Which e minimizes the following loss function for a data set D comprised of (xi , yi). First is the left mostanswer and fourth is the right most. (this question requires differentiation)L(0, D) = (u - Ox.)i=1O 0 =O 0 =ΣΗfourthfirstO thirdO second

The given loss function is L(θ,D)=∑i=1nyi-θxi2 To find θ which minimizes the…

Answered: Which e minimizes the following loss…

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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We showed that in a simple linear regression, the MLE estimates for B, and Bo are the same as the OLS estimates. Show that the MLE estimate for o? is -EL(y - B - Bx;)*. (Hint: take derivative of the Li=1() n LL w.r.t o?).
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1. You estimated a regression with the following output. Source | SS df MS Number of obs = 210 -------------+---------------------------------- F(1, 208) = 940.28 Model | 5529353.01 1 5529353.01 Prob > F = 0.0000 Residual | 1223155.7 208 5880.55624 R-squared = 0.8189 -------------+---------------------------------- Adj R-squared = 0.8180 Total | 6752508.71 209 32308.6541 Root MSE = 76.685 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 13.66711 .4457062 30.66 0.000 12.78843 14.54579 _cons | 103.7139 41.86814 2.48 0.014 21.17362 186.2542…
The variation of Y around its mean can be decomposed into which two parts?
2. You estimated a regression with the following output. Source | SS df MS Number of obs = 332 -------------+---------------------------------- F(1, 330) = 2.32 Model | 71599.1822 1 71599.1822 Prob > F = 0.1284 Residual | 10170207.7 330 30818.8111 R-squared = 0.0070 -------------+---------------------------------- Adj R-squared = 0.0040 Total | 10241806.9 331 30942.0147 Root MSE = 175.55 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | .7575183 .4969893 1.52 0.128 -.2201484 1.735185 _cons | 28.87757 42.80371 0.67 0.500 -55.32498 113.0801…

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Which e minimizes the following loss function for a data set D comprised of (xi , yi). First is the left most answer and fourth is the right most. (this question requires differentiation) L(0, D) = (y - Ox.) %3D i=1 Yi O 0 = Li-1 Yi O 0 =L O fourth first third second