Question

Given the following sample observations, draw a scatter diagram on a separate piece of paper. (Round your answers to 3 decimal places.)

X:	-8	-16	13	3	16
Y:	60	249	159	2	339

The coefficient of correlation is  . Does the relationship between the variables appear to be linear?  (Click to select)  Yes  No

Try squaring the X- variable and then determine the correlation coefficient.  .

Answer 1

Here in this Question we have to calculate the correlation coefficient between x and y ,

Further the correlation coefficient is calculated using following steps :

The scatter plot of given data is,

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	-8	60	-480	64	3600
	-16	249	-3984	256	62001
	13	154	2002	169	23716
	3	2	6	9	4
	16	339	5424	256	114921
Sum =	8	804	2968	754	204242

The correlation coefficient rr is computed using the following expression:

The correlation coefficient between X and Y is 0.226 .

Which is very low Positive correlation between x and y Variable.

No the data is not linear.

Now,

We squared the all value of X and then find the correlation coefficient is as below,

The scatter plot of squared x values with y is,

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	64	60	3840	4096	3600
	256	249	63744	65536	62001
	169	154	26026	28561	23716
	9	2	18	81	4
	256	339	86784	65536	114921
Sum =	754	804	180412	163810	204242

The correlation coefficient rr is computed using the following expression:

When we squared the value of X then the correlation coefficient is 0.965 which is strong positive correlation coefficient.

After squaring the value of x the data founds the linear relationship.

Thank you.