# Give the following data, which is the equation of the

Teddy Dillard 2021-12-11 Answered
Give the following data, which is the equation of the regression line?
$\begin{array}{|c|c|} \hline X&0&3&4&5&12\\ \hline Y&8&2&6&9&12\\ \hline \end{array}$
a. $$\displaystyle{y}={4.88}+{0.625}{x}$$
b. $$\displaystyle{y}={4.98}+{0.425}{x}$$
c. $$\displaystyle{y}={4.98}+{0.725}$$
d. $$\displaystyle{y}={4.88}+{0.525}$$

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Step 1
Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered.
Solution:
Given:
$\begin{array}{|c|c|} \hline X&0&3&4&5&12\\ \hline Y&8&2&6&9&12\\ \hline \end{array}$
Equation of regression line is,
$$\displaystyle{Y}={a}+{b}{X}$$
where, $$\displaystyle{a}={\frac{{{\left(\sum{y}\right)}{\left(\sum{x}^{{{2}}}\right)}-\sum{x}{\left(\sum{x}{y}\right)}}}{{{n}{\left(\sum{x}^{{{2}}}\right)}-{\left(\sum{x}\right)}^{{{2}}}}}}$$
$$\displaystyle{b}={\frac{{{n}{\left(\sum{x}{y}\right)}-{\left(\sum{x}\right)}{\left(\sum{y}\right)}}}{{{n}{\left(\sum{x}^{{{2}}}\right)}-{\left(\sum{x}\right)}^{{{2}}}}}}$$
Step 2
Table for calculation:
$\begin{array}{|c|c|} \hline X&Y&XY&X^{2}\\ \hline 0&8&0&0\\ \hline 3&2&6&9\\ \hline 4&6&24&16\\ \hline 5&9&45&25\\ \hline 12&12&144&144\\ \hline \sum=24&\sum=37&\sum=219&\sum=194\\ \hline \end{array}$
$$\displaystyle\therefore{a}={\frac{{{37}\times{194}-{24}\times{219}}}{{{5}\times{194}-{24}^{{{2}}}}}}$$
$$\displaystyle={4.88}$$
and $$\displaystyle{b}={\frac{{{5}\times{219}-{24}\times{37}}}{{{5}\times{194}-{24}^{{{2}}}}}}$$
$$\displaystyle={0.525}$$
Therefore regression equation is,
$$\displaystyle{Y}={4.88}+{0.525}{X}$$
Answer : Equation of regression line is $$\displaystyle{Y}={4.88}+{0.525}{X}$$.