PYQs Based Test - 20 : Correlation and Regression Analysis

Calculate the correlation coefficient between the following values :

x: 3, 5, 1, 7, 5

y: 4, 3, 0, 8, 2

There is no value of x that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find the value of x that minimizes the sum of squares of the errors in the two equations. __________

2x = 3

4x = 1

In the regression model ( y = a + bx) where x̅ = 2.50, y̅ = 5.50 and a = 1.50 (x̅ and y̅ denote mean of variables x and y and a is a constant), which one of the following values of parameter 'b' of the model is correct?

Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is _______ (round off to 2 decimal places).

The two-regression equation of variable $\mathrm{x}$ and $\mathrm{y}$ are

$\mathrm{y}=0.8x+9.8$ and $\mathrm{x}=10.2+0.6y$

The coefficient of correlation between $\mathrm{x}$ and $\mathrm{y}$ is