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Correlation and Scatterplots: Analyzing the Relationship between Two Quantitative Values -, Study notes of Statistics

Georgia Southern University–Armstrong Campus Statistics

Prof. Lorrie L. Hoffman

An introduction to correlation and scatterplots, focusing on the analysis of the relationship between two quantitative values. The concept of correlation, the calculation of the correlation coefficient, and the interpretation of the results. The document also includes examples and exercises to help students understand the concepts. This resource is useful for students in statistics, mathematics, or research-oriented fields.

Typology: Study notes

Pre 2010

Uploaded on 08/04/2009

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Tidbits

o Test 1 mean=



o Test 2 standard deviation =  = s =

o N = n =

o What general statements can you make?

o Going to the lab to do XL when? ____

Onto correlation.

Previously, we dealt with 1 qualitative value

(like birth season) or 2 qualitative values (like

birth season and sex).

Also, we dealt with 1 quantitative value (like

credit hours). But what about 2 quantitative

values?

EX1. AASU prof’s salaries and age

EX2. Time of day and # cars on campus

EX3. distance traveled to AASU and exam grade

EX4. amount of education and salary

EX5. height and IQ

Discover Study notes of Statistics Georgia Southern University–Armstrong Campus

Partial preview of the text

Download Correlation and Scatterplots: Analyzing the Relationship between Two Quantitative Values - and more Study notes Statistics in PDF only on Docsity!

Tidbits

o Test 1 mean= x^ 

o Test 2 standard deviation =  = s =

o N = n =

o What general statements can you make?

o Going to the lab to do XL when? ____

Onto correlation.

Previously, we dealt with 1 qualitative value

(like birth season) or 2 qualitative values (like

birth season and sex).

Also, we dealt with 1 quantitative value (like

credit hours). But what about 2 quantitative

values?

EX1. AASU prof’s salaries and age

EX2. Time of day and # cars on campus

EX3. distance traveled to AASU and exam grade

EX4. amount of education and salary

EX5. height and IQ

View scatterplots

1. Look for direction

2. Look for form

3. Look for scatter – watch for outliers

We say that 2 values are correlated if their

scatterplot shows a tight linear relationship.

We can calculate a value r called the correlation

coefficient. Properties:

1. -1 < r < 1 (r is between –1 and +1)

2. We may use one of the values as the

independent=explanatory=predictor variable

and call it X. The other value is the

dependent=response variable and is called Y.

EX. Amount of education vs. salary

3. r is labelless

4. No matter how close to -1 or 1 r is we can not use

that to infer causation.

EX. Number of students late to class vs.

Admits to ER 8:30-9:

5.If r is near 0 we see wide scatter and we say “a big

X can pair with either a big or a small Y”. If r is near

1 we say “big X’s pair with big Y’s”. If r is near –

we say ‘big X’s pair with small Y’s”

n

x y

i 1

z * z

r

(n 1)

 Look for this formula in your text

G 90

R

A 70

D

E 50

NAME

Plot the points. What do you see in form and direction? 7. Does it make sense to conduct a regression analysis? Do so regardless of your answer. DDXL provides the following:

CORRELATION WORKSHEET

DATA

Col. 1 Col.2 Col.3 Col.4 Col.

X Y ZX ZY ZX* ZY

# of grade

letters

Mean x^ = 6.0 Mean y^ = 78.

Standard Standard

Deviation s = 1.58 Deviation s = 11.

Put X’s z-scores in column 3. 2. Put Y’s z-scores in column 4. 3. Multiply column 3 and column 4 together and place in column 5. 4. Total the numbers in column 5.

5. Divide that total by (#pairs - 1). What is r’s

interpretation? Ans: so near

Plot the points. What do you see in form and direction? Note: Omit section ‘straightening scatterplots’ on p. 122 Example X=Miles to campus Y=odometer reading Z for x Z for Y product (in 1,000 miles) of 2 prior cols 5 6 -.9 -1.3 1. 10 126 -.5 .4 -. 30 176 1.4 .10 1. 15 97 0 -.1 0

mean=15 mean=101.2 2.37 so r=2.37/(4-1)=. stdev=10.8 stdev=71.

Correlation and Scatterplots: Analyzing the Relationship between Two Quantitative Values -, Study notes of Statistics

Related documents

Partial preview of the text

Download Correlation and Scatterplots: Analyzing the Relationship between Two Quantitative Values - and more Study notes Statistics in PDF only on Docsity!

Tidbits

o Test 1 mean= x^ 

o Test 2 standard deviation =  = s =

o N = n =

o What general statements can you make?

o Going to the lab to do XL when? ____

Onto correlation.

Previously, we dealt with 1 qualitative value

(like birth season) or 2 qualitative values (like

birth season and sex).

Also, we dealt with 1 quantitative value (like

credit hours). But what about 2 quantitative

values?

EX1. AASU prof’s salaries and age

EX2. Time of day and # cars on campus

EX3. distance traveled to AASU and exam grade

EX4. amount of education and salary

EX5. height and IQ

View scatterplots

1. Look for direction

2. Look for form

3. Look for scatter – watch for outliers

We say that 2 values are correlated if their

scatterplot shows a tight linear relationship.

We can calculate a value r called the correlation

coefficient. Properties:

1. -1 < r < 1 (r is between –1 and +1)

2. We may use one of the values as the

independent=explanatory=predictor variable

and call it X. The other value is the

dependent=response variable and is called Y.

EX. Amount of education vs. salary

3. r is labelless

4. No matter how close to -1 or 1 r is we can not use

that to infer causation.

EX. Number of students late to class vs.

Admits to ER 8:30-9:

5.If r is near 0 we see wide scatter and we say “a big

X can pair with either a big or a small Y”. If r is near

1 we say “big X’s pair with big Y’s”. If r is near –

we say ‘big X’s pair with small Y’s”

n

x y

i 1

z * z

r

(n 1)

 Look for this formula in your text

G 90

R

A 70

D

E 50

NAME

CORRELATION WORKSHEET

DATA

Col. 1 Col.2 Col.3 Col.4 Col.

X Y ZX ZY ZX* ZY

# of grade

letters

Mean x^ = 6.0 Mean y^ = 78.

Standard Standard

Deviation s = 1.58 Deviation s = 11.

5. Divide that total by (#pairs - 1). What is r’s

interpretation? Ans: so near