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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Expert Answer

Debbie Moore
Answered 2021-12-12 Author has 5319 answers
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 \(\displaystyle{Y}={4.88}+{0.525}{X}\).
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