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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 least squares. (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 for the sum of squares of the vertical distances, Q?

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 least squares. (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 for the sum of squares of the vertical distances, Q?

Advanced Engineering Mathematics
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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Question 6
4. You wish to test H.:µ = 10 versus Ha:µ# 10 using the data from a random 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 this indicate? 5. Show that the least squares line y= B, + B,x will always pass through the point (x,7). 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 least squares. (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 for the sum of squares of the vertical distances, Q? 7. (X1, X2,..., Xn) are independent and identically distributed random |X| 1 variables with density function f ((x|0) = –e¯. Find the MLE of 0. 20
Transcribed Image Text:4. You wish to test H.:µ = 10 versus Ha:µ# 10 using the data from a random 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 this indicate? 5. Show that the least squares line y= B, + B,x will always pass through the point (x,7). 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 least squares. (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 for the sum of squares of the vertical distances, Q? 7. (X1, X2,..., Xn) are independent and identically distributed random |X| 1 variables with density function f ((x|0) = –e¯. Find the MLE of 0. 20
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