List of practice Questions

One of the normal equations for fitting a straight line \(y=a+bx\) is
One of the normal equations for fitting a straight line \(y=a+bx\) is
Correlation coefficient is independent of
The regression lines of a sample are $x + 6y = 6$ and $3x + 2y = 10$. Then the sample means and the correlation coefficient are
Let $X$ be a random variable having probability density function $f_{X}(x)=\begin{cases}2x & 0<x<1 \\ 0 & \text{otherwise}\end{cases}$ then the density of $Y=\frac{1}{X^{\frac{1}{\alpha}}}$ is
In bivariate data following results were obtained.
Mean value of X = 53, Mean value of Y = 27, byx = -1.5, bxy = 0.2. Find the regression equation of X on Y and Y on X.
Equations of two lines of regression are \( 2x - 5y + 33 = 0 \) and \( 3x - 9y - 108 = 0 \). Which one is the regression line of \( y \) on \( x \)?
Regression analysis is a mathematical measure of the _______ of relationship between two or more variables.
The term "Residual" is defined as:
If \(2Y - X - 50 = 0\), \(3Y - 2X - 10 = 0\) are the two regression equations, then the mean values of the variables \(X\) and \(Y\) respectively are:
If \( \bar{x} = 4 \), \( \bar{y} = 8 \), \( \sigma_x = 2 \), \( \sigma_y = 3 \), and \( r = 0.3 \), then the line of regression of \( y \) on \( x \) is
Three points in the $x$–$y$ plane are $(-1,0.8)$, $(0,2.2)$, and $(1,2.8)$. The value of the slope of the best fit straight line in the least square sense is \underline{\hspace{1cm}} (Round off to 2 decimal places).
In regression analysis independent variable is also called as
Given below are two statements:
Statement I: Line of regression of y on x is the line which gives the best estimate for the value of y for any specified value of x. 
Statement II: Line of regression of x on y is the line which gives the best estimate for the value of x for any specified value of y. 
In the light of the above statements, choose the correct answer from the options given below:
The regression analysis confined to the study of only two variables at a time, is called as
Which of the following is the linear regression equation