The following table shows final grades of 10 students in Algebra and Physics.
Algebra (x) 75 80 93 65 87 71 98 68 84 77
Physics (y) 82 78 86
72
91 80 95 72 89 74
(1) Find both the least squares lines.
(ii) If a student receives 75 marks in Algebra, what is his expected score in Physics?
(iii) If a student receives 95 marks in Physics, what is his expected score in Algebra?
Answers
Given : The following table shows final grades of 10 students in Algebra and Physics.
Algebra (x) 75 80 93 65 87 71 98 68 84 77
Physics (y) 82 78 86 72 91 80 95 72 89 74
To Find : (1) Find both the least squares lines.
(ii) If a student receives 75 marks in Algebra, what is his expected score in Physics?
(iii) If a student receives 95 marks in Physics, what is his expected score in Algebra
Solution:
Algebra Physics
x y
75 82
80 78
93 86
65 72
87 91
71 80
98 95
68 72
84 89
77 74
y = 0.661x + 29.12
R² = 0.760
a student receives 75 marks in Algebra
expected score in Physics = 0.661(75) + 29.12 = 78.7
Physics Algebra
y x
82 75
78 80
86 93
72 65
91 87
80 71
95 98
72 68
89 84
74 77
x = 1.150y - 14.39
R² = 0.760
95 marks in Physics
=> expected score in algebra = 1.150(95) - 14.39 = 94.86
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