Homework Answers
(a)
rm(list=ls())
x=rnorm(100,-1,2.5)
sig=rnorm(100,0,3)
y=0
for(i in 1:100){
y[i]=2.5+2*x[i]+sig
}
y
(b)
hist(y)
qqplot(y,x)
qnorm(.89,-1,2.5)
plot(x,y,col=2)
lines(x,y,ltyp=2,col=3)
Conclusion; Here we see that this the best fit.
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How do I set the problems below in R? Use the rnorm function in R to...
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Sketch regions
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an iterated integral of a function
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How do I set the problems below in R? Use the rnorm function in R to generate 100 samples of X ~N(-1.0,2.5) (for help use ?rnorm ) and for each draw, simulate Yǐ from the simple linear regression model = 2.5+2.0x,+티, where e, N N(0,3 ). (iii) What is the marginal sample mean for Y? What is the true marginal mean?
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I need to plot a histogram for estimates of Beta_0 and Beta_1
(over the 100 simulations). I know I can use the coefficients
function with the model to display these estimates for each
simulation, but how can I access them individually, or save them to
a column vector such that I can plot the histogram as needed?
Suppose we want to simulate the following linear model: Bo + BiX; + Ei where ti~ N(0,22). Assume Xi~ N(0,12), Bo = 0.5...
Use the transformation
and
to evaluate the integral
where
is the region bounded on the
by the ellipse
Let S be the image of R under
T on the .
Sketch regions
R and S. Set up the integral as
an iterated integral of a function
over region S. Use technology to evaluate the
integral. Give the exact answer.
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