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"source": [
"## Problem 7 (5+5 points)\n",
"\n",
"The most common form of least-squares is linear regression, i.e. fitting $m$ data points $(a_i, b_i)$ to a model of the form $a(b) = x_1 + b x_2$.\n",
"The most common form of least-squares is linear regression, i.e. fitting $m$ data points $(a_i, b_i)$ to a model of the form $b(a) = x_1 + a x_2$.\n",
"\n",
"Suppose the data points $b_i$ have independent random errors with equal variances $\\sigma^2$ (i.e. they are \"homoscedastic\"). (This is the case in which GaussMarkov says that ordinary least-squares minimizes the variance.) In this case, many sources give simple explicit formulas for the variances of the fit coefficients $x_1$ and $x_2$\n",
"\n",