Question

The data below relates to income levels and expenses of foods in U.S dollars (00).

Income (X)	Expenditure (Y)
35	9
49	15
21	7
39	11
15	5
28	8
25	9

 

 

 

 

 

 

 

 

 

Calculate the Pearson correlation and interpret the results.

Answer 1

The Pearson correlation coefficient

\(\mathrm{r}=\frac{s_{x y}}{\sqrt{S_{x x} S_{y y}}}\)

where;

\(\mathrm{S}_{\mathrm{xy}}=\Sigma x y-\frac{\Sigma x \Sigma y}{n}\)

\(\mathrm{S}_{\mathrm{xx}}=\Sigma x^{2}-\frac{(\Sigma \mathrm{x})^{2}}{n}\)

\(\mathrm{S}_{\mathrm{yy}}=\Sigma y^{2}-\frac{(\Sigma y)^{2}}{n}\)

Income (X)	Expenditure (Y)	X2	Y2	XY
35	9	1225	81	315
49	15	2401	225	735
21	7	441	49	147
39	11	1521	121	429
15	5	225	25	75
28	8	784	64	224
25	9	625	81	225
∑= 212	∑= 64	∑= 7222	∑= 646	∑= 2150

 

 

 

 

 

 

 

 

 

 

\(\mathrm{S}_{\mathrm{xy}}=2150-\frac{(212 \times 64)}{7}=211.71\)

\(\mathrm{~S}_{\mathrm{xx}}=7222-\frac{(212)^{2}}{7}=801.4\)

\(\mathrm{~S}_{\mathrm{yy}}=64-\frac{(64)^{2}}{7}=60.86\)

\(\mathrm{r}=\frac{s_{x y}}{\sqrt{S_{x x} S_{y y}}}=\frac{211.71}{\sqrt{801.4 \times 60.86}}\)

r = 0.9586

There is a strong positive correlation between income and expenditure.

There is a strong positive correlation between income and expenditure.