KFind a least-squares solution of Ax=b by (a) constructing the normal equations for x and (b) solving for x1Hb=52A =1 -4-1034334a. Construct the normal equations for x without solving.x= (Simplify your answers.)b. Solve for xx=(Simplify your answer.)

Answered: Find a least-squares solution of Ax=b…

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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We want to write the least-squares equation ý a+ bx, using the given printout. Predictor Coef SE Coef Constant 316.27 28.31 11.24 0.002 Elevation -32.660 3.511 -8.79 0.003 S 11.0603 R-iq 95.1N Recall that a is the intercept and b is the slope of the line. Since the elevation is the explanatory variable, x, the coefficient of the x-term is the slope of the line. From the printout, this corresponds to the table value in the "Elevation" row, and "Coef" column. Therefore, The intercept is given by the value of the constant term. There is no variable, but the Minitab printout classifies this value as a "coefficient." (Note: This may or may not coincide with your previous experience with the terms "constant" and "coefficient," but it is mathematically correct for reasons that we will not explore in this tutorial.) The value in the "Constant" row and "Coef" column is 316.27, Therefore, a Substitute these values into the least-square equation. 9 -a+ bx
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How do I do this: "Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)"
The equation of the least-squares regression line is ý = 68.5 + 11.4x, where ý is the number of students enrolled and x is number of years the school has been The number of students enrolled at a school varies from year to year. For the first eight years the school is open, the number of students enrolled is recorded in the table shown. open. Which shows the residual plot? Students 92 Year 2. 94 100 104 80 4 60 113 131 40 7. 8. 147 176 20 -20 0. 2. 4. 8. Number of Years 3. 56
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Find a quadratic model for the data, Then use the model to predict the number of bikes sold in November. (Note represent the months as number for example: January = 1, February = 2 etc.)
Use the following linear regression equation to answer the questions. X1 = 1.5 + 3.6x2 - 7.7x3 + 2.3x4 (a) Which variable is the response variable? O X4 O X2 O 3 Which variables are the explanatory variables? (Select all that apply.) O 3 O X4 O X1 O ×2 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient X, coefficient X4 coefficient (c) If x2 = 4, x3 = 9, and x4 = 10, what is the predicted value for x,? (Use 1 decimal place.) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope." O If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." O If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." O If we look at all coefficients together, the sum of them can be thought of as the overall…
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A fisherman has collected data about the length in inches, L, and weight in ounces, w, of fish he has caught. The resulting line of best fit for the data is w=−37.1+3.2L. Would predicting the weight of a 26-inch fish be interpolation or extrapolation? Explain. L 13 14 15 16 18 21 23 23 w 3 10 10 15 20 35 38 45 Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is outside the range of the lengths in the data. Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is inside the range of the lengths in the data. Using the model to predict the weight of a 26-inch fish is extrapolation because 26 inches is inside the range of the lengths in the data. Using the model to predict the weight of a 26-inch fish is interpolation because 26 inches is outside the range of the lengths in the data.
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Use the following linear regression equation to answer the questions. X1 = 1.2 + 3.6x2 - 7.6x3 + 2.5x4 (a) Which variable is the response variable? O x1 O X4 O x2 O x3 Which variables are the explanatory variables? (Select all that apply.) O x1 O X4 O X3 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient X3 coefficient X4 coefficient (c) If x2 = 8, X3 = 6, and x4 = 4, what is the predicted value for x1? (Use 1 decimal place.) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope." If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." O If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line. O If we hold all other explanatory variables as fixed constants, then we can look at…

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Find a least-squares solution of Ax=b by (a) constructing the normal equations for x and (b) solving for x. 1 -4 3 1 -4 2 A = -1 10 3 435 P a. Construct the normal equations for x without solving. x=(Simplify your answers.) b. Solve for x x=(Simplify your answer.)