In attempting to draw the \"best\" line through your data points you probably so

Question

In attempting to draw the "best" line through your data points you probably sought to find one that is on average closest to all the points. There is a quantitative way to determine such a line. Consider a set of data points: (x_1, y_1), (x_2, y_2), ... One seeks to find the "best" coefficients A and B such that the sum of squared vertical distances of the data to the line f(x) = Ax + B is minimized. Let D = sigma [y_i - f(x_i)]^2. By requiring the first derivatives of D with respect to both A and B each to vanish, find expressions for the values of A and B in terms of the data points. Why are these derivatives made to vanish?

Explanation / Answer

So for the best fit line through data points
the vertical distances of data points form any line Ax + B = f(x) is to be minimised, and that will be our best fit curve
so the formula becomes,. D = sum ation from i = 0 to i = 1 (yi - f(xi))^2
now, the value of D depends on value of f(xi) [ where xi is ith data points x coordinte]
and f(xi) depends on A and B
so, to minimise D, the derivatives D with respect to A and B should be zero
that is the condition of maxima and minima
if one function f(y) has a maxima/minima at a point
then d(f(y))/dy at that point is 0

so , dD(A,B)/dA = d(D(A,B))/dA = 0

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.