Question

For problems 9 - 10, find the correlation coefficient value, determine the strength of the value, and find the regression equation 9) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. Current GPA 3.6 3.7 3.9 3.6 Entering GPA 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7 3.9 3.8 3.7 3.9 3.8 4.0

Answer 1

Solution: let X= Entering GPA Y = Current GPA. Х 3.5 3.8 3.6 3.6 3.5 3.9 400 3.9 3.5 3.7 Epc = 37 nEO 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0 Ey= 37.9 T= {x n 37 10 3.7 2= 3.7 y = Ey 37.9 10 = 3,79 n y = 3.79

formula to calculate correlation coefficient 7= E(x-7)(y-7) E(x-70)2. Ely-7)? Now, we have to calculate {(x-7) ² Ely-7² and {(x-7)(y-7)

X = 37 , Y = 3-71 2 (x) 어 G-4) 0 19 -0009 11 x 3.5 3. 8 306 306 3.5 3.9 0 3.9 3.5 307 B06 13.ㅋ 1309 1306 39 318 307 309 308 -0.2 01 - 0 1 -01 -0.2 0.11 (<-T).(y-T) 01038 -00009 - 01011 01011 - 0 1022 (X-T) 0109 0101 0 0 o0l 004 009 009 00에 Oo9 사 0.001 0.00 81 이리 010361 0012) 0.0 001 0.0081 0 이 2 ) 0 0 001 0.04 11 (V)= 0.161 02. 0 1002. -19 에 o이 -0.01 0 | 아이 02 0 3 012 -0.2 - O-027 0022 01002 . 0 0 0 0 S(X-文)= 0.32 (X-X). (N-) = 0. 이

NE Oool 0.32 0.169 8= oool Oool 0.23255 0:05408 correlation p=0.043 Strength of relationship = weak (very) Direction of Relationship = positive . Regression line is given by y = a + bx where y = current gpa 2= entering apa a = Intercept b = slobe

formula to calculate slope (b) b= {(x-7), (y-7) (4-3) b 0.01 0132 0.03125 b=0003125 formule to calculate Intercept (a) a Y -b Ž = 3.79 – 0.03125 X 3.7 3. 79 - 0:115625 3.674375 a= 3.674375 Regression line : Y = 3.674375 + 0.03125 X Y = Current GP X = Entering GPA.