Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

21.
Regression of saving (s) of a family on income y may be expressed as s = a + $\frac{y}{m}$ , where a and m are constants. In a random sample of 100 families the variance of savings is one quarter of the variance of incomes and the correlation coefficient is found to be 0.8, the value of m is

0.8

1.25

0.25

None of these

None of these

$Given, s = a + \frac{y}{m}, {σ_{s}}^{2} = \frac{1}{4} {σ_{y}}^{2} and r = 0.8 ∴ s = a + \frac{y}{m} Now, s - s = \frac{1}{m} (y - y) . . . (i) \Rightarrow \sum (s - s) (y - y) = \frac{1}{m} \sum {(y - y)}^{2} \Rightarrow cov (s, y) = \frac{1}{m} {σ_{y}}^{2} . . . (ii) Since, r = \frac{cov (s, y)}{σ_{s} σ_{y}} ∴ 0.8 = \frac{\frac{1}{m} {σ_{y}}^{2}}{σ_{s} σ_{y}} \Rightarrow 0.8 = \frac{1}{m} . \frac{σ_{y}}{σ_{s}} \Rightarrow 0.4 = \frac{1}{m} [∵ σ_{s} = \frac{1}{2} σ_{y}] \Rightarrow m = 2.5$

Previous Year Papers

Test Series

Test Yourself

Linear Programming

Multiple Choice Questions