Find the equation of the least squares regression lineof y on x, for the following sets of data:(a)3489.11 144 5 78.y1249

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Answered: Find the equation of the least squares…

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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The following table presents the percentage of students who tested proficient in reading and the percentage who tested proficient in math for 5 randomly selected states in the United States. Compute the least-squares regression line for predicting math proficiency from reading proficiency. State Texas Michigan New York California Florida Send data to Excel Percent Proficient in Reading 73 73 75 60 66 Percent Proficient in Mathematics 78 The equation for the least squares regression line is y 66 70 59 68 Round the slope and y-intercept to four decimal places as needed.
The data for temperature (x) and number of ice cream cones sold per hour (y) is shown. x 65 70 75 80 85 90 95 100 105 y 8 10 11 13 12 16 19 22 23 It would be reasonable to use the least squares regression line to predict the number of ice cream cones sold when it is 50 degrees. True False
A study of IT companies has found the following data on the age of each company and its annual volume of sales: Age (years) Sales (000) 2 22 2.5 34 3 33 4 37 4.5 40 4.5 45 5 49 3 30 6 58 6.5 58 (a) Determine the least squares regression that relates the age of company variable to the sales variable in the form y = a + bx. (b) Provide a practical interpretation of the coefficients a and b. (c) Determine the ‘goodness of fit’ (R2) of the estimated regression line. d) Using the estimated regression line determined in (a), calculate what volume of sales would be predicted for a company that is 3.5 years of age. (e) If it was found that…
The following data are the average annual repair cost (in O.R.) and the age of automobiles ( in years). Car age (x) 1 2 3 4 5 Repair Cost (y) 100 150 320 350 380 Find the equation of Y on X by least-squares regression method.
A seafood-sales manager collected data on the maximum daily temperature, T, and the daily revenue from salmon sales, R, using sales receipts for 30 days selected at random. Using the data, the manager conducted a regression analysis and found the least-squares regression line to be Rˆ=126+2.37T. A hypothesis test was conducted to investigate whether there is a linear relationship between maximum daily temperature and the daily revenue from salmon sales. The standard error for the slope of the regression line is SEb1=0.65. Assuming the conditions for inference have been met, which of the following is closest to the value of the test statistic for the hypothesis test? t=0.274 A t=0.65 B t=1.54 C t=3.65 D t=193.85 E
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Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where X is the age of the crab in months and Y is the predicted value of Y, the size of the male crab in cm. Y = 8.2052 + 0.5693X What is the value of Ý when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places. Interpret the value of Ý. The value of Ý is the probability that a crab will be 21.7865 months old. the predicted number of crabs out of the 1,000 crabs collected that will be 21.7865 months old. the predicted incremental increase in size for every increase in age by 21.7865 months. the predicted size of a crab when it is 21.7865 months old.
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Find the equation of the least squares regression line of y on x, for the following sets of data: (a) X 1 3 4 6 8 9 11 14 9 y 1 2 44578