Correlation and Regression Analyses

Question 1

What is a model?

Answer 1

1. Representation of some phenomenon

2. Non-Math/Stats Models

Question 2

What is a Math/Stats Model?

Answer 2

1. Often describes the relationship between variables

2. Types: Deterministic (no randomness), Probabilistic (with randomness)

Question 3

Deterministic Models

Answer 3

1. Hypothesizes exact relationships
2. Suitable when prediction error is negligible
3. Example: Body Mass Index (BMI) is measure of body-fat based

Question 4

Metric BMI Formula

Answer 4

Weight in Kilograms/(Height in Meters)^2

Question 5

Non-Metric BMI Formula

Answer 5

Weight (in pounds)* 703/(Height in Inches)^2

Question 6

Probabilistic Models

Answer 6

1. Hypothesize 2 Components
   • Deterministic
   • Random Error
2. Example: Systolic blood pressure of newborns Is 6 Times the Age in days + newborns Is 6 Times the Age in days + Random Error
3. Random Error May Be Due to Factors Other Than age in days (e.g. Birthweight)

Question 7

Types of Probabilistic Models

Answer 7

1. Regression Models
2. Correlation Models
3. Other Models

Question 8

Rationale

Answer 8

It is often often desirable to determine whether the scores of one distribution are related to the scores of another distribution.

Question 9

Purposes of the Rationale

Answer 9

1. to assess linear relationship between variables
2. to provide an initial step for prediction
3. to provide an initial assessment of possible causal relationship
4. to assess test-retest reliability (of instruments)

Question 10

Correlational Design

Answer 10

two (uncontrolled) variables at either an interval or ratio measurement scale

Question 11

Scatterplot

Answer 11

 a plot of the pairs of values of two (quantitative) variables on a rectangular coordinate plane
 an effective tool for presenting possible relationships between two (quantitative) variables

Question 12

Possible relationships in a scatterplot

Answer 12

1. None
2. Linear (numerically assessed by a correlation)
3. Non-linear

Question 13

Correlation coefficient

Answer 13

1. expresses quantitatively the magnitude and direction of the relationship between two variables using a normalized scale (i.e., ranging from -1 to 1)
2. a measure of the strength of the linear association between two variables
3. any correlation coefficient has two components: (1) the sign indicates either a positive or a negative linear relationship (i.e. direction); (2) the absolute value indicates the strength of the relationship (i.e., magnitude).

Question 14

Types of Linear Relationship

Answer 14

1. Direction: +: direct linear relationship, -: inverse linear relationship
2. Magnitude: closer to 1: strong to almost perfect (linear) relationship; closer to 0: weak to almost no (linear) relationship

Question 15

Pearson’s R

Answer 15

1. also known as the Pearson’s Product - Moment Correlation Coefficient
2. describes the linear relationship between interval and/or ration variables
3. a measure of the extent to which paired scores occupy the same or opposite positions within their own distributions

Question 16

Regression Models

Answer 16

• Relationship between dependent variable and explanatory variable(s)
• Use equation to set up relationship
• Numerical dependent (response) variable
• 1 or More Numerical or Categorical Independent (Explanatory) Variables
• Use mainly for prediction and estimation

Question 17

Simple regression

Answer 17

• Simple regression analysis is a statistical tool that gives us the ability to estimate the mathematical relationship between a dependent variable (usually called y) and an independent variable (usually called x)
• The dependent variable is the variable for which we want to make a prediction
• While various non-linear forms may be used, simple linear regression models are the most common

Question 18

Historical Origin of Regression

Answer 18

• Regression analysis was first developed by Sir Francis Galton, who studied the relation between heights of sons and fathers
• Heights of sons of both tall and short fathers appeared to “revert” or “regress” to the mean of the group

Question 19

Types of Regression Models

Answer 19

1. Simple

2. Multiple

Question 20

How many explanatory variables does a simple regression model have?

Answer 20

1 explanatory variable

Question 21

How many explanatory variables does a multiple regression model have?

Answer 21

2+ explanatory variables