Least squares Definition and 158 Threads

I have a problem that says to find the least squares solution to \newcommand{\colv}[2] {\left(\begin{array}{c} #1 \\ #2 \end{array}\right)} K x = \colv{2}{2} for K = \left( \begin{array}{cc} 1 & 2\\ 2 & 4 \end{array} \right). Then express the solution in the form x = w + z, where w is in the...

Can someone help with the folowing? Suppose L1 is the line through the origin in the direction of a1 and L2 is the line through b in the direction of a2. I am supposed to find the closest points x1a1 and b+x2a2 on the two lines. So I am trying to find the equations that would minize...

We all know the least squares method to find the best fit line for a collection of random data. But I wonder if it is the best method. Suppose we have two random variables y and x that appear to have a linear relation of the type y = ax+b. What we want is, given the next type x signal to...

Hi, I was working on a problem and I can't figure out what I'm supposed to do. It reads, find the vector in subspace S that is closest to v; write v as the sum of a vector in S and a vector in S^a; and find the distance from v to S. S spanned by {(1,3,4)} v = (2,-5,1) Ok, what I did was...

Question states Consider the vector space C[-1,1] with an inner product defined by <f,g> = the integral from 1 to -1 of f(x)g(x) dx a) Show that u1(x)= 1/(2^.5) u2(x)= ((6^.5)/2)x form an orthonormal set of vectors b) Use the result from a) to find the best least squates...

It seems to me that Linear Regression and Linear Least Squares are often used interchangeably, but I believe there to be subtle differences between the two. From what I can tell (for simplicity let's assume the uncertainity is in y only), Linear Regression refers to the general case of fitting...

Hi, I am having some difficulty with this problem: what would be Y^h^a^t if s_y_/_x = 439, n = 24 and 95% confidence interval estimate for the average Y given a particular value of X is 1125 and 1695. ----------------- I know Y^h^a^t = b_o + b_1x but I am not sure how I can use the...

Construct the normal equations for the linear polynomial least squares to fit the data x = [1 0 -1], y=[3;2;-1]. (a) Find the parameters of the linear regression u1, u2 using QR decomposition, and plot the data and the fit curve in a graph (paper and pencil). (b) Calculate the eigenvalues of the...