Question

The data below represent the number of days absent, x, and the final grade, y, for a sample of college students at a large university. Complete parts (a) through (e) below. No. of absences, x 0 1 2 3 4 5 6 7 8 9 Final grade, y 87.6 84.7 81.8 79.4 76.4 72.0 62.6 670 64.1 61.2 (a) Find the least squares regression line treating the number of absences, x, as the explanatory variable and the final grade, y, as the response variable. + (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. For every day absent, the final grade falls by on average OB. For every unit change in the final grade, the number of days absent falls by days on average Click to select your answer(s).

Answer 1

a)

S.No х 1 2 3 4 5 6 7 8 9 10 Total 0 1 2 3 4 5 6 7 8 9 45 87.6 84.7 81.8 79.4 76.4 72 62.6 67 64.1 61.2 (x-x) 20.2500 12.2500 6.2500 2.2500 0.2500 0.2500 2.2500 6.2500 12.2500 20.2500 82.5000 SSX (y-7) 193.77 121.44 65.93 32.72 7.40 2.82 122.77 44.62 91.78 155.75 838.9960 (x-x)(y-7) -62.6400 -38.5700 -20.3000 -8.5800 -1.3600 -0.8400 - 16.6200 -16.7000 -33.5300 -56.1600 -255.3000 736.8 73.6800 Mean 4.500 SSY SXY sample size n: 10 4.5000 y = 73.6800 SO (X-X) = Sw Z(X-X)(y-7)= slope- B. = S./5.- intercepta B. = V-B,x= 82.500 -255.300 -3.0945 Co 87.6055

y^ = -3.095x+87.605

b)

for slope : option A is correct : blank is : 3.095

for intercept : option A is correct ":blank is :87.605

predicted grade=87.605+5*-3.095=

72.1

residual =76.4-72.1 =4.3

Final grade is above average