Find \({b_{xy}}\) from the given data ∑x = 50, ∑y = 40, ∑x² = 625, ∑y² = 576, ∑xy = 1780, n = 6.

Concept:

b_xy = slope of the regression line of x on y, and calculated as:

\({b_{xy}} = \frac{{n\sum xy - \left( {\sum x} \right)\left( {\sum y} \right)}}{{n\sum {y^2} - {{\left( {\sum y} \right)}^2}}}\)

Calculation:

Given:

Mean \(\bar x = \frac{{\sum x}}{n} = \;\frac{{50}}{6} = 8.333\) and 

\(\bar y = \frac{{\sum y}}{n} = \;\frac{{40}}{6} = 6.667\)

\({b_{xy}} = \frac{{n\sum xy - \left( {\sum x} \right)\left( {\sum y} \right)}}{{n\sum {y^2} - {{\left( {\sum y} \right)}^2}}}\)

\(b_{xy} = \frac{{6 \times 1780 - 50 \times 40}}{{6 \times 576 - {{\left( {40} \right)}^2}}} \)

\(b_{xy}= \frac{{10680 - 2000}}{{3456 - 1600}} = \frac{{8680}}{{1856}} = 4.67\)

Important Pointsbyx = slope of the regression line of y on x, and calculated as:

\({b_{yx}} = \frac{{n\sum xy - \left( {\sum x} \right)\left( {\sum y} \right)}}{{n\sum {x^2} - {{\left( {\sum x} \right)}^2}}}\)