3. 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 hours a night. show your work. can anyone ?

A) the least squares regression equation has form: y = m·x + bin 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·y3) perform the sums:   ∑x,  ∑y,  ∑x² and  ∑xy4) 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= -0.343therefore the least squares regression equation is: y = 0.091·x - 0.343b) use the inverse of the previously found equation to calculate x (= test score) when y = 8: x = (8  + 0.343) / 0.091    = 91.7hence, a  student who sleeps an average of 8 hours a night scores on average 91.7% on a test.