There's enough arithmetic involved in this that it is convenient to let a machine solver of some sort figure it out. Most graphing or scientific calculators will work this problem for you (consult the manual for yours). If you insist on doing it by hand, you must compute several average values:
• a1 = the average of sleep hours (h)
• a2 = the average of test scores (%)
• a3 = the average of the product of sleep hours and test scores (h×%)
• a4 = the average of the square of sleep hours (h×h)
a) The equation of your best-fit (least-squared-error) line is then
% = (a3 - (a1×a2))/(a4 - (a1)²)×(h - a1) + a2
In numbers, this is
% = 6.33333h + 38.6875
b) For h=8, the equation gives
6.33333×8 + 38.6875 ≈ 89.4
• a1 = the average of sleep hours (h)
• a2 = the average of test scores (%)
• a3 = the average of the product of sleep hours and test scores (h×%)
• a4 = the average of the square of sleep hours (h×h)
a) The equation of your best-fit (least-squared-error) line is then
% = (a3 - (a1×a2))/(a4 - (a1)²)×(h - a1) + a2
In numbers, this is
% = 6.33333h + 38.6875
b) For h=8, the equation gives
6.33333×8 + 38.6875 ≈ 89.4