A random sample of eight pairs of values of $x$ and $y$ is used to obtain the following equations of the regression lines of $y$ on $x$ and of $x$ on $y$ respectively.
$y=-\frac{7}{10}x+\frac{151}{10}$, $x=-\frac{7}{6}y+20$
Seven of the pairs of data are given in the table.
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Find the eighth pair of values of $x$ and $y$. [5]
Determine the value of the product moment correlation coefficient, and say what it leads you to expect about the scatter diagram for this sample. [4]
Let $Y$ be the value obtained by substituting a sample value of $x$ into the equation of the regression line of $y$ on $x$. Evaluate $Y$ for each of the eight values of $x$ and verify that ${\sum (y - Y)^2 = 8.8}$.[4]
For each of the eight sample values of $x$, ${Y}'$ is given by ${Y}'=a+bx$, where $a$ and $b$ are any constants. What can you say about the value of $\sum{{{\left( y-{Y}' \right)}^{2}}}$?[2]

A random sample of eight pairs of values of $x$ and $y$ is used to obtain the following equations of the regression lines of $y$ on $x$ and of $x$ on $y$ respectively.

$y=-\frac{7}{10}x+\frac{151}{10}$, $x=-\frac{7}{6}y+20$

Seven of the pairs of data are given in the table.

Find the eighth pair of values of $x$ and $y$. 

Determine the value of the product moment correlation coefficient, and say what it leads you to expect about the scatter diagram for this sample. 

Let $Y$ be the value obtained by substituting a sample value of $x$ into the equation of the regression line of $y$ on $x$. Evaluate $Y$ for each of the eight values of $x$ and verify that ${\sum (y - Y)^2 = 8.8}$.

For each of the eight sample values of $x$, ${Y}'$ is given by ${Y}'=a+bx$, where $a$ and $b$ are any constants. What can you say about the value of $\sum{{{\left( y-{Y}' \right)}^{2}}}$?

N2003 P2 Q11

N2003 P2 Q11

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