- #1

chwala

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- Homework Statement
- See attached.

- Relevant Equations
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The question is as shown below. ( Text book question).

The textbook solution is indicated below.

Discussion;

Now they seemingly used ##r=1## to arrive at ##x=0.8+0.2y##. That is,

##y=-4+5x##

then, since ##r=1##, ...implying perfect correlation therefore,

##5x=4+y##

##x=0.8+0.2y##

My other way of doing this (as we we would not always have ##r=1##) would be;

##\bar x=a+b\bar y##

##b=\dfrac{S_{xy}}{S_{yy}}##=##\dfrac{87.5}{437.5}=0.2##

##a=\dfrac{21}{6}-\dfrac{0.2×81}{6}=0.8## therefore,

##x=0.8+0.2y##

Any other approach or insight is highly welcome.

The textbook solution is indicated below.

Now they seemingly used ##r=1## to arrive at ##x=0.8+0.2y##. That is,

##y=-4+5x##

then, since ##r=1##, ...implying perfect correlation therefore,

##5x=4+y##

##x=0.8+0.2y##

My other way of doing this (as we we would not always have ##r=1##) would be;

##\bar x=a+b\bar y##

##b=\dfrac{S_{xy}}{S_{yy}}##=##\dfrac{87.5}{437.5}=0.2##

##a=\dfrac{21}{6}-\dfrac{0.2×81}{6}=0.8## therefore,

##x=0.8+0.2y##

Any other approach or insight is highly welcome.

Last edited: