23 Determine, by means of the least squares method and assuming that theonly significant errors are in the y values, the best straight linerelationship to fit the following data:y657268 71727580 82777480 84 87 93 9878 89 91 96 95

The given data points are x 65 68 71 75 77 80 84 87 93 98 y 72 72 80 82 74 78 89 91 96 95…

Answered: 23 Determine, by means of the least…

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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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
Q1.2
The table below shows the heights (inches) and weights (pounds) of 9 randomly selected children. Child Data Height (inches), x 36 56 58 59 61 63 65 69 73 Weight (pounds), y 69 89 96 74 110 90 123 110 128 (a) Construct a scatter diagram for the data, where the weight of the child is the response variable. (b) Determine the least-squares regression line for the data and graph the line on the scatter diagram from part (a). (use calculator) (show what did you do on the calculator) (c) Interpret the slope and the y–intercept in the context of the problem. (d) Predict the weight of a child that is 57 inches tall. Comparing with the observed value, what is the residual? Is the observed weight above or below average? (e) Determine the correlation coefficient, r. Is there a correlation? Discuss the strength of the correlation and why. (f) Are heights and weights of children linearly related? Why or why not? Be sure to justify your answer by using the appropriate method. (g)…
The following table gives the gold medal times for every other Summer Olympics for the women's 100 meter freestyle (swimming). Year Time (seconds) 1912 82.2 1924 72.4 1932 66.8 1952 66.8 1960 61.2 1968 60.0 1976 55.65 1984 55.92 1992 54.64 2000 53.8 2008 53.1 Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.) Find the correlation coefficient r. (Round your answer to four decimal places.)r = Find the estimated gold medal time for 1924. (Use your equation from part (d). Round your answer to two decimal places.) Find the estimated gold medal time for 1992. (Use your equation from part (d). Round your answer to two decimal places.) Use the least squares line to estimate the gold medal time for the 2012 Summer Olympics. (Use your equation from part (d). Round your answer to two decimal places.) ch12#1
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Lse 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
You ask a small sample of 6 students what percentage score they obtained in a recent exam and how many hours they spent preparing for the exam. The data you obtained is summarised in the table below. Time spent studying (hours) 12 9 23 Answer: 7 13 11 Exam score (out of 100) 70 56 91 60 52 58 You fit a least squares line to the data which can be used to predict exam scores from the time spent studying. You find that the intercept of the line is equal to 37.691, and the slope is 2.145. Calculate the t-statistic used to the test the null hypothesis that the true population slope is zero. (Round the result to three decimal places.)
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Data for motor vehicle production in a country for the years 1997 to 2004 are given in the table. Year 1997 1998 1999 2000 2001 2002 2003 2004 Thousands 1,578 1,671 1,805 2,009 2,391 3,219 4,415 5,092 (A) Find the least squares line for the data, using x = 0 for 1990. y = (Use integers or decimals for any numbers in the expression. Do not round until the final answer. Then round to the nearest tenth as needed.)

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23 Determine, by means of the least squares method and assuming that the only significant errors are in the y values, the best straight line relationship to fit the following data: 5 x y 65 72 68 71 75 72 80 82 77 80 84 87 93 98 74 78 89 91 96 95