Question

Given the following set of data on ages versus CGPA of a group of selected graduate students: 30 34 35 44 45 Age, x 27 CGPA, Y 3.6 3.7 3.5 3.6 3.2 3.3 Draw a scatter diagram for the above data (3 marks) li. Find the regression line of yon x using the least squares method. (15 marks) il What would be the age, xif the CGPA is 3.87 (2 marks) 1. Calculate the Pearson's product moment correlation coefficient, (5 marks) V. Explain the relationship from the value obtained in (lv). (2 marks) vi. Determine the coefficient of determination, (3 marks)

Answer 1

3.8 3.6 Y-Dependent 3.4 - 3.2+ 27 32 37 42 47 X-Independent

Date Page T 30 |- Ma July (X-Mo. ² fy my? (oc-Ma) (Y -M.) 27 13.6 +8.833 78.0280 0.014 2.-1.031 13.7 75.833 0.217 34.028 6.067 -1.264 34 13.5 -1.833 0.017 3.361 R 0.031 35 |-0.833 0.117 0.694 0.014 10, 8-0.097 44 13.2 8. 167 -0.283 66.694 0,080 -2.314 45 9. 167 -0.183 84.028 0.034 -1.681 215 35.833 3.483 266,833 0.188 - 6.417 Mx= 35.83 My = 3.48 ssy SP 13.6 13.3 20.9 N (6) Regresion line Regression equation = ŷ = bata Here ba SP 6.42 Sx 266.83 -0.02405 = My-b moc = 3.48-C-0.02 x 35.83) 4.34503 ( Mx = 215 35.83 and My = 20.9 23.48 G -0.02405x + 4.34503 put (1) Age of a it CGPA I is 3.87 it on equation 3.8=-0.02405x + 4.34503 0.02405x = 0.54503 22.66

Date Page & Correlation Coefficient r = {(x-M.x) (y-May) Jessx) (ssy) -6.417 C266,833) (0.188) Oo9052 v The Relationship from vale obtained in Civ) This is a strong nagative (croelution which means that high & vaniable scores go with lowy vuniable Scone (and vice verra) 2 Coefficient of determination = Co.g052) 0.8194 2 k