Question

If you want to fit a linear regression line y=a+bx from the above data, then what is the value of 'a'?

Answer 1

$$\bar{x}=\dfrac{\sum_ix_i}{n}$$

$$\bar{y}=\dfrac{\sum_iy_i}{n}$$

$$SS_{xx}=\sum_i(x_i-\bar{x})^2=\sum_ix_i^2-n(\bar{x})^2$$

$$SS_{yy}=\sum_i(y_i-\bar{y})^2=\sum_iy_i^2-n(\bar{y})^2$$

$$SS_{xy}=\sum_i(x_i-\bar{x})(y_i-\bar{y})=\sum_ix_iy_i-n\bar{x}\bar{y}$$

$$b=\dfrac{SS_{xy}}{SS_{xx}}$$

$$a=\bar{y}-b\bar{x}$$