Q68 · CSIR NET Chemistry, June 2012
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
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
| 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 |
(a)$\mathrm{m}_{\mathrm{A}}>\mathrm{m}_{\mathrm{B}}, \mathrm{C}_{\mathrm{A}}>\mathrm{C}_{\mathrm{B}}$
(b)$\mathrm{m}_{\mathrm{A}}<\mathrm{m}_{\mathrm{B}}, \mathrm{C}_{\mathrm{A}}>\mathrm{C}_{\mathrm{B}}$
(c)$\mathrm{m}_{\mathrm{A}}>\mathrm{m}_{\mathrm{B}}, \mathrm{C}_{\mathrm{A}}<\mathrm{C}_{\mathrm{B}}$
(d)$\mathrm{m}_{\mathrm{A}}<\mathrm{m}_{\mathrm{B}}, \mathrm{C}_{\mathrm{A}}<\mathrm{C}_{\mathrm{B}}$
Answer
Answer: C ✓ checked by 4AB · confidence high
Explanation
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).
Study loop for Data Analysis