Question

Please show HOW.. preferably with technology..

Answer 1

$\\ Find\ X\cdot Y\ and\ X^2$

X	Y	X⋅Y	X⋅X
41.9	34.2	1432.98	1755.61
17.8	73.5	1308.3	316.84
8.4	81.2	682.08	70.56
53.4	29.4	1569.96	2851.56
28.5	56.2	1601.7	812.25
-14.6	101.1	-1476.06	213.16
-9.3	74.4	-691.92	86.49
32.6	39.5	1287.7	1062.76
17.3	70.7	1223.11	299.29

$\\ Find\ the\ sum\ of\ every\ column\\ \sum{X} = 176 ~,~ \sum{Y} = 560.2 ~,~ \sum{X \cdot Y} = 6937.85 ~,~ \sum{X^2} = 7468.52\\\\ \\ \\ \\ Find\ a\ and\ b\\ \begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 560.2 \cdot 7468.52 - 176 \cdot 6937.85}{ 9 \cdot 7468.52 - 176^2} \approx 81.754 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 9 \cdot 6937.85 - 176 \cdot 560.2 }{ 9 \cdot 7468.52 - \left( 176 \right)^2} \approx -0.998\end{aligned}\\ \\ \\ substitute\ a\ and\ b\ in\ regression \ formula \\ \begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~81.754 ~-~ 0.998 \cdot x\end{aligned}\\$

$\\ regression\ equation\ \ \ \boldsymbol{y=81.754-0.998 x}$