The Method of Least Squares

The method applied for deriving the regression equations is known as

Find the regression equation of $X$ on $Y$ given that $n=5$, $\sum x = 30$, $\sum y = 40$, $\sum xy = 214$, $\sum x^2 = 220$,$\sum y^2 = 340$.

Write the regression equation of $Y$ on $X$ and its normal equations.

Find the linear regression equation of percentage worms $\left(Y\right)$ on size of the crop $\left(X\right)$ based on the following seven observations.

Find the regression equation of $X$ on $Y$ given that $n=5$, $\sum x = 40$, $\sum y = 50$, $\sum xy = 300$, $\sum x^2 = 350$,$\sum y^2 = 400$.

Using the method of least square, calculate the regression equation of $X$ on $Y$ from the following data.

Write the regression equation of $y$ on $x$ and its normal equations.

The regression equation of $y$ on $x$ for the following data:

$\begin{array}{lllllllllll}x& 41& 82& 62& 37& 58& 96& 127& 74& 123& 100\\ y& 28& 56& 35& 17& 42& 85& 105& 61& 98& 73\end{array}$

Is given by

Using the method of least square, calculate the regression equation of $X$ on $Y$ and $Y$ on $X$ from the following data and estimate $X$ where $Y$ is $16$.

Also determine the value of correlation coefficient

Using the method of least square, calculate the regression equation of $X$ on $Y$ from the following data.