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Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 21CM

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Fit the function y = A x^B by the method of least squares

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Each month for several months, the average temperature in °C (x) and the number of pounds of steam (y) consumed by a certain chemical plant were measured. The least-squares line computed from the resulting data is y = 245.82 + 1.13x. Predict the number of pounds of steam consumed in a month where the average temperature is 65°C. If two months differ in their average temperatures by 5°C, by how much do you predict the number of pounds of steam consumed to differ?
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The least squares line ŷ =10 + 5x describes the following coordinates: (1, 15), (2, 20), (3, 25), and (4, 30). Using these data as a specific example, explain the meaning of "least squares." The line ŷ = 10 + 5x minimizes the sum of the squared horizontal distances from the points to the line. The line ŷ = 10 + 5x minimizes the sum of the squared difference between the x and y values. The line ŷ = 10 + 5x minimizes the sum of the vertical distances from the points to the line. The line ŷ = 10 + 5x minimizes the square of the standard deviation. The line ŷ = 10 + 5x minimizes the sum of the squared vertical distances from the points to the line.
A motorist found that the efficiency of her engine could be increased by adding lubricating oil to fuel. She experimented with different amounts of lubricating oil and the data are Amount of lubricating oil (ml) Efficiency (%) 0 25 50 75 100 | 60 70 75 81 84 (a) Obtain the least squares fit of a straight line to the amount of lubricating oil. (b) Test whether or not the slope B, = 0. Take a = 0.05 as your level of significance. (c) Construct a 90% confidence interval on the mean response at xo = 10 ml.
Temperatures (°C) are measured at various points on a heated plate, which are reported in the following table. Estimate the temperature when X=4 and Y=3.2, X=4.3 and Y=2.7. Image I need to know how to do this problem for the least squares method since we only used 2 data which were X and Y, but here we are using the Temperature and I have not been able to do it. I hope you can help me, thank you very much.
Find a least-squares best fit line for the points (1, 1), (2, 5), (3, 5). Write your answer as a function of x.
he scatter plot below shows the average cost of a patient staying one day in a hospital (with no surgery) in a sample of years between 2000 and 2015. The least squares regression line modeling this data is given by yˆ=−4815+3.765x. A scatterplot has a horizontal axis labeled Year from 2005 to 2015 in increments of 5 and a vertical axis labeled Price ($) from 2660 to 2780 in increments of 20. The following points are plotted: (2003, 2736); (2004, 2715); (2007, 2675); (2009, 2719); (2013, 270). All coordinates are approximate. Interpret the slope of the least squares regression line. Select the correct answer below: The average cost of a day in a hospital decreased by $3.765 each year between 2000 and 2015. The average cost of a day in a hospital increased by $3.765 each year between 2000 and 2015. The average cost of a day in a hospital decreased by $4815 each year between 2000 and 2015. The average cost of a day in a hospital increased by…
A wildlife biologist has spent the past 5 years studying the relationship between the length (inches) and the average weight (lb) of the striped bass. His results are summarized in the table below. Length (inches) 14 18 22 26 Weight (lb) 3 |11 14 Find the least squares regression line y = ax + b for the data in the table, where x represents the length of the fish in inches and y represents the weight in pounds. Use this regression line to estimate the average weight of a striped bass that is 21 inches in length. Oy=0.75(21) - 9.5 = 6.25 lb O y = 0.65(21) - 10.5 = 3.15 lb y = 0.95(21) - 10.5 = 9.45 lb y = 0.95(21)-8.5 = 11.45 lb y = 0.85(21) 12.5 = 5.35 lb
The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x + 41.337. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon. (a) The coefficient of determination of the expanded data set is R = %. (Round to one decimal place as needed.) Data Table How does the addition of the twelfth car to the data set affect R? Miles per Weight |(pounds), x A. It increases R. Gallon, y Car 1 3,771 22 B. It decreases R2. Car 2 3,990 19 C. It does not affect R2. 3,534 Car 3 20 Car 4 3,172 24 (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Car 5 2,579 27 Car 6 3,730 20 A. No, it is not influential. Yes, it is an outlier. Car 7 2,605 25 B. Yes, it is influential. No, it is not an outlier. Car 8 3,777 19 C. No, it is not influential. No, it is not an outlier. Car 9 3,308 19 D. Yes, it is influential. Yes, it is an outlier. Car…
If I have a list of data and use the least squares error, why would the function be a function of m

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