Question

10. The average price of a gallon of gasoline, and the average cost of a barrel of oil, are shown for a five-week period several years ago:

Gasoline ($)	Oil ($)
2.089	37.55
2.199	46.20
2.989	77.15
3.009	73.78
3.029	85.78

Calculate the correlation coefficient to four decimal places, and state whether it indicates a strong positive, strong negative, weak positive, weak negative, or no correlation.

Answer 1

.

X	Y	X⋅Y	X⋅X	Y⋅Y
2.089	37.55	78.44195	4.363921	1410.0025
2.199	46.20	101.5938	4.835601	2134.44
2.989	77.15	230.60135	8.934121	5952.1225
3.009	73.78	222.00402	9.054081	5443.4884
3.029	85.78	259.82762	9.174841	7358.2084

$\\ Find\ the\ sum\ of\ every\ column \ we\ get\\ {\sum{X}=13.315 ~,~ \sum{Y}=320.46 ~,~ \sum{X \cdot Y}=892.46874 ~,~ \sum{X^2}=36.362565 ~,~ \sum{Y^2}=22298.2618}\\ \\ So,\ correlation\ coefficient \ is\\ \\ \begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 5 \cdot 892.46874 - 13.315 \cdot 320.46 } {\sqrt{\left[ 5 \cdot 36.362565 - 13.315^2 \right] \cdot \left[ 5 \cdot 22298.2618 - 320.46^2 \right] }} \approx 0.9796\end{aligned}\\ \\ Correlation\ coefficient\ is\ positive\ and\ greater\ than\ 0.7\\ So,\ it\ is\ \boldsymbol{{\color{Red} strong \ positive}}\ correlation$