Find a least-squares solution of Ax = b by (a) constructing the normal equations for x and (b) solving for x. - 1 2 A = - 3 - 1 2 a. Construct the normal equations for x. X1 X2 (Simplify your answers.) b. Solve for x. X = (Simplify your answer.)

Prove the result that the R^2 associated with a restricted least squares estimator is never larger than that associated with the unrestricted least squares estimator. Conclude that imposing restrictions never improves the fit of the regression.

Find the least-squares regression line y^=b0+b1x through the points (−2,2),(3,6),(4,15),(8,20),(12,26) and then use it to find point estimates y^ corresponding to x=4 and x=8.   For x=4, y^ = For x=8, y^ =

We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=b0+b1x1+b2x2.  HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. The following is a chart of baseball players' salaries and statistics from 2016. Player Name RBI's HR's Salary (in millions) Adrian Beltre 104 32 18.000 Justin Smoak 34 14 3.900 Jean Segura 64 20 2.600 Justin Upton 87 31 22.125 Brandon Crawford 84 12 6.000 Curtis Granderson 59 30 16.000 Aaron Hill 38 10 12.000 Miquel Cabrera 108 38 28.050 Adrian Gonzalez 90 18 21.857 Jacoby Ellsbury 56 9 21.143 Mark Teixeira 44 15 23.125 Albert Pujols 119 31 25.000 Matt Wieters 66 17 15.800 Logan…

A regression analysis between weight (y in pounds) and height (x in inches) resulted in following least squares line: y^= 120+5x. this implies that if the height is increased by 1 inch, the weight is expected ?

Suppose Derrick is an insect enthusiast who measured the body length and weight of three insects in his backyard. His data are shown in the table.   Length (mm) Weight (mg) Variable ?x ?y Insect 1 7 28 Insect 2 21 42 Insect 3 35 70 Derrick used the data to compute the least squares regression line.   ?̂ =1.5?+15.167y^=1.5x+15.167   Calculate the residual value for each of Derrick's data points and the sum of the residual values. Report your answers precise to three decimal places. Residual 1:     Residual 2:     Residual 3:     Sum of the residuals:

Find the coefficients for the least-squares regression line y^=b0+b1x through the points (−2,0),(2,6),(4,14),(9,20),(9,25) b0 =.          b1 =