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
16 people to line-up ( 12 boys 4 girls). in how many ways could they line-up with all 4 girls in last (anyorder)?

Momentum and Energy Statement 1: If there is a definite force there is a definite displacement, which means that work is done definitely by the force. And Statement 2: The wor

The next step is to determine the sources of data to be used. The researcher has to decide whether he has to collect primary data ror depend exclusively on secondary data. Sometime

Budgeted accounts Accounts that are theme to the misappropriation or sometimes to appropriation and/or allotment process. Refer to APPROPRIATION and portion.

a) Statistics are collecting, organizing, summarizing and presenting a set of data. b)  Inferential statistics is the learn of a sample that enables us to make estimates about t

Use the concepts of sampling error and z scores to explain the concept of distribution of sample means.

identify a research report published by reputable agencies and evaluate the following ;the problem that was addressed

Problems and solutions in marginal costing

This is not a statistics course, but you need to conduct some analyses to help solidify your knowledge and understanding about statistical data analysis.  Now you will use the ' pr

solved example with data of bi variate frequency distribution