest abong all R^2 values. So this explains 79% of the variability in Y
(b) So using backward elimination procedure the first model that hits the eys is model g due to its higest R^2 value, however if we use the 3 independent variabls separately we see and R^2 value of 0.020 for variable X3 in Model c. So if we eliminate this we get model (d) whose R^2 is 0.778 which is not very far from 0.791
Doing it likewise by elimination each variable ena dseeing the resultant R^2 we see that model e is the best by the backward elimination procedure as difference between 0.786 and 0.791 is not statistically significant
(c) By doing the stepwise regression we start with no variables , testing the addition of each variable using a chosen model fit criterion, adding the variable (if any) whose inclusion gives the most statistically significant improvement of the fit, and repeating this process until none improves the model to a statistically significant extent.
Doing this we arrive at model e as the best model again
(d) We have arrived at a different conclusion in part (a) and (b) and (c) as (b) and (c) are based on seeing if addition or deletion of variables causes a statistically significant change in R^2 while in part(a) we are just manually comparing models and selecting the one with best R^2
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