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
Type of Variable in Regression Analysis There are two types of variable in regression analysis. These are: a.      Dependent variable b.      Independent variable

If the sample size is less than 30, then we need to make the assumption that X (the volume of liquid in any cup) is normally distributed. This forces    (the mean volume in the sam

A monopolist firm''s demand curve is given by P:100-2q. (a) Find its marginal revenue function.

Examining the Population Variance Business decision making does not limit itself to setting up the hypothesis to test for the equality of more than two means or proportions sim

Mid year population 440000 Late fatal death          29 No. of live birth           5200 No. of infant death      423 No. of maternal death 89 No. of infant deaths i

What does the confidence level of a confidence interval tell you? Suppose that a population has mean, µ, and standard deviation, σ.  What does the central limit theorem tell us

Range Official Exports Target 2000-2001 Product ($ million) Plantation 500 Agriculture and Alli

difference between large sample test and small sample test

Consider the following new business venture. An agent is considering investment in one of three real estate parcels: • Option 1: multiunit rentals • Option 2: commercial building

Scenario : Mrs dick's year 1s and 2s carried out a level-one science investigation to explain the changes in a particular plant over a period of time.  As part of the investigation