JEE Main & Advanced Mathematics Statistics Question Bank Self Evaluation Test - Statistics

For 10 observations on price (x) and supply (y), the following data was obtained: \[\sum{x=130,\sum{y=220,}}\] \[\sum{{{x}^{2}}=2288,\sum{{{y}^{2}}=5506}}\] and \[\sum{xy=3467}\] What is line of regression of y on x?

A) \[y=0.91x+8.74\]

B) \[y=1.02x+8.74\]

C) \[y=1.02x-7.02\]

D) \[y=0.91x-7.02\]

Correct Answer: B

Solution :

[b] Line of regression of y on x is:

\[y-\bar{y}={{b}_{yx}}(x-\bar{x})\]

\[\bar{y}=\frac{\Sigma y}{n};\bar{x}\frac{\Sigma x}{n}\Rightarrow \bar{y}=\frac{220}{10}=22;\bar{x}=\frac{130}{10}=13\]

\[{{b}_{yx}}=r.\frac{{{\sigma }_{y}}}{{{\sigma }_{x}}}\]

\[r=\frac{n\Sigma xy-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma {{x}^{2}}-{{(\Sigma x)}^{2}}][n\Sigma {{y}^{2}}-{{(\Sigma y)}^{2}}]}}\]

\[=\frac{10(3467)-(130)(220)}{\sqrt{[(10\times 2288)-{{130}^{2}}][(10\times 5506)-({{220}^{2}})]}}\]

\[{{\sigma }_{y}}=\sqrt{\frac{\Sigma {{y}^{2}}}{n}-{{\left( \frac{\Sigma y}{n} \right)}^{2}}}\Rightarrow {{\sigma }_{y}}=8.2;{{\sigma }_{x}}=7.73.\]

\[\Rightarrow {{b}_{xy}}=0.962\times \frac{8.2}{7.73}=1.02\]

\[\Rightarrow \]Line of regression of y on x is;

\[y-22=1.02(x-13)\]

\[\Rightarrow y=1.02x+8.74\]