Need help with only question 2.3

1 Question 1 I. Figure 1 you see two lines (equations). a) Write down the equations for both of these lines. You can visually see where the two lines intersect. b) Set up a linear system and solve it to find the x and y coordinate of the intersection. 3 mualion 1 equation2 2 1 1 7 -3 - -1 1 Figure 1: Figure corresponding to question 1 10 14 12 10 0- 24. . . -0.5 00 05 10 15 2.0 2.5 Figure 2: data for question 2 2 Question 2 Given are the data points I = (-1,0.0.5.1.2, 2.5), y = (2,2, 2, 1.11.16) as shown in figure 2. There may be noise in the data. For the following questions, use all data except i = 0.5, y = 2) and (f = 2.5, y = 16) for filing the polynomials. We will call (r=0.5.y = 2) and (x = 2.5, y = 16) the validation data and keep it separate for another goal. The data that we use for curve fitting is called the training data in this homework. 2.1 Set up a linear system for the least-squares technique and proceed with solving via the normal oquations to fit a polynomial using just the first coefficient (a polynomial of the form (I) = C). What statistical meaning does this procedure have! 2.2 Set up a linear system for the least squares technique and proceed with solving via the normal equations to fit a polynomial using just the first three coefficients (a polynomial of the form px) = c++ox-). Use LU-factorization to solve the normal cquations. Write down the expression for the final polynomial that you obtained 2.3 Compute the 69-norm residual between predicted and observed training data (v), based on the polynomial that you obtained in the previous question (p(z) = 0+2+x2). First, write down the matrix-vector product that will provide the predicted data. Second, compute the residual that is of the form -..-...12 2.4 Besides the 2 num residual computed from the training data, we can also compute this quantity for the validation data (x = 0.5, y = 2) and (1 = 2.5, y = 16), again based on pl)=+011+022" from question 2.2. Set up a new linear system that describes the polynomial for the validation data, and formulate the matrix-vector product that uses the coefficients obtained in question 2.2. to preclict y-values for x = 0.5 and r - 2.5. Also compute the difference in 1, sense between the y-values of the validation data and the predicted values. 2.5 Figure 3 contains all overview of the data and some of the results for the previous questions. Annotate/describe what each curve represents. Include a copy of the annotated figure in your submission