Nerya Fozailov 2022-05-23
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asked 2022-04-25

Simple Linear Regression - Difference between predicting and estimating?
Here is what my notes say about estimation and prediction:
Estimating the conditional mean
"We need to estimate the conditional mean β0+β1x0 at a value x0, so we use Y0^=β0^+β1^x0 as a natural estimator." here we get
Y0^~N(β0+β1x0,σ2h00)  where  h00=1n+(x0x)2(n1)sx2
with a confidence interval for E(Y0)=β0+β1x0 is
(b0^+b1^x0csh00,b0^+b1^x0+csh00)
where c=tn2,1α2 Where these results are found by looking at the shape of the distribution and at E(Y0^) and var(Y0^)
Predicting observations
"We want to predict the observation Y0=β0+β1x0+ϵ0 at a value x0"
E(Y0^Y0)=0  and  var(Y0^Y0)=σ2(1+h00)
Hence a prediction interval is of the form
(b0^+b1^x0csh00+1,b0^+b1^x0+csh00+1)

asked 2022-04-17
asked 2022-04-02

Using the integral test, find the positive values of p for which the series ∑∞ k=2 1/ (k(ln(k)))^p converges. Show your work and explain your reasoning.

asked 2022-05-03
asked 2022-04-26

 

asked 2022-04-22

Two small charged objects repel each other with a force F when separated by a distance d. If the charge on each object is reduced to 1/4 of its original value and the distance between them is increased 2 times, what will the force between them become?


 

asked 2022-04-09

by using substitution method, integratee4x3e4x-2dx

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