Question

How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms).

x	3	6	12	20	26
y	60	95	140	170	177

(a) Make a scatter diagram of the data.

Then visualize the line you think best fits the data.

(b) Use a calculator to verify that ?x = 67, ?x² = 1265, ?y = 642, ?y² = 92,454, and ?xy = 10,432.

(c) Compute r. (Round to 3 decimal places.)

Answer 1

A )

We have to find scatter plot

By using the excel we can find out the scatter plot as

First enter all data in excel

Select all data ----------> Click on Insert --------> Scatter ------->Click on first graph ------> OK

***FOR ADDING THE REGRESSION LINE ON SCATTER DIAGRAM**

Right click on any point on scatter diagram --------> Add treadline ----------> Click on Display Equation chart ---> OK

We get the output as

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yes the regression line best fits the data.

B ) By using calculator we can calculate it as

	x	y	x^2	y^2	x*y
	3	60	9	3600	180
	6	95	36	9025	570
	12	140	144	19600	1680
	20	170	400	28900	3400
	26	177	676	31329	4602
Total	67	642	1265	92454	10432

C ) Correlation coefficient ( r ) gives the strength of linear relationship between x and y.

Correlation Coefficient ( r) can be calculated as

$r = \frac{\sum (x-\bar x)*(y-\bar y) }{\sqrt{\sum (x-\bar x)^2*\sum (y-\bar y)^2})}$

From the given data we get

$\bar x =\frac{\sum x}{n}=\frac{67}{5}=13.4$

$\bar y =\frac{\sum y}{n}=\frac{642}{5}=128.4$

we can calculate the correlation coefficient as

	x	y	( x-xbar )	(y-ybar)	(x-xbar)*(y-ybar)	( x-xbar )^2	(y-ybar)^2
	3	60	-10.4	-68.4	711.36	108.16	4678.56
	6	95	-7.4	-33.4	247.16	54.76	1115.56
	12	140	-1.4	11.6	-16.24	1.96	134.56
	20	170	6.6	41.6	274.56	43.56	1730.56
	26	177	12.6	48.6	612.36	158.76	2361.96
Total	67	642			1829.2	367.2	10021.2
xbar	13.4
ybar	128.4

we get   $r = \frac{\sum (x-\bar x)*(y-\bar y) }{\sqrt{\sum (x-\bar x)^2*\sum (y-\bar y)^2})}$

From the above data put all the values we get   

$r = \frac{1829.2 }{\sqrt{367.2*10021.2}}$

we get  $r=0.954$ .......( Answer )

we get Correlation coefficient = r = 0.954   .......( Answer )