On simplifying (-342-8) - (-5/2 + 1)

Step-by-step explanation:

A) The least squares regression equation has form:

y = m·x + b

In order to calculate slope and intercept, you need to follow these steps (remember x = test scores and y = average sleep, N = total number of students):

1) For each value, calculate x² 

2) For each couple of values, calculate x·y

3) perform the sums: ∑x, ∑y, ∑x² and ∑xy

4) Calculate the slope by the formula:

5) Calculate the intercept by the formula:

6) Assemble the equation.

For steps 1, 2 and 3 values are in the table attached

= 0.091

= -0.343

Therefore the least squares regression equation is:

y = 0.091·x - 0.343

B) Use the inverse of the previously found equation to calculate x (= test score) when y = 8:

x = (8 + 0.343) / 0.091

  = 91.7

Hence, a student who sleeps an average of 8 hours a night scores on average 91.7% on a test.