## compare the quality of the different estimations, Basic Statistics

Assignment Help:

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)

(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?

#### ..#title, formula for z test.

formula for z test.

solution manual

#### Job costing order, note: Raw material costs 15 500 Direct Labor Costs: 14 7...

note: Raw material costs 15 500 Direct Labor Costs: 14 750 Overhead costs 11 800 plant Finished Goods 37 500 Raw materials are charged into an order that is still in the process

#### Calculate the expected profit and probability , An individual has \$ 100 ini...

An individual has \$ 100 initially. He repeatedly plays a game of chance in which he earns \$ 100 with probability 0.8 or loses \$ 100 with probability 0.2. The stops playing at the f

#### Report on the residual plots, Report on the residual plots – are the assump...

Report on the residual plots – are the assumptions of the regression met

#### Rockford Practice Set 14th Edition, I need help with the adjusting entries....

I need help with the adjusting entries.

#### Accounts, types of netwoths

types of netwoths

#### Detemine lambda , A.  A computer rejuvenation facility receives systems fro...

A.  A computer rejuvenation facility receives systems from the fleet at 24 systems/day (assume this is a Poisson process).  It takes the triage function 30 minutes (assumed exponen

#### Homework, 9. From 11 positive integer scores on a 10-point quiz, the mean i...

9. From 11 positive integer scores on a 10-point quiz, the mean is 8, the median is 8, and the mode is 7. Find the maximum number of perfect scores possible on this test.

#### Standard deviation, define standard deviation. their purpose,uses,advantage...

define standard deviation. their purpose,uses,advantages nd disadvantages,examples ,formula for grouped and ungrouped.  