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.

A) answer: the least regression equation is y = 6.3x + 38.7the least regression equation is the equation of the line that best fits the set of data, therefore it will be in the form: y = m·x + bin order to find the least regression equation, consider the pairs of data (x, y) where x = hours of sleep and y = test score (see the attached picture).1) count how many pairs you have: n.2) for each pair, compute x² and x·y.3) perform the sums: ∑x, ∑y, ∑x², ∑x·y.4)  the slope can be found by the formula  = 6.333333the y-intercept can be found by the formula: = 38.6875hence, the least regression equation is  y = 6.3·x + 38.7b) answer: the approximate test score of a student who sleeps an average of 8 h per night is 89.in order to estimate the test score for a certain amount of hours of sleep, we can use the least regression equation; let's find the value of y if x = 8 by substituting in the formula: y = 6.3·x + 38.7 if x = 8y = 6.3·8 + 38.7     y = 89.1hence, we expect that a student who sleeps 8 hours scores on average 89 on a test.

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