Paper: CSIR-NET June 2012 · Subject: Physical Chemistry · Chapter: Data Analysis · Topic: Regression Fitting · Marks: 2 · Difficulty: Medium
Two data sets involving the same variables X and Y are given below
X
4.1
4.2
4.3
4.4
4.5
4.6
Y(set A)
10.2
10.6
10.9
11.5
11.8
12.2
Y (set B)
10.2
10.6
11.1
11.3
11.8
12.2
If the slopes and intercepts of the regression lines for the two sets are denoted by $\left(\mathrm{m}_{\mathrm{A}}, \mathrm{m}_{\mathrm{B}}\right)$ and $\left(\mathrm{C}_{\mathrm{A}}, \mathrm{C}_{\mathrm{B}}\right)$ respectively are
Both sets have the same mean Y (11.2) and the same X values. Set A differs from B only by −0.2 at x = 4.3 and +0.2 at x = 4.4, so S_xy(A) > S_xy(B) and m_A > m_B. C = ȳ − m x̄ then gives C_A < C_B (c).