Question

64. What is the process through which we can calculate a line that goes through a scatter plot with a linear pattern?

Short answer

The process through a line that goes through a scatter plot with a linear pattern is linear regression.

Step-by-step solution

Given Information

A line that goes through a scatter plot with a linear pattern.

Explanation

Linear regression is a linear equation of two variables from which one is independent and dependent on the other. Let $X$be the independent variable, and $Y$ be the dependent. Then linear equation is represented by:
$Y=a+bX$
where $a$and $b$are coefficients.

Calculation

And the formula for calculating this coefficients is as follows:
$\widehat{b}=r\times \frac{s_y}{s_x}$
$\widehat{a}=\overline{y}-\widehat{b}\overline{x}$

$\widehat{y}=\widehat{a}x+\widehat{b}$

$r=\frac{n\sum xy-\sum x\sum y}{\sqrt{\left(n\sum x^2-{\left(\sum x\right)}^2\right)\left(n\sum y^2-{\left(\sum y\right)}^2\right)}}$

Also, if we want to obtain the line on the scatter plot without the prior computation, we must label data under variables $X$ and $Y$ and select the scatter plot in Excel. Then add a trendline with an equation, and we'll get a scatter with a fit line and an equation that must be the same as the equation we got through computation.