Skip to main content

Suppose we observe a training set {Dox-(1,ail,rar . . , rip)) for i-l, m ,n subjects. We want to fit a linear regression model /(x) otXI ,, to the training data to minimize the residual sum ofsquares RSS(β) Σǐ 1 (Vi r β)2 where β = (A 屆,-. W pm (a)(10%) Please derive the solution ßt. arg ming RSS(β) in terms of Y-|h li) Ar (b)(10%) in ridge regression, we find ßridge rgminß RSS(β) subject to Σ./ Please write out the equivalent Lagrangian form of the optimization problem. st. (c) (10%) Please derive the form of ßridge in terms of Y # (yī and the Lagrange multiplier λ YnF, X x(zh t


ANSWER

d RSS() and so

Comments

Post a Comment

Popular posts from this blog

Osmosis Data Sheet

Data Sheet: Activity - Osmosis Name Course Date Activity Data Code       Procedure I -Test Solution 1: Water Complete the tablesand questions below using your data and information found under the Background tab Data Table I Note: Difference in Final Volumes = Final Volume of Test Sol - Final Volume of Water Trial Starting Volume of Test Solution (L) Starting Volume of Water (L) Final Volume of Test Solution (L) Final Volume of Water (L) Difference in Final Volumes (L) 1 1.28 1.75 1.51 1.52 -0.01 2 1.28 2.00 1.64 1.64 0 Observations and Questions [1] Given that the final heights (and volumes) are the same for the water and test solution, what can you...
2 comments
Read more
Question: prove by induction 2^2 + 4^2 + 6^2 + ... + (2n)^2 = (2n)(2n+1)(2n+2)/6 ANSWER we will use induction on n base case : n=1 we have, 2^2 = 2*3*4/6 = 4 which is true inductive hypothesis let it be true for n = k i.e.,  2^2 + 4^2 + ... + (2k)^2 =   [(2k)(2k+1)(2k+2)]/6 inductive case let n = k+1 then we have 2^2 + 4^2 + .... + (2k)^2 + (2(k+1))^2 =   [(2k)(2k+1)(2k+2)]/6 + (2k+2)^2 =(2k+2)*[(2k)(2k+1)/6 + (2k+2)] =(2k+2)*[ (4k^2+2k)/6 + (12k + 12)/6 ] =(2k+2)*[ (4k^2+14k+12)/6 ] = =(2k+2)*[(2k)(2k+1)/6 + (2k+2)] =(2k+2)*[ (4k^2+2k)/6 + (12k + 12)/6 ] =(2k+2)*[ (4k^2+14k+12)/6 ] = (2k+2)*[ (4k^2 + 8k + 6k + 12)/6 ] = (2k+2)*[ (4k(k + 2) +6(k+2))/6 ] = (2k+2)*[ (4k+6)(k+2)/6 ] =  (2k+2)*[ 2 (2k+3)(k+2)/6  ] =   (2k+2)*[  (2k+3)*2*(k+2)/6  ] =   (2k+2)*[  (2k+3)(2k+4)/6  ] = [(2*(k+1))(2*(k+1)+1)(2*(k+1)+2)]/6 replacing k+1 by m, we get replacing k+1 by m, we get [(2*m)(2*m+1)(2*m+2)]/6 this completes our proof b...
12 comments
Read more

IT management

FIGURE P1.1 The File Structure for Problems 1-4 1.       How many records does the file contain? How many fields are there per record? 2.       What problem would you encounter if you wanted to produce a listing by city? How would you solve this problem by altering the file structure? 3.       If you wanted to produce a listing of the file contents by last name, area code, city, state, or zip code, how would you alter the file structure? 4.       What data redundancies do you detect? How could those redundancies lead to anomalies? Figure P2.4 The DealCo relational diagram 4. Identify each relationship type and write all of the business rules. 5.       Create the basic Crow’s Foot ERD for DealCo. FIGURE P3.17 The Ch03_TransCo Database Tables     17. For each table, identify the primary key and the for...
Post a Comment
Read more