Question

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

Answer 1

`y=0.76316x+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=0.76316x+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.