Mathegoras

Functions › Quadratic functions and parabolas › Quadratic from its values

Fitting b through sample means

High school · ●●○○○ 20 pts

A sample of six points (x1,y1),…,(x6,y6)(x_1, y_1), \ldots, (x_6, y_6) is scattered around the curve y=bx2−13y = bx^2 - \frac{1}{3}, where bb is a real number. Given ∑i=16xi=11\sum_{i=1}^{6} x_i = 11, ∑i=16yi=13\sum_{i=1}^{6} y_i = 13 and ∑i=16xi2=21\sum_{i=1}^{6} x_i^2 = 21, find bb using the regression line in the variable t=x2t = x^2. Round to two decimal places.

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linear regressionleast squaressample mean