A certain experiment produces the data(1,1.7), (2, 2.7), (3, 3.2), (4, 3.7), (5, 3.9)Describe the model that produces a least-squares fit of these points by a function of the formy =B₁x + B₂x². Such a function might arise, for example, as the revenue from the sale of x units ofa product, when the amount offered for sale affects the price y set for the product.Give the normal equation to the inconsistent system Ax=y and the equation for the least squareerror solution y =B₁x +B₂x².The normal equation for the inconsistent system is47.5[8₁]-[475]2a.b.d.e.55 225225 979B₁B₂SIIHB₁18₂155 225225 97955 225225 97958 225225 990ܝرته32/2/51198=39.75151.55619851 225 B₁45225 979 B₂ 200and y= 1.6x -0.18x²and y= 1.67x -0.18x²and y= 1.5x -0.19x²and y=1.67x-0.18x²and y=1.67x -0.18x²

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Answered: A certain experiment produces the data…

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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Find the required linear model using least-squares regression. The following table shows the number of operating federal credit unions in a certain country for several years. 2011 2012 2013 2014 4426 4255 4094 3919 Year Number of federal credit unions (a) The linear model for these data is y = (Round to the nearest tenth as needed.) (a) Find a linear model for these data with x = 11 corresponding to the year 2011. (b) Assuming the trend continues, estimate the number of federal credit unions in the year 2018. X + 2015 (b) The estimated number of credit unions for the year 2018 is (Round to the nearest integer as needed.) 3752
The heights (y) and lengths of forearms (x) were measured in inches for a sample of men. The following summary statistics were obtained: x= 10.1 Sx=0.8 y= 70.1 Sy=2.5 r=0.81 a. Compute the least- squares regresson line for predicting height from forearm length. b. Joe's forearm is 1 inch longer than Sam's. How much taller than Sam do you predict Joe to be? c. Predict the height of a man whose forearm is 9.5 inches long.
A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[1] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and O otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender Because Female is a dummy variable, the problem provides us with enough information to figure out the exact regression line equation. What is the numerical value of a?
After ingesting 15 mL of 95% alcohol, the blood alcohol level of a 75 kg adult male rises rapidly to a maximum level then gradually decreases over time. Measurements of the subject's blood alcohol level at time t (in minutes) since the maximum blood alcohol level was observed gave the following results: Time t (in minutes) Blood alcohol level, B (in mg/L) 10 25 60 70 90 150 160 130 70 60 40 20 a) Using least squares regression, determine an equation of the form B= Be-kt that best fits the relationship shown. You do not need to graph the data. (Note any transformations you have applied to your data: x→, y→, round the values that appear in your final equation to three significant figures, and use the correct variable names...not x and y.)| b) Using your equation from part a), estimate the time t at which the subject's blood alcohol level will be 90 mg/L? Round your answer to the nearest minute.
a. Give the design matrix, the observation vector, and the unknown parameter vector. Choose the correct design matrix X below. b. Find the associated least-squares curve for the data
A certain experiment produces the data (2,7.3), (3,5.3), and (4, -0.2). Describe the model that produces a least-squares fit of these points by a function of the form y = A cos x + B sinx. The model is y=XB+e, where y = (Type an exact answer.) X=B= and ε = E₁ 82 £3
The following data give the diffusion time (hours) ofa silicon wafer used in manufacturing integrated circuitsand the resulting sheet resistance of transfer:Diffusion time, x 0.56 1.10 1.58 2.00 2.45Sheet resistance, y 83.7 90.0 90.2 92.4 91.6(a) Find the equation of the least squares line fit to thesedata.(b) Predict the sheet resistance when the diffusion time is1.3 hours.
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A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The least squares equation was found Y; = -13258.594 + 2.422X;, where X; is the program per-year tuition and Y; is the predicted mean starting salary. To perform a residual analysis for these data, the following results are obtained. of regression have been seriously violated. Residual index plot QQ Plot of Residuals Residuals Residuals 20000- 20000 0. -20000 -20000 a) To evaluate whether the assumption of linearity has been violated, which of the following graph shou be examined? A. Predicted Values vs. Residuals B. Residual index plot C. QQ plot of residuals D. Residuals vs. Progrm Per-Year Tuition ($) b) To evaluate whether the assumption of normality has been violated, which of the following graph…
The number of speeding tickets issued (Y) and the number of radar traps set up by police officials on an expressway (X) during nine weekends are shown below: No. of speed traps X: 10 12 15 8 8 12 11 7 13 14 No. of speeding tickets issued Y: 76 84 93 61 79 70 55 84 85 (a) Draw a scatter plot of the data. (b) Find the equation of the least squares regression line using the information below: x, -102, Σx-1212, Σν- 687, Σν,-53649, ΣΧ.y, 8036. (Show the details of your work.) T

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