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 is55 225 B₁ 47.5225 979184a.b.C.d.e.55 225225 979В5182] [[3]-[В 155 225225 97958 225225 99051 225225 97921₁B₂ 198B₂ /=/51IH39.75151.556198and y= 1.6x-0.18x²45200and y= 1.67x -0.18x²and y= 1.5x -0.19x²and y= 1.67x -0.18x²]and 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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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
Derive the least squares estimates of a and ß for the centred form of the simple linear regression model given by Yi = a + B(x; – I) + €; i= 1,2,..,n. Check that the estimates do give a minimum in the same way as we saw for the standard form of the simple linear regression model.
Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x %3D where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct an 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:
The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor Constant Weight S = 0.517508 Coef 0.8462 0.39512 R-Sq 97.0% (a) Write out the least-squares equation. ŷ = = 0.8462 + 0.39512 X SE Coef 0.4148 0.02978 T 2.06 13.52 P (c) What is the value of the correlation coefficient r? (Use 3 decimal places.) X 0.84 0.000 (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.) 0.39512
Show calculations or explanation for each question. a) Which of the following techniques is used to predict the value of one variable on thebasis of other variables?a. Correlation analysisb. Coefficient of correlationc. Covarianced. Regression analysis b) In the least squares regression line, y^=3-2x the predicted value of y equals:a. 1.0 when x = −1.0b. 2.0 when x = 1.0c. 2.0 when x = −1.0d. 1.0 when x = 1.0 c) In the simple linear regression model, the y-intercept represents the:a. change in y per unit change in x.b. change in x per unit change in y.c. value of y when x = 0.d. value of x when y = 0.
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