Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Least Squares Method
Maximum Likelihood Estimation
Formulas
y_t = a + b * t + u_t
Least squares estimator: min_a,b sum((y_t - (a + b * t))^2)
Maximum likelihood estimator with normal distribution: L(a, b) = product of (1 / sqrt(2*pi*sigma^2) * exp(-(y_t - (a + b * t))^2 / 2*sigma^2))
Theorems
Gauss-Markov Theorem
Normal Distribution Properties in MLE
Suitable Grade Level
Undergraduate - Statistics
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