Could you please solve the subparts d and e? The following data represents a report about the x: carbon amount (in mg per 1gsteel) and y: the ultimate tensile strength of steel (in MPa):200 200150 | 150142 180 | 210 | 190300 300 | 350 402440 390 | 600 | 610100125125250 250406y155320 | 280 | 400 | 430670a. Find the least squares estimate of the regression line with assuming the simple linear regressionis valid. (Find the coefficients of the model)b. Write down the probabilistic and deterministic models (equations) with the estimatedcoefficients.c. Find the sum of squares of the regression and error and their corresponding mean squares.d. Test the usefulness of the regression model and the slope of the line of means.e. Find the coefficient of correlation and coefficient of determination of the regression model andinterpret your results.

As the subparts are specified to be solved subparts d and e will be solve Data is given

c. Find the sum of squares of the regression and error and their corresponding mean squares. d. Test the usefulness of the regression model and the slope of the line of means. e. Find the coefficient of correlation and coefficient of determination of the regression model and interpret your results.

c. Find the sum of squares of the regression and error and their corresponding mean squares. d. Test the usefulness of the regression model and the slope of the line of means. e. Find the coefficient of correlation and coefficient of determination of the regression model and interpret your results.

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 32EQ

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Question

Could you please solve the subparts d and e?

The following data represents a report about the x: carbon amount (in mg per 1g
steel) and y: the ultimate tensile strength of steel (in MPa):
200 200
150 | 150
142 180 | 210 | 190
300 300 | 350 402
440 390 | 600 | 610
100
125
125
250 250
406
y
155
320 | 280 | 400 | 430
670
a. Find the least squares estimate of the regression line with assuming the simple linear regression
is valid. (Find the coefficients of the model)
b. Write down the probabilistic and deterministic models (equations) with the estimated
coefficients.
c. Find the sum of squares of the regression and error and their corresponding mean squares.
d. Test the usefulness of the regression model and the slope of the line of means.
e. Find the coefficient of correlation and coefficient of determination of the regression model and
interpret your results.

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