Find-the-regression-coefficient-b-xy-between-x-and-y-for-the-following-data-x-24-y-44-xy-306-x-2-164-y-2-574-and-n-4-

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Question Number 17 by user1 last updated on 25/Jan/15

$$\mathrm{Find}\mathrm{the}\mathrm{regression}\mathrm{coefficient}{b}_{xy}\mathrm{between}$$$$x\mathrm{and}y\mathrm{for}\mathrm{the}\mathrm{following}\mathrm{data}:$$$$\mathrm{\Sigma }x=24,\mathrm{\Sigma }y=44,\mathrm{\Sigma }xy=306,\mathrm{\Sigma }{x}^2=164,$$$$\mathrm{\Sigma }{y}^2=574\mathrm{and}n=4.$$

Answered by user1 last updated on 30/Oct/14

$$\mathrm{The}\mathrm{given}\mathrm{data}\mathrm{may}\mathrm{be}\mathrm{written}\mathrm{as}$$$$\mathrm{\Sigma }{x}_i=24,\mathrm{\Sigma }{y}_i=44,\mathrm{\Sigma }{x}_i{y}_i=306,\mathrm{\Sigma }{x}_i^2=164,$$$$\mathrm{\Sigma }{y}_i^2=574,\mathrm{and}n=4$$$$\therefore b_{yx}=\frac{\{\mathrm{\Sigma }{x}_i{y}_i-\frac{\left(\mathrm{\Sigma }{x}_i\right)\left(\mathrm{\Sigma }{y}_i\right)}{n}\}}{\{\mathrm{\Sigma }{x}_i^2-\frac{{\left(\mathrm{\Sigma }{x}_i\right)}^2}{n}\}}$$$$=\frac{\{306-\frac{24\times 44}{4}\}}{\{164-\frac{{\left(24\right)}^2}{4}\}}$$$$=\frac{42}{20}=2.1$$

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