In this question, you will find the least-squares line,

y=Ax+B

through the points

(0,3), (1, 2), (4, 3)

and

(7, 5).

The error (sum of squared errors) is a function ofAandB. State this function. (Give an answer in terms ofAandB.)

E=

We want to find the values ofAandBthat minimize this function. As usual, we do this by calculating partial derivatives and then solving the simultaneous equations that result from setting both derivatives equal to zero. Calculate the partial derivatives. (Give answers in terms ofAandB.)

E

A

=

E

B

=

Set both partial derivatives equal to zero. Rearrange the equation

E

A

= 0

to giveAin terms ofB. A=

Now, substitute the above into the equation

E

B

= 0

and solve forB. (Give an exact numerical answer with no variables. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) B=

Finally, find the value ofA. (Give an exact numerical answer with no variables. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) A=