Question

Help on this question of Linear Algebra, thanks.

Find the equation of the least squares line for the following data: (1,2), (2,4), (3,7), (4,8), (5,10) Then make a table that displays data point 2-values, data point y-values, and the least square line values at data point x-values.

Answer 1

In tabular form the data is shown as

х X^2 1 у 2 4 ху 2 8 1 4 N 3 7 21 9 8 32 16 4 5 10 50 25 Total 15 31 113 55

Now the eqution of line of best fit is of the form

$y=ax+b$

TO determine a and b we have the normal equations as

$\sum y=a\sum x+nb \\~~~~~ \sum xy=a\sum x^2 +b \sum x$

Use the values from the table above we get

Solving the two we get

Hence the least square line of best fit is $y=2x+0.2$   

The data points along with the least square line is shown below

+ 10 (5.10) 8 (4.8) (3.7) 6 (2,4) (1.2) X 1 2 3 4 5 6