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=== Interpretation about the slope ===
By multiplying all members of the summation in the numerator by : <math>
<math display="block">\begin{align}
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\end{align}</math>
We can see that the slope (tangent of angle) of the regression line is the weighted average of <math>\frac{
=== Interpretation about the intercept ===
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| The residuals and {{mvar|x}} values are uncorrelated (whether or not there is an intercept term in the model), meaning:
<math display="block">\sum_{i=1}^n x_i \widehat{\varepsilon}_i \;=\; 0</math>
| The relationship between <math>\rho_{xy}</math> (the [[Pearson_correlation_coefficient#For_a_population|correlation coefficient for the population]]) and the population variances of <math>y</math> (<math>\sigma_y^2</math>) and the error term of <math>\
<math display="block">\sigma_\
For extreme values of <math>\rho_{xy}</math> this is self evident. Since when <math>\rho_{xy} = 0</math> then <math>\sigma_\
}}
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==See also==
*
* [[Linear trend estimation]]
* [[Segmented regression|Linear segmented regression]]
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