Taylor series
f(xi+1)=f(xi)+f'(xi)h+(f''(xi)/2!)h2+(f'''(xi)/3!)h3+.....
given
f''(xi)=(-f(xi+3)+4f(xi+2)-5f(xi+1)+2f(xi))/h2
what is the order of error o(h2)
Taylor series
f(xi+1)=f(xi)+f'(xi)h+(f''(xi)/2!)h2+(f'''(xi)/3!)h3+.....
given
f''(xi)=(-f(xi+3)+4f(xi+2)-5f(xi+1)+2f(xi))/h2
1) Find the Taylor series (to second order terms) of the
function f(x,y) = x^2 −4x + y + 9 around the point x = 3, y =
−1.
2)Explain why the corresponding Taylor Series (to third order
terms) will be the same as the second-order series.
1. Find Taylor series centered at 1 for f(x) = e^ (x^2). Then
determine interval of convergence.
2. Find the coeffiecient on x^4 in the Maclaurin Series
representation of the function g(x) = 1/ (1-2x)^2
Given are five observations for two variables,
xi
yi
1
3
2
8
3
5
4
11
5
14
Round your answers to two decimal places.
a. Estimate the standard deviation of ŷ* when x = 4. 2
b. Develop a 95% confidence interval for the expected value of y
when x = 4.
c. Estimate the standard deviation of an individual value of y
when x = 4.
d. Develop a 95% prediction interval for y when x =...
1.-Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
4
7
4
10
15
(d) Develop the estimated regression equation by computing the
values of b0 and b1 using b1
=(Σ(xi − x)(yi − y))/Σ(xi −
x)2 and b0 = y −
b1x.
(e)Use the estimated regression equation to predict the value of
y when x = 2.
2.-Companies in the U.S. car rental market vary greatly in terms
of the size of...
Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
4
7
7
11
15
The estimated regression equation for these data is ŷ = 1 +
2.6x.
Compute SSE, SST, and SSR using the following equations (to 1
decimal).
SSE
SST
SSR
Compute the coefficient of determination r2
(to 3 decimals).
Does this least squares line provide a good fit?
Compute the sample correlation coefficient (to 4
decimals).