Question 5 You wish to test H.:µ = 10 versus Ha:µ# 10 using the data from arandom sample of size n = 10. You calculate a test-statistic of – 1.28.Calculate the p-value. Is your test significant at the .05 level? What does thisindicate?5.Show that the least squares line y= B, + B,x will always passthrough the point (x,J).6.Given the data (1, 2), (3, 7), and (5,50):(a) Fit a straight line of the form to these values by the method of leastsquares.(b) Fit a parabola of the form to these values by the method of least squares.(c) Which model, the straight line or the parabola, has the smallest value forthe sum of squares of the vertical distances, Q?(X1, X2,..., Xn) are independent and identically distributed random|X|variables with density function f ((x|0) = –e¯. Find the MLE of 0.204.7.

Least square method is used to estimate the best line that fit the data set. It also reduces the…

Answered: Show that the least squares line y=B,…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data: x 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y 75.4 71.3 58.1 48.5 74.1 73.7 67.7 59.5 58.0 48.6 (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)y = Interpret the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope.A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. (b) Calculate the coefficient of determination.…
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For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data: x 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y 74.6 71.1 57.5 48.4 74.0 72.9 68.3 59.8 57.6 48.0 (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)y = −32.6485+0.9943x Interpret the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. (b) Calculate the coefficient of…
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The following data show the number of class sessions missed during a semester of SOC221 and the final grade for a sample of 8 students selected at random. Number of Sessions Missed Final Grade (x) (y) 0 96 2 88 12 68 6 91 8…
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Show that the least squares line y=B, +B,x will always pass through the point (x,5). 5.