[Question 6] (17 points)Consider the following data set123f(x)-14.255.881.750.8810Use Least Squares method to fit the data to a function of the form f (x)%3DVa+b x-Use the obtained function to estimate f(6). Show all details.

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Answered: [Question 6] (17 points) Consider the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 33EQ

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The position of a particle x(t) on an axis has been monitored. The results are shown in the following table. t x(t)0 41 114 129 12 By the least squares method, fit the data to a quadratic model: Report x(10)
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Question 1 Provide an algebraic proof that the least squares estimator is not consistent when Cov(x,e)=0 with the regression model y =B1+B2E(x)+e where E(e)=0 So that E(y) = B1 + B2E(x) Full explain this morning and text typing work only thanks
Solve the following problems completely. An article in the Journal of Environmental Engineering (1989, Vol. 115(3), reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage). Draw a scatter diagram of the data. Fit the simple linear regression model using the method of least squares. Find an estimate of σ2. Estimate the mean chloride concentration for a watershed that has 1% roadway area. Find the fitted value corresponding to x = 0.47 and the associated residual. Test the hypothesis H0: β1 = 0 versus H1: β1 ≠ 0 using the analysis of variance procedure with α = 0.01. Find a 99% confidence interval of Mean chloride concentration when roadway area x = 1.0% Find a 99% prediction interval on chloride concentration when roadway area x = 1.0%. Plot the residuals versus ŷ and versus x. Interpret these plots.…
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 Coef SE Coef T P Constant 0.8678 0.4148 2.06 0.84 Weight 0.40376 0.02978 13.52 0.000 S = 0.517508 R-Sq = 94.6% (a) Write out the least-squares equation. = + x (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)(c) What is the value of the correlation coefficient r? (Use 3 decimal places.) 4.
E) Use the original least squares line to predict the gestation period of a human being, assuming a longevity of 75 years. F) why does your answer for part (e) differ so much from the average gestation period of a human (280 days)?
(a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.) y= ?
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 Coef SE Coef T PConstant 0.8570 0.4148 2.06 0.84Weight 0.38243 0.02978 13.52 0.000 S = 0.517508 R-Sq = 97.4% (a) Write out the least-squares equation. y^= ______ + _____x (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)
Based on the data presented in the table below, please calculate the values of b0 and b1 using OLS (ordinary least squares) and for the equation: q1 = β0 + β1pi + ui. qi pi 1 2 2 3 3 5
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The accompanying data were compiled by the admissions office at a college during the past 5 years. The data relate the number of college brochures and follow-up letters (x) sent to a preselected list of high school juniors who had taken the PSAT and the number of completed applications (y) received from these students (both measured in units of a thousand). x 4 4.5 5 5.5 6 y 0.5 0.7 0.9 1 1.3 (a) Determine the equation of the least-squares line for these data.y =

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[Question 6] (17 points) Consider the following data set 3. f(x) -14.25 5.88 1.75 0.88 10 Use Least Squares method to fit the data to a function of the form f (x) = Use the obtained function to estimate f(6). Show all details.