ce Problems x + canvas.pdx.edu/courses/106252/assignments/1102408?module_item_id=4856656 m Proctor ments THIS IS THE second question of exdin where you have to Snow compere work to get run points. If you use TI calculator functions, you may write your work along with functions and values you I used and answers on a paper or type on an empty Word document or Excel file. If you use Ti calculator app on your computer or phone, you may provide screen shots of those on a word document or Excel file. Clearly provide the function along with values for the work. If you use Excel, you may use the Excel calculator or Excel as a calculator on your computer to provide complete work and the final answer on it. Please provide all the answers to the following questions on the same Excel sheet. If you use formula, you may write all your steps with numbers on a paper and submit a photo of it. Otherwise, you may type all those steps on a Word document or an Excel file. Do NOT round in the middle steps…

Suppose the model for certain data is a parabola y = Bo+B1x+B2x² with observations (1, 2.2), (2, 6.9), (3, 16.1), (4, 28.7), (5, 46.1). Describe the design matrix, the observation vector, and the parameter vector. Using these write down the system of equations to be approximated Xẞ = y, the parts of the normal equations XTX and XTy and write down the normal equations. Solve and determine the residual vector €. You may use a calculator for the computations but show the steps as described above.

. This problem will yield a standard formula given in elementary statistics for a least squares line, making use of the normal equations. (a) Given pairs of data points (x1, Y1), (x2, Y2), ..., (xn, Yn) consider approximating lines of the form y = mx+b. The error e; for the ith pair is the distance between y; and the height (y value) of the line at xi. This is ei = Yi — (mxi + b). If we consider the equations b + x;m = Yi for i n in the variables b and m we can = 1,2, = think of this as a system of equations Ax = 6 where A 1 x1 x2 = : [m] Хп Y1 Уп numbers. Here, note that the variables are m and b and the xi, Yi are given The least squares approximation for this system (which gives the intercept b and slope m of the best least squares line for the data) is the solution to the normal equations AT Ax = ATb. Determine ATA (a 2×2 matrix) and AT (a 2×1 matrix). The entries will be sums of terms involving the x; and y₁. Write these, first using Σ notation and then simplify the notation using…