Explain ridge regression, Applied Statistics

Using log(x1), log(x2) and log(x3) as the predictors, do pair wise scatterplots of all pairs of variables (including the response) and comment (use the pairs function). Do you think that multi collinearity might be a problem with these data?

Plot the ridge trace for a grid of 50 values for the shrinkage parameter  over the range [0; 1]. Based on this plot suggest a reasonable value for . Find the estimates of the coecients for a ridge re gression with your chosen value of  (using centred and scaled predictors).

(The following question is based on Exercise 8.5 of Myers (1990), Classical and Modern Regression with Applications (Second Edition)," Duxbury).

With centred and scaled predictor variables, the ridge regression estimator for the coecients of the predictors is where y is the vector of responses, X is the design matrix for the centred and scaled predictors, is

1709_basic linear models.png

the shirnkage parameter and I denotes the identity matrix. We write n for the number of observations and k for the number of predictors. Writing biR for the ith component of bR, we will prove in this question that where 2 is the variance of the responses, and vi, i = 1,.......k are the eigenvalues of XTX. The di erent parts of the question below lead you through the proof.

735_basic linear models1.png

(a) Write XTX = QDQT for the eigenvalue decomposition of XTX, where D = diag(v1,........vk) is the diagonal matrix of eigenvalues and Q is an orthogonal matrix (QTQ = I) where the columns are the eigenvectors of XTX. Show that XTX +I = Q(D+I)QT .

2344_basic linear models2.png

where V ar(bR) denotes the covariance matrix of bR. (Hint: recall the result from basic linear models that if Y is a k  1 random vector with V ar(Y ) = V and if A is a k  k matrix and Z = AY then V ar(Z) = AV AT ).

Posted Date: 2/28/2013 12:46:51 AM | Location : United States







Related Discussions:- Explain ridge regression, Assignment Help, Ask Question on Explain ridge regression, Get Answer, Expert's Help, Explain ridge regression Discussions

Write discussion on Explain ridge regression
Your posts are moderated
Related Questions
Characteristics of Index Number  On the analysis of various definitions of index number the following may be its characteristics: 1.      Expressed in Number : Index number

Test for Equality of Proportions For example, we may want to test whether the percentage of smokers (p 1 ) among the males equals the percentage of female smokers (p 2 ). W

Lorenz Curve   It is a graphic method of measuring dispersion. This curve was devised by Dr. Max o Lorenz a famous statistician.  He used this technique for wealth it i

Formation of Continuous Frequency Distribution:    Continuous frequency distribution is most popular in practice. With reference to the formation of this type of frequency distr

Admixture in human populations The inter-breeding amongst the two or more populations which were previously isolated from each other for the geographical or the cultural reason

Weighted Arithmetic Mean Another aspect to be considered is the importance we assign to each observation. The arithmetic mean as we calculated it so far gives equal


prepare a critical analysis of a quantitative study focusing on protection of human participants data collection data management and analysis problem statement and interpretation o

There exists an unclassified data set with hidden data structures in it. The task in this assignment is to perform comprehensive Cluster Analysis in order to reveal the structures

Muti linear regression model problem An investigator is studying the relationship between weight (in pounds) and height (in inches) using data from a sample of 126 high school