Statistics Homework help!?

Question

Piersons R question.


The question is =

The data is:

Years sentencedAge
2025
2522
1547
1051
2128
1060
2223
2525
1845
1235

Using the Piersons r... I am having a problem with the equation obviously, b.c the last few questions Ive done Ive come out with the answer 0. 00Something. EIther way it always comes out to 0.00. I dont think this is possible. So, with this one....

This was what I plugged into the equation. If someone has the time and can go over this and maybe find my mistake, I would be greatful!

Pr= N{XY-{X{Y
-------------------
SQ. ROOT OF (N{X(SQUARED)-({X)SQUARED) SQUARE ROOT OF (N{YSQUARED- ({Y) SQUARED

Just a reminder of the equation as best as I could if anyone needs a refresher.

So, I got....


Pr= (10)(6054)-(178)(381)
------------------------------------------------
((10)(3468)-(178)squared) (10(16507)-(381)squared)

Then.
R= 60540-67818
-----------------------------
(34680-31684) (165070-145161)

And then.
-7278
---------------
(2996) (19909)



And.
-7278
---------
59647364


Which comes out to -0.00.

HELP!

Sry! The age didnt come out on it...
The data is:

Years sentenced Age
2025
2522
1547
1051
2128
1060
2223
2525
1845
1235

Age25
22
47
51
28
60
23
25
45
35

Answer 1

Correlation is a measurement that accesses the strength of linear correlation between 2 variables. The value range from -1 to +1.

The value of 0 indicates that the two variables are not linearly correlated.

The value of 1 indicates that 2 variables are strongly positively linearly correlated. It means that if the value of one variable increases then value of the other variable will tend to increase as well and vice versa.

The value of -1 indicates that 2 variables are strongly negatively linearly correlated. It means that if the value of one variable increases then value of the other variable will tend to decrease and vice versa.

The result of the correlation coefficient of your data is -0.86366 which indicate that there is a strong negative linear correlation between years sentenced and the age variables.

The details of computations are listed as of follow:

Sample size=10

Sample mean for years sentenced: (20+25+…+18+12)/10=17.18

Sample mean for age: (25+22+…+45+35)/10=36.1

Sample variance for years sentenced:

{(20-17.18)^2 + (25-17.18)^2 +…+(18-17.18)^2 +(12-17.18)^2 }/(10-1) =33.28889

Sample variance for age:

{(25-36.1)^2 + (22-36.1)^2 +…+(45-36.1)^2 +(35-36.1)^2 }/(10-1) =186.1

Covariance between years sentenced & age:

{(20-17.18)* (25-36.1) + (25-17.18)* (22-36.1) +…+(18-17.18)* (45-36.1) +(12-17.18)* (35-36.1) }/(10-1) = -61.18

Pearson Correlation coefficient:

Covariance / {sqrt(sample variance for age*sample variance for years sentenced)}
=-61.18 /sqrt(186.1*33.28889) = -0.86366