Question

Five items was taken from the output of factory. The length and weight of 5 items are given below. Length (meter): 5 6 7 9 12 Weight (KG): 13 15 18 19 20

Answer 1

In order to compute the regression coefficients, the following table needs to be used:

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c} & X & Y & XY & X^2 & Y^2 \\ \hline & 5 & 13 & 65 & 25 & 169 \\ \hdashline & 6 & 15 & 90 & 36 & 225 \\ \hdashline & 7 & 18 & 126 & 49 & 324 \\ \hdashline & 9 & 19 & 171 & 81 & 361 \\ \hdashline & 12 & 20 & 240 & 144 & 400 \\ \hdashline Sum= & 39 & 85 & 692 & 335 & 1479 \\ \hdashline \end{array}$$ $$\bar{X}=\dfrac{1}{n}\sum _{i}X_i=\dfrac{62}{9}=6.89$$

$$\bar{Y}=\dfrac{1}{n}\sum _{i}Y_i=\dfrac{89}{9}=9.89$$

$$SS_{XX}=\sum_iX_i^2-\dfrac{1}{n}(\sum _{i}X_i)^2$$ $$=335-\dfrac{39^2}{5}=30.8$$

$$SS_{YY}=\sum_iY_i^2-\dfrac{1}{n}(\sum _{i}Y_i)^2$$ $$=1479-\dfrac{85^2}{5}=34$$

$$SS_{XY}=\sum_iX_iY_i-\dfrac{1}{n}(\sum _{i}X_i)(\sum _{i}Y_i)$$ $$=692-\dfrac{39(85)}{5}=29$$

$$r=\dfrac{SS_{XY}}{\sqrt{SS_{XX}SS_{YY}}}=\dfrac{29}{\sqrt{30.8(34)}}$$ $$=0.896155$$

Strong positive correlation.