Question

In a bivariate data, $\sum _{}x=30,\sum _{}y=400,\sum _{}{x}^2=196,\sum _{}xy=850,$ and $n=10$. The regression coefficient of $y$ on $x$ is

• A. $-3.1$
• B. $-3.2$
• C. $-3.3$
• D. $-3.4$

Answer 1

The correct option is C

$-3.3$

Explanation for the correct option.

Find the value of $b_{yx}$.

The regression coefficient of $y$ on $x$ is given by the formula ${\mathit{b}}_{\mathbf{y}\mathbf{x}}\mathbf{=}\frac{{\displaystyle \sum _{}xy-\frac{1}{n}\left(\sum _{}x\sum _{}y\right)}}{{\displaystyle \sum _{}{x}^2-\frac{1}{n}{\left(\sum _{}x\right)}^2}}$.

Now substitute the values $\sum _{}x=30,\sum _{}y=400,\sum _{}{x}^2=196,\sum _{}xy=850,n=10$ in the formula and find the coefficient.

$\begin{array}{rcl}{b}_{yx}& =& \frac{{\displaystyle \sum _{}xy-\frac{1}{n}\left(\sum _{}x\sum _{}y\right)}}{{\displaystyle \sum _{}{x}^2-\frac{1}{n}{\left(\sum _{}x\right)}^2}}\\ & =& \frac{850-{\displaystyle \frac{1}{10}}\left(30\times 400\right)}{196-{\displaystyle \frac{1}{10}}{\left(30\right)}^2}\\ & =& \frac{850-1200}{196-90}\\ & =& \frac{-350}{106}\\ & =& -3.3\end{array}$

The regression coefficient of $y$ on $x$ is $-3.3$.

Hence, the correct option is C.