compare the quality of the different estimations, Basic Statistics

To illustrate the importance of model selection. We will use only the first four observations to estimate the function f such that ini t. h = f(h. d) for two different models.

We will then use the last three observations to compare the quality of the different estimations.

(a) We consider first a quadratic regression model: f(x) = ax2 + bx + c. We carry out the regression of h. d on the vector (ini t .h.init.h'")

f1=gH1: 4J

f2=g2 [1: 4J

LinReg1=lm(f2 ~ f1+I(f1A2))

summary (LinReg1)

What are the estimated values of a, b, c? What is the value of the coefficient of determination?

(b) We consider next the regression model: f(x) = ax2 + bx + c + dexp(x/20). We carry out the regression of h. d on the vector (ini t .h.init.h'' ,einit.h/20)

LinReg2=lm(f2 ~ f1+I(f1A2)+I(exp(f1/20)))

summary(LinReg2)

What are the estimated values of a, b, c, d? What is the value of the coefficient of determination? Is this sufficient to conclude that this model is better than the quadratic model ?

(c) To better answer the previous question, we compute and display the prediction on the last tree observations obtained for each of the previous models.

t=(2500:6000)/10

new=data. frame (f1=t)

pred1=predict(LinReg1, new, interval ="none")

pred2=predict(LinReg2, new, interval ="none")

par(bg='cornsilk')

plot(g1,g2,pch = 20,col="black",cex=2,ylim=c(0,1000))

points(t,pred1,pch = 20,col="blue",cex=0.2)

points(t,pred2,pch = 20,col="red",cex=0.2)

What is your conclusion?

(d) We are now using the package leaps of R to perform the model selection. library (leaps)

f1=g1 [1: 5]

f2=g2 [1: 5J

explain=matrix(c(f1,f1A2,exp(f1/20)),ncol=3)

leaps (x=explain, y=f2)

What do we use the instruction explain=matrix(c (£1, f1 A2,exp (£1/20)) ,ncol=3) for? Given the value of the Cp criterion, which one of the seven model do you select?

Posted Date: 3/20/2013 3:20:12 AM | Location : United States







Related Discussions:- compare the quality of the different estimations, Assignment Help, Ask Question on compare the quality of the different estimations, Get Answer, Expert's Help, compare the quality of the different estimations Discussions

Write discussion on compare the quality of the different estimations
Your posts are moderated
Related Questions
how would we find cumulative frequency for the median of discrete series

An assessment time frame for certain purchases and debt equipment that reviews on the stability piece only that part of their face value that shows major and interest acquired curr

Circular motion  is termed as when an object experiences the right amount of  net force which is  directed toward the center of the circle / curve. The net acceleration of an objec

The fluctuations in the stock market induce some investors to sell and move their money into more stable investments. To determine the degree to which recent fluctuation affected o

Questions 1.  What would be the appropriate statistical procedure to test the following hypothesis:  "Triglyceride values are a good predictor of weight in obese adults." 2.

i) For a 3 term averagin filter, write a difference eqatuon governing the filter and dervie the corresponding z transform Sketch a pole zero plot, would this filter be stable, why

A researcher is interested in comparing tastiness of different parts of cheese in grilled cheese sandwiches.  The researcher expects that Cheddar cheese grilled sandwiches are rate

Question: Sharp Discounts Wholesale Club has two service desks with one server at each desk.  There is one desk at each entrance of the store.  Customers arrive at each

The methods and records established to recognize, set up, evaluate, move, record, and report the state’s purchases and to maintain responsibility for its obligations and resources

The foundation sales whereby income are acknowledged when gained and considerable regardless of when collected; and costs are noted on a corresponding basis when suffered. All amaz