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# Linear Regression online calculator

INSTRUCTION: Use ',' or new line to separate between values

## $$Equation\;of\;created\;line\;is\; Y = 0.931034x + 0.172416$$

$$\displaylines{---}$$
$$\displaylines{First\;we\;have\;to\;find\;mean\;of\;x\;values \\ \\ Mean = \frac{\sum_{i=1}^{n}x_{i}}{n} \\ \\ \,=\frac{2+4+6+7+8}{5} \\ \\ \,=\frac{27}{5} \\ \\ \Rightarrow \bar{x}= 5.4 \\ \\ Second\;we\;have\;to\;find\;mean\;of\;y\;values \\ \\ Mean = \frac{\sum_{i=1}^{n}y_{i}}{n} \\ \\ \,=\frac{3+3+5+6+9}{5} \\ \\ \,=\frac{26}{5} \\ \\ \Rightarrow \bar{y}= 5.2 \\ \\ }$$
$$No$$
$$x_{i}$$
$$y_{i}$$
$$(x_{i} - \bar{x})$$
$$(y_{i} - \bar{y})$$
$$(x_{i} - \bar{x})*(y_{i} - \bar{y})$$
$$(x_{i} - \bar{x})^2$$
$$1$$
$$2$$
$$3$$
$$-3.4$$
$$-2.2$$
$$7.48$$
$$11.56$$
$$2$$
$$4$$
$$3$$
$$-1.4$$
$$-2.2$$
$$3.08$$
$$1.96$$
$$3$$
$$6$$
$$5$$
$$0.6$$
$$-0.2$$
$$-0.12$$
$$0.36$$
$$4$$
$$7$$
$$6$$
$$1.6$$
$$0.8$$
$$1.28$$
$$2.56$$
$$5$$
$$8$$
$$9$$
$$2.6$$
$$3.8$$
$$9.88$$
$$6.76$$
$$Total$$




$$21.6$$
$$23.2$$
$$\displaylines{}$$
$$\displaylines{b= \frac{\sum_{i=1}^{n}(x_{i} - \bar{x})(y_{i} - \bar{y})}{\sum_{i=1}^{n}(x_{i} - \bar{x})^{2}} \\ \\ From\;the\;table\;total\;we\;will\;get\;numerator\;and\;denominator \\ \\ \Rightarrow \frac{21.6}{23.2} \\ \\ \Rightarrow \mathbf{\color{Red}{0.931034}} \\ \\ a = \bar{y}-b* \bar{x} \\ \\ \Rightarrow \mathbf{\color{Red}{0.172416}} \\ \\ Equation\;of\;line\;\Rightarrow\;y\;=\;a+b*x \\ \\ \Rightarrow y = 0.172416+0.931034*x \\ \\ }$$