that is closest, in the sense of least squares, to passing through the through the following data points:(t₁, b₁) = (−2, –6),(t2, b₂) = (0,7),(t3, b3) = (2,-2),(t4, b4) =(4,-1).What are the y-intercept C and the slope D of this line?C =Use a least squares approximation to find the best linear fit (i.e., the best line),L(t) = = C + Dt,D =

Answered: Use a least squares approximation to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(3) Find, using the Least Squares Method, a line of the best fit y = ax +b for the set of points (1,3), (2, 4), (3, 4) аnd (4,5).
ly 1) Find the least squares line 2) Find the coefficient of correlation 3/08
The scatter plot below shows data for the average cost of a high-end computer (y, in dollars) in the year x years since 2000. The least squares regression line is given by yˆ=−1677+314x. A coordinate plane has a horizontal x-axis labeled Year from 4 to 12 in increments of 2 and a vertical y-axis labeled Cost in dollars from 0 to 2000 in increments of 500. The following points are plotted: left-parenthesis 6 comma 250 right-parenthesis, left-parenthesis 7 comma 550 right-parenthesis, left-parenthesis 9 comma 1000 right-parenthesis, left-parenthesis 10 comma 1300 right-parenthesis, and left-parenthesis 11 comma 2000 right-parenthesis. A line rises from left to right, passing through left-parenthesis 7 comma 550 right-parenthesis and left-parenthesis 10 comma 1500 right-parenthesis. All coordinate are approximate. Interpret the slope of the least squares regression line. Select the correct answer below: On average, the average cost of a high-end computer is…
Given the bivariate data: x 1 2 3 5 6 y 8 5 4 2 1 (b) Find n, Σx, Σy, Σx2, (Σx)2, and Σxy. n = Σx = Σy = Σx2 = (Σx)2 = Σxy = (c) Find a, the slope of the least-squares line, and b, the y-intercept of the least-squares line. (Round your answers to two decimal places.) a = b = (d) Draw the least-squares line on the scatter diagram from part (a). My question is F asked
4. Determine the equation of the least-squares approximating line that is the best fit for the data points (2, 6), (0, 2), and (1, 1).
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
When the predicted overnight temperature is between 15°F and 32°F, roads in northern cities are salted to keep water from freezing on the roadways. Suppose that a small city was trying to determine the average amount of salt y (in tons) needed per night at temperature x. They found the following least squares prediction equation: y = 20,000 - 2,500x Interpet the slope. a) 2,500 tons is the decrease in the amount of salt needed for a 1 degree increase in temperature. b) 2,500 tons is the increase in the amount of salt needed for a 1 degree increase in temperature. c) 20,000 is the increase in the amount of salt needed for a 1 degree increase in temperature. d) 2,500 tons is the expected amount of salt needed when the temperatures is 0° C.
Consider the data points (2, 0), (3, 1), and (4, 5). Compute the least squares error for the given line. y = -4 + 2x Plot the points and the line. (Be sure to plot all points, even if they lie on the line.) No Solution 7 6 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 Help Graph Layers Clear All Delete After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill WebAssign. Graphing Tool
Find the best-fitting least-squares linear and quadratic approximations to the data set{(1,2),(3,4),(5,7),(7,9),(9,12)}.
Each of the following pairs represents the number of licensed drivers (X) and the number of cars (Y) for seven houses in my neighborhood: Drivers X Cars Y 5 4 5 3 2 2 2 2 3 2 1 1 2 2 Construct a scatterplot to verify a lack of pronounced curvilinearity. Determine the least squares equation for these data. (Remember, you will first have to calculate r, SSy, and SSx) Determine the standard error of estimate, sy|x, given that n = 7. Predict the number of cars for each of two new families with two and five drivers.
Complete Table 3 and find the values of A and B for the straight line that provides the best least-squares fit to the data Table 3 y xy 1 2 3 7 4 9 5 12 Ex = Ey = Σxy Ex² =
The model, y = Bo + B₁×₁ + ß₂×2 + ε, was fitted to a sample of 33 families in order to explain household milk consumption in quarts per week, y, from the weekly income in hundreds of dollars, x₁, and the family size, x₂. The total sum of squares and regression sum of squares were found to be, SST = 162.1 and SSE(R) = 90.6. The least squares estimates of the regression parameters are bo = -0.022, b₁ = 0.051, and b₂ = 1.19. A third independent variable-number of preschool children in the household-was added to the regression model. The sum of squared errors when this augmented model was estimated by least squares was found to be 83.1. Test the null hypothesis that, all other things being equal, the number of preschool children in the household does not affect milk consumption. Use α=0.01. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. ''1' M P2 P3 Find the critical value. The critical value is 7.60⁰. (Round to…

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