Lesson 2: Examples

BA501 : The Class : Stats : Correlation : Examples
Correlation Analysis
Example 1- Correlation: Punts and Points Scored

§ Lession 2: Examples §

Example 1- Correlation: Punts and Points Scored

(A) Application of the correlation analysis-

(1) Problem: What is the relationship between the number of punts and the number of points scored in data gathered from 5 football games?

(2) Data: x = # of punts

y = # of points scored

x_i	y_i
1	24
2	21
2	14
3	10
4	7

(3) Look at the plotted data.

(a) Negative ( inverse ) relationship between the number of punts (x) and the number of points scored (y).

(b) Data:

	x_i	y_i	x_iy_i	x_i²	y_i²
	1	24	4	1	576
	2	21	42	4	441
	2	14	28	4	196
	3	10	30	9	100
	4	7	28	16	49
Totals	12	76	152	34	1,362

[1] r = [S xy - (S x)(S y) / n] / Ö [S x² - (S x)² / n]Ö [S y² - (S y)² / n]

= [152 - (12)(76) /5] /Ö [ 34 - (12)² /5]Ö [ 1,362- (76)²/ 5]

[2] = SCP_xy / Ö [SS_x] Ö [SS_y]

= - 30.4 / Ö [5.2]Ö [ 206.8 ]

= - 30.4 / [2.28][14.38] = - 30.4 / 32.79

= - 0.927

where,

[a] SCP_xy = [S xy - (S x)(S y) / n] = - 30.4

[b] SS_x = [S x²- (S x)² / n] = 5.2

[c] SS_y = [S y²- (S y)² / n] = 206.8

(c) r = - 0.927 indicates a strong negative linear relationship between x and y (the number of punts and the number of points scored). (click me)

Is it obvious from this example that the number of punts per game helps determine the number of points scored? Yes No (chick one)

Example 2- Hypothesis Testing on the Populating Correlation, r : Punts and Points Scored

(A) One tail test (left) on r using data from Example 1:

(click me)

(1) Problem: Is there a statistically significant linear relationship between the number of punts and the number of points scored in data gathered from 5 football games? Test the claim that the population correlation coefficient for r is negative.

(2) One-tail left hypothesis:

H_o: r ³ 0

H_a: r < 0

(3) Table statistic:

If a = 0.10,

then t _{0.10,(5 - 2)}= t _{0.10, 3} = - 1.638

(4) Computed value:

t* = r / Ö[(1 - r²) / (n - 2)]

= - 0.927 / Ö [(1- (- 0.927)²) / (5- 2)]

= - 4.28

(5) Since t* < - t _0.10,3

-4.28 < - 1.638, reject H_o

(6) One Tail Hypothesis Test (Left) on the Population

Correlation Coefficient, r

H_o: r _³0

H_a: r < 0

Reject H_o if t* < - t a _{,(n - 2)}

FTR(Support) H_o if t* ³ - t a _{,(n -
2)}

(7) Since t* = - 4.28 < t _0.10,3 = - 1.638, then r = - 0.927 is statistically so far away from H_o: r ³ 0 that one can not believe H_o is true; thus, reject H_o.

(8) FTR (Support) H_a: r < 0. There is a significant negative linear relationship between the number of punts and the number of points scored.

Why is the alternative hypothesis in this problem H_a: r < 0? (a) the researcher believes there is a neagive relationship (b) the only possible relationship is negative. (chick one)

Once you have finished you should:

Go on to Excel and Equations
or
Go back to Correlation Analysis: Activities and Assignments

or
Go back to Lession 1: Introduction

Please reference "BA501 (your last name) Assignment name and number" in the subject line of either below.

E-mail Dr. James V. Pinto at BA501@mail.cba.nau.edu
or call (928) 523-7356. Use WebMail for attachments.