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MidtermMakeUpSolns - 1 Start with k = 0 and i = 1 For the...

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Spring 2007 - STA 4702/5701 - Midterm Make Up Quiz Solutions Name: Directions : This Make Up Quiz is worth 30 points. The points will be added to your Midterm Exam Score. Please read the question carefully and answer it fully to the best of your ability. 1. (30) Define cross validation, describing in detail the steps necessary to perform it for a princi- ple components regression, including the statistic used and how the procedure benefits the researcher. solution Cross validation is a procedure whereby the prediction error of a model is estimated by sequentially leaving out blocks of data during model fitting and then calculating the prediction error on the left out data. The most commonly used is leave-one-out cross validation, where the block size equals 1.
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Unformatted text preview: 1. Start with k = 0 and i = 1. For the model with k ≤ p factors, at step i , the i th observation is removed. 2. The k components are extracted and the regression is fit on the remaining data. 3. The predicted value for the left out point is calculated. 4. Repeat steps 1-3 on all points. 5. The difference between the sum of squared predicted residuals for the model with k compo-nents and the sum of squared predicted residuals for the minimizing model is calculated. 6. Repeat steps i-v on all models with k ≤ p factors, and 1 ≤ i ≤ n , and choose the model with the smallest number of factors that is significantly different from the minimizing model. 1...
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