Find the least-squares error E for the least-squares line fit t the four points in Fig. 5. 8. y = 1.1x + 3 4 3 2 1 2 3 4 Figure 5
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- Which of the following statements proves the usage of a least squares line? The residual plot shows extreme observations in residuals. Plots of scrambled residuals against the predictor do not show any pattern. The scatterplot of the fitted values against the response shows a linear relationship. Group of answer choices (i) I only (ii) II only (iii) III only (iv) I and II only (v) II and III onlyHello there, can you help me solve the problem with two subparts (b and c) Problem: (the image is attached) Subparts: b. Find the least-squares curve of the form above to fit the data (4, 1.57), (6, 2.05), (8, 2.5), (10, 2.7), (12, 3.1), (14, 3.6), (16, 3.8), and (18, 4.35), where x and y represent sales and costs in thousands. Produce a graph that shows the data pts and the graph of the cubic approximation. y = __x + (__)x2 + (__)x3 c. (the image is attached)Consider the data points (2, 1), (0, –4) and (−2,−3). Given that the least squares line of best fit is y = x − 2 ,which one of the following is the least squares error? √38 +√6 √6
- What is the correct solution?The data points in ExerciseIn each of Exercises, we have presented two linear equations and a set of data points. For each exercise,a. plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.b. construct tables for x, y,ŷ e, and e2 like Table (page 626).c. determine which line fits the set of data points better, according to the least-squares criterion.TABLEDetermining how well the data points in Table are fit by (a) Line A and (b) Line Ba. Line A: y= -1 + 2x x y ŷ e e2 1 3 1 2 4 2 1 3 -2 4 3 5 5 0 0 8 b. Line B: y= -1 + x x y ŷ e e2 1 3 2 1 1 2 1 3 -2 4 3 5 4 1 1 6 TABLE Three data points x y 1 3 2 1 3 5 Line A: y=3-0.6x, Line B: y=4-xData Points x 0 2 2 5 6 y 4 2 0 -2 1 ŷ =14-3x x 1 3 4 4 y 13 -1 3 5Simulate the solution of the given problem using Excel such that when the given five data points (x and y values) are changed, a new equation is formed. 1. By the method of least squares, fit a line y = a + bx to the points 0 2 y -1 -1 2 9 3 10 5 14
- 2. The Mach number of a moving object is the ratio of its speedto the speed of sound. The following table shows the speeds of a jet aircraft, in terms of Mach numbers, and the time tafter it starts to accelerate. Find the least- squares line of s as a function of t. t(min) 0.00 s(Mach Number) 0.88 0.60 0.97 1.20 1.03 1.80 1.11 2.40 1.19 3.00 1.25Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent variable.) (-1, 2), (1, 1), (3,-2) y 2 w|N 3 - X XLse five decimal places Fit the following data by the equation y=- ax using the Least squares method 2 4 10 13 15 32 40 124
- Suppose you are given the following x,y data pairs: x- 1,3,4 y-2,1,6 Show that the least squares equatuon is y=1.143+1.071x Now suppose you are given these data pairs x-2,1,6 y-1,3,4 Show that the least squares equation for these is y=1.595+0.357x In the data for parts a and b did we simply exchange the x and y values for each data pair? Solve 0.143+1.071x for x. Do you get the least squares equation of part b with symbols x and y exchanged? If we solve this equation for x, will we necessarily get the least squares equation for the set of data pairs y,x with x and y exchanged? ExplainIt is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. 4 y 48 42 33 26 A USE SALT Complete parts (a) through (e), given Ex = 15, Ey = 149, Ex² = 77, Ey² = 5833, Exy = 489, and r= -0.9106. (a) Draw a scatter diagram displaying the data. 55 Graph Layers After you add an object to the graph you 50 can use Graph Layers to view and edit its properties. Fill 45 40 35 No Solution 30 25 20 O Help WebAssign. Graphing Tool ( b) Verify the given sums Σχ, Σγ, Σχ, Σy, Σχy, and the value of the sample correlation coefficient r. (Round your value forr to four decimal places.) Σχ Ey = Ex? = Ey? = Exy = r =