Question
Calculate coefficient of correlation from the following data and interpret the result:
No. of years of schooling of farmers $0$ $2$ $4$ $6$ $8$ $10$ $12$
Annual yield per acre in $‘000 (₹)$ $4$ $4$ $6$ $10$ $10$ $8$ $7$

Answer

No. of year of schooling (X)  $\text{x}=(\text{X}-\overline{\text{X}})$ $x^2$ Annual yield (Y) $\text{y}=(\text{Y}-\overline{\text{Y}})$ $y^2$ $xy$
$0$ $-6$ $36$ $4$ $-3$ $9$ $18$
$2$ $-4$ $16$ $4$ $-3$ $9$ $18$
$4$ $2$ $4$ $6$ $-1$ $1$ $12$
$6$ $0$ $0$ $10$ $3$ $9$ $0$
$8$ $2$ $4$ $10$ $3$ $9$ $6$
$10$ $4$ $16$ $8$ $1$ $1$ $4$
$12$ $6$ $36$ $7$ $0$ $0$ $0$
$\Sigma\text{X}=42$ $\Sigma\text{x}=0$ $​​\Sigma\text{x}^2=112$ $\Sigma\text{Y}=49$ $​​\Sigma\text{y}=0$ $​​\Sigma\text{y}^2=38$ $​​\Sigma\text{xy}=42$
Interpretation: Moderate degree co-relation exists between the given two variables.
$\overline{\text{X}}=\frac{\Sigma\text{X}}{\text{N}}=\frac{42}{7}=6$ $\overline{\text{Y}}=\frac{\Sigma\text{Y}}{\text{N}}=\frac{49}{7}=42$
$\text{r}=\frac{\Sigma\text{xy}}{\sqrt{\Sigma\text{x}^2\Sigma\text{y}^2}}$
$=\frac{42}{\sqrt{112}\sqrt{38}}=\frac{42}{10.58\times6.16}=\frac{42}{65.17}=0.64 $

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