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

1 Answer
Trevor Ryan.
Jan 10, 2016

#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.

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