Question

Find the regression coefficients $b_{yx}$ for the data
$\sum x=55,\sum y=88,\sum x^2=385,\sum y^2=385,\sum xy=586,n=10$

• A. $0.3$
• B. $0.4$
• C. $0.5$
• D. $0.6$

Answer 1

The correct option is A $0.3$

$\frac{\sum ny}{N}=\frac{586}{10}=58.6,\frac{\sum y}{N}=\frac{55}{10}=5.5,\frac{\sum y}{N}=\frac{88}{10}=8.8$

Cov$(x,y)=\frac{\sum xy}{N}-\frac{\sum x}{N}\frac{\sum y}{N}=58.6-(5.5\times 8.8)=10.2$

$\frac{\sum y^2}{N}=\frac{385}{10}=38.5,,{\sigma }^{2}y=\frac{\sum y^2}{N}-{\left(\frac{\sum y}{N}\right)}^2=38.5-(8.8{)}^2=38.94$

$bxy=\frac{Cov(x,y)}{{\sigma }^{2}y}=\frac{10.2}{38.94}\approx 0.3$