(Solved): Find linear curve fit for given three data points \( \left(x_{i}, y_{i}\right):(0,1),(1,9) \), and ...

Find linear curve fit for given three data points \( \left(x_{i}, y_{i}\right):(0,1),(1,9) \), and \( (2,21) \), using least square method. In other words, determine \( a_{0} \) and \( a_{1} \) to best "represent" the above given data points, using the following relation, \[ f(x)=a_{1} x+a_{0} \] Fill in the blanks below, and the answers are all numeric values. (a) Define the sum of squared error using the given data above, \( \Pi \), i.e., \[ \Pi=\sum_{i=1}^{n}\left[y_{i}-f\left(x_{i}\right)\right]^{2} \] where \( i \) is the index for given data points, and \( n \) is the total number of given data. From \( 01 / c a_{0}=0 \), we have What are \( \mathrm{f}= \) \( f a_{0}+3 a_{1}=8 \) in above expression? From \( d I / \partial a_{l}=0 \), we have \[ 3 a_{0}+h a_{1}=t \] What are \( \mathrm{h}= \) and \( \mathrm{i}= \) in above expression? (c) Determine \( a_{0} \) and \( a_{1} \), from above equations, i.e., \( f(x)=a_{1} x+a_{0} \) to best "represent" above given data pords. What are a0 =