Professor John Morton has just been appointed chairperson of the Finance Department at Westland University. In reviewing the department$$s cost records, Professor Morton has found the following total cost associated with Finance $101$ over the last five terms:

Term Number of Sections Offered Total Cost

Fall, last year $2$ $ $7,500$

Winter, last year $6$ $ $13,000$

Summer, last year $5$ $ $10,000$

Fall, this year $3$ $ $8,000$

Winter, this year $4$ $ $9,500$

Professor Morton knows that there are some variable costs, such as amounts paid to graduate assistants, associated with the course. He would like to have the variable and fixed costs separated for planning purposes.

$2-$a$.$ Using the least$-$squares regression method, estimate the variable cost per section and the total fixed cost per term for Finance $101.$

$2-$b$.$ Express these estimates in the form Y $=$ a $+$ bX$.$Professor John Morton has just been appointed chairperson of the Finance Department at Westland University. In reviewing the department$$s cost records, Professor Morton has found the following total cost associated with Finance $101$ over the last five terms:

Term Number of Sections Offered Total Cost

Fall, last year $2$ $ $7,500$

Winter, last year $6$ $ $13,000$

Summer, last year $5$ $ $10,000$

Fall, this year $3$ $ $8,000$

Winter, this year $4$ $ $9,500$

Professor Morton knows that there are some variable co sts$,$ such as amounts paid to graduate assistants, associated with the course. He would like to have the variable and fixed costs separated for planning purposes.

$3-$a$.$ Assume that because of the small number of sections offered during the Winter Term this year, Professor Morton will have to offer eight sections of Finance $101$ during the Fall Term. Compute the expected total cost for Finance $101.$

$3-$b$.$ Can you see any problem with using the cost formula from part $(2)$ to derive this total cost figure?