Question

a certain experiment produces he data (1, 1.8), (2,2.7), (3, 3.4), (4, 3.8), (5,3.9). Suppose we wish to find a least-squares fit of these points by a function of the form y = Bo + Bix. Give the design matrix, the observation vector, and the unknown parameter vector for this model and data.

Answer 1

The design matrix, observation vector, and unknown parameter vector for the given model and data are calculated using matrix representations.

Step-by-step explanation:

To find the design matrix, observation vector, and unknown parameter vector for the given data and the function y = Bo + Bix, we can represent the equation in matrix form:

Y = XB

Where:

Y is the observation vector, which contains the y-values of the data points

X is the design matrix, which contains the x-values and a column of ones to represent Bo (intercept) and B (slope)

B is the unknown parameter vector, which contains the intercept and slope

For the given data: (1, 1.8), (2,2.7), (3, 3.4), (4, 3.8), (5,3.9)

The observation vector (Y) would be: Y = [1.8, 2.7, 3.4, 3.8, 3.9]

The design matrix (X) would be: X = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5]]

Now, we can use matrix multiplication to solve for the unknown parameter vector (B).