# What is the regression equation based on the following?: {(4,2),(1,3),(2,3),(4,6),(6,7)}

Jan 10, 2016

$y = 0.76316 x + 1.60526$

#### Explanation:

Inputting these values into a calculator in double stat mode (linear regression mode) yields :

y-intercept : $a = 1.60526$.

gradient : $b = 0.76316$.

coefficient of correlation : $r = 0.68621$.

Hence the equation of the least squares line of best fit through all the data points is given by

$y = 0.76316 x + 1.60526$.

Graphically :

graph{0.76316x+1.60526 [-5.62, 14.38, -2.28, 7.72]}

Since $r$ is not that close to $1$, it implies that a linear fit is not a very good approximation for this data and lots of actual data points will lie very far off the least squares line of best fit.