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- Give 1 specific example on how to use linear regression applied in your field of specialization. (Any field of specialization)Explain with proof Least Squares Regression Unbiased Estimators y^Determine whether each of these functions is a bijection from R to R. f(x) = x^2 + 1 f(x) =(x^2 +1)/(x^2 + 2) f(x) =IxI f(x) =x/2
- Linear regression was performed on a dataset and it was found that the best least square fit was obtained by the line y = 2x + 3. The dataset on which regression was performed was corrupted in storage and it is known that the points are (x, y): (-2,a), (0,1), (2, B). Can we recover unique values of a, B so that the line y = 2x + 3 continues to be the best least square fit? Give a mathematical justification for your answer.Hey could I get some help with my MATLAB code for q4? The format should be correct, so i'm assuming I solved it wrong, but I'm not 100% sure. q3 is correct, but q4 isn't and I'm not sure why syms t x y z; rbar3 = [3*t,-3*t+1,t+1]; f_3 = x - (3 * y.^2); q3=int(simplify(subs(f_3,[x,y,z],rbar3)*norm(diff(rbar3,t))),t,0,1) rbar4 = [cos(t),sin(t),1]; f_4 = (x.^2) + (y.^4) q4=int(simplify(subs(f_4,[x,y,z],rbar4)*norm(diff(rbar4,t))),t,0,1)You have obtained measurements of height (in inches) of 29 female and 81 male students (Studenth) at your university. An estimated regression of this height on a constant and the following binary variables is indicated below: (BFemale) which takes a value of one for females and is zero otherwise, (BMale), which takes a value of one for males and is zero otherwise, Estimated(Studenth) = 71.0 - 4.84(BFemme) , R = 0.40, SER = 2.0 Standard errors are as here: SE(intercept) = (0.3) SE(BFemme) = (0.57) (Values in parentheses are the heterskedasticity-robust standard errors of coefficients, respectively) (a) What are the interpretation of the intercept and slope, respectively? (b) Test the hypothesis that females, on average, are shorter than males, at the 5% level (use any of the explained three approaches that seems fit, and consider the t-statistic for the difference in means = -8.49). (C) Is it likely that the error term is homoskedastic in here? Briefly explain. (d) Suppose that an you…
- Give Three Functions of Wronskian ?You have obtained measurements of height in inches of 29 female and 81 male students (Studenth) at your university. A regression of the height on a constant and a binary variable (BFemme), which takes a value of one for females and is zero otherwise, yields the following result: = 71.0 – 4.84×BFemme , R2 = 0.40, SER = 2.0 (0.3) (0.57) Values in parenthesis are standard errors. (a) What is the interpretation of the intercept? What is the interpretation of the coefficient of the dummy variable? How tall are females, on average? (b) Test the hypothesis that females, on average, are shorter than males, at the 1% significance level.