Question

Question 5: A mathematics placement test is given to all 1st year students at a small college. A student who receives a grade above 35 must take an extra mathematics course. The placement test scores and the final grades for 20 students who took the regular course were recorded. a. Find the equation of the regression line to predict course grades from placement test scores. b. If 60 is the minimum passing grade, below which placement test score should students in the future be denied admission to this course? Placement Test 50 35 40 55 80 Course Grade 53 41 56 68 91 to

Answer 1

Solution: We have two type of data. → take variable x as placement test. -> take variable y as Course grade. Now, we make linecon Alegression line to predict Course grade decal equation , 8 = bx +a where b = (x-Mx)(y-My) Elx-Mx)? 00 and a= My - bmx.

50 53 4 - 2 41 289 - 12 144 40 55 3 28 6,2 29.2 2x = 260 > Mx = 52 >> My = 260 EX 5 Now, b => b= 1277 We make below table 6 -> X y X - Mx Y-My (x-mx)3 (x-Ma)(y-my) 17.00 85 .-20.8 363.6 56 --5.8 69.6 68 9 12.00 80 91 84 817.6 EY - 309 E(X-MX32-1230 Eu-M)(1-2y) - 1277 is Mean Mx = Ex (n=5 obsesivations) η Mean My = Ey 61.8 => My = 309 => My = 5 Elx-M) (Y-My) >> b= 1.03821 1230 E (X-Mx)? My - b Mx -> a = 61.8 - (1.03821) (52) => a = 7.81301 io Linear regression equation is, û = 1,03821 X + 7,81301 @ Now we predict placement test four passing grade - 60 , =60 in above regreession equatior. 60 =1.03824 x + 7.81301 => 1.038 21% = 60 - 7,81301 => 52.18699 1.03821 50.27 At 60 grade . It must need 50,27 placement test Score: 409 students in the future be denied admission to this course. a = b & Take ĝ- x = X D 0

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