Question

For a given data set
x 5 15 25 35 45 50
y 10 18 20 25 32 45
i. Find the value of , and
ii. Write the normal equations and estimate the equation of line of regression of Y on x.
iii. Find the value of sample correlation coefficient for the above data.

Answer 1

Answer on Question #46539 – Math – Statistics and Probability

Problem.

For a given data set

x 5 15 25 35 45 50

y 10 18 20 25 32 45

i. Find the value of, and

ii. Write the normal equations and estimate the equation of line of regression of Y on x.

iii. Find the value of sample correlation coefficient for the above data.

Remark: The part of question is missed. I suppose that the correct statement is

" For a given data set

i. Find the value of $\sum x^{2}$ , $\sum y^{2}$ and $\sum xy$

ii. Write the normal equations and estimate the equation of line of regression of Y on x.

iii. Find the value of sample correlation coefficient for the above data."

(see http://www.bits-pilani.ac.in/uploads/ReadPDFDOC/AAOC C111 515 C 2009 2.doc)

Solution:

i.

Then $\sum x^{2} = 6625, \sum y^{2} = 4498$ and $\sum xy = 5385$ .

ii. The normal equation for $a$ and $b$ are $a\sum x + nb = \sum y$ and $a\sum x^2 + b\sum x = \sum xy$ . Hence

$175a + 6b = 150$ and $6625a + 175b = 5385$ . Then $a = \frac{1212}{1825}$ and $b = \frac{411}{73}$ . Hence the equation of

the regression line is $y = ax + b = \frac{1212}{1825} x + \frac{411}{73}$ .

Answer: $y = \frac{1212}{1825} x + \frac{411}{73}$ .

iii. The sample correlation coefficient

$$r = \frac {\sum_ {i = i} ^ {6} (x _ {i} - \bar {x}) (y _ {i} - \bar {y})}{\sqrt {\sum_ {i = i} ^ {6} (x _ {i} - \bar {x}) ^ {2}} \sqrt {\sum_ {i = i} ^ {6} (y _ {i} - \bar {y}) ^ {2}}} \approx 0. 9 4 7.$$

Answer: $r \approx 0.947$ .

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