the table shows the test scores and the sleep averages of several students.
test score (%) 88,75,76,92,96,94,83,90,99,65,77,88 ,82,83,94,97
average sleep (h) 7,6.5,6,7.5,8,7,6.5,8,8.5 5,7,9,8,8.5,8.5,9
(a)write the least squares regression equation that models the data. let x = the test score and y = average sleep.
(b)use the equation to determine the approximate test score of a student who sleeps an average of 8 h a night. i understand if you don't want to give me the answer but can you at least explain what i have to do.

To begin with, there are few values that we need to work out first. We need:
∑xy ⇒ in words, multiply each pair of value x and y, then add the answers)
∑x² ⇒ in words, square each value of x, then add the answers)
∑x ⇒ in words, add all values of x
∑y ⇒ in words, add all values of y

in total, we have 16 pairs of data, so we have n=16

∑xy = 10466
∑x² = 120207
∑x = 1379
∑y = 120

The regression equation is given by , where
and a=(mean of y)+b(mean of x)

∑xy-(∑x∑y)/n

∑x²-((∑x)²/n)

then

Mean of x = ∑x/n = 1379/16 = 86.1875
Mean of y = ∑y/n = 120/16 = 7.5

Hence the equation is

Iagree that is the answer to the question