\bar{x}= \displaystyle \frac {0.3+0.5+0.7+1.2}{4}=0.675\\
\bar{y}= \displaystyle \frac {4.20+5.03+5.82+7.81}{4}=5.715\\
S_{XX}=0.3^2+0.5^2+0.7^2+1.2^2 - 4\cdot0.675^2=0.09+0.25+0.49+1.44-1.8225=0.4475\\
S_{YY}=4.2^2+5.03^2+5.82^2+7.81^2-4\cdot 5.715^2=17.64+25.3009+33.8724+60.9961-130.6449=7.1645\\
S_{XY}=0.3\cdot4.2+0.5\cdot5.03+0.7\cdot5.82+1.2\cdot7.81 - 4\cdot0.675\cdot5.715=1.26+2.515+4.074+9.5282-15.4305=1.9467\\
\hat{\beta}= \displaystyle \frac {1.9467}{0.4475}=4.35\\
4.35\neq4.285