Linear Regressions (need help as soon as possible please!)

Question

A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 68.

Homework Grade (x)	Test Grade (y)
57	62
85	75
80	76
75	68
87	89
50	38
58	45
79	64

Regression equation:________________

Final Answer:__________

Answer 1

regression equation: Y= bX+a,

b=about 1.08, a=about -12.03

Y=1.08278X - 12.03350

or

Y= 1.08X -12.03, rounded off to 2 decimal places

Y = 1.08(68)-12.03

=estimated 61.45 test grade

if 68 =homework grade

sum of X's =571

sum of Y's = 522

sum of X^2 = 1417.875

sum of XY's = 1535.25

n=8

using S for the capital Greek letter Sigma

b = (nSXY -SXSY)/(nSX^2 - (SX)^2)

a =(SY-bSX)/n

plug in the values, solve for a and b, by tedious long hand

or use an online regression equation calculator

or hand held calculator

just a rough check on the solution

look for two homework grades near 68

just below 68 and about the same just above. that's 58 and 79

58 is 10 below 68, 79 is 11 above

corresponding test grades are 45 and 69

take their average (45+69)/2 = 114/2 = 57

that's relatively close to the predicted 61.45, off by 4.45

the solution looks in the right range.

6 of the 8 test grades are lower than the homework grades

so you expect the test grade for the 68 homework grade to be less than 68

even if you hadn't seen the table of values, you'd expect test grades to be less than homework grades, given likely time pressure on the test relative to homework, plus homework allows access to more resources than during a test