Find the line y = mx + b that best approximates the data points (0, 0), (1, 2), (2, 1) in the sense of least squares.

The least squares fit line for the points (3, 3.1), (2,2.3), and (1, 2.1) has form ŷ = mx + b. First, let f be the sum of the square errors between the predicted values ŷ and y-values for the three points. f(m, b) = Minimize this function to find the m and b of the least square line, then write down equation of least squares line. y

If we have a series of experimental data of 2 variables A and B, with both sets of data related by the expression: A = B + C, where C is a constant. If by plotting A against B we obtain a straight line with a theoretical slope m and ordinate at the origin C, and by applying the least squares method we could determine C. But, as the previous expression can be transformed into B = A - C, we could also plot B against A and obtain C from the ordinate at the origin with a changed sign. Should the same value of C be obtained by both methods?(A). Yes, because the step from "A = B + C" to "B = A - C" is an exact algebraic transformation(B). Only in the case where A and B are equal(C). Only in the case where the errors of A and B are high, since the least squares method compensates for them(D). The most normal thing is that the same value is not obtained

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Find the best-fitting least-squares linear and quadratic approximations to the data set{(1,2),(3,4),(5,7),(7,9),(9,12)}.

Find the least squares fit solution for paramters a & b of function: y = a/(x^2+b)  Express the result for a & b in terms of the data (xi, yi), i=1,...,n

In a study, nine tires of a particular brand were driven on a track under identical conditions. Each tire was driven a particular controlled distance (measured in thousands of miles) and the tread depth was measured after the drive. Tread depth is measured in "mils." Here, 1 mil is 0.001 inch. The equation of the least-squares regression line is: y-hat 360.64 - 11.39x Also, r = 0.9762. For every 1,000 miles driven, the decrease in tread depth (in mils) can be estimated as: 246.74 mils. 11.39 mils. 275.6 mils. O 360.64 mils.

Which of the following best describes the least-squares line fit to the data shown in the plot? (i) bo = 0, bị =-1 (ii) bo = -3, b₁ = 1 (iii) bo-5, b₁ = 2 (iv) bo = −3, bị =-1 (v) bo = 0, b₁ = -3 2 X

We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations. A Minitab printout provides the following information. Predictor Constant Elevation Coef 315.00 -29.166 SE Coef 28.31 3.511 I 11.24 -8.79 P 0.002 0.003 S = 11.8603 R-Sq = 96.44 Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (c) The printout gives the value of the…

Explain the concept and use of the method of Least Squares