CHAPTER 3: CORRELATION AND REGRESSION Flashcards
What is correlation analysis?
Relationship or Association of two variables
What is bivariate analysis?
To see the difference of the two scores of a person
What are the two ways to see the result of correlational analysis?
Scatter diagram and regression analysis
What is scatter diagram?
It is a way to see the relationship of two variables in a picture
What is regression analysis?
It is the analysis that a change of one variable (y) can predicts another variable (X)
Linear equation
What are two ways to get the equation of regression?
Intercept and slope
What is intercept?
The value is given to y when X is zero
What is slope?
The degree of relatedness of two variables
What is the value of intercept?
0 or zero
What will you do if the value of intercept is zero?
Use z scores to standardized units
What is the result of correlation analysis?
Correlation coefficient (r) It assess the magnitude and direction of relationship
What are the three interpretation of correlation?
Positive, Negative and No correlation
It is the influence of external that could be a reason of the relationship of two variables
Third variable
How to determine the strength of correlational relationship?
- Coefficient of Determination
2. Coefficient of Alienation or Non-determination
What is coefficient of determination?
% of variation of one variable to another variable
What is coefficient of alienation?
% of variation of unknown information of one variable to another variable
It is the best-fitting line and principle of least squares
Regression line or trend line
Regression line is describe by ___?
Regression equation
What is the formula of regression equation?
Y = a + bX
It is the ratio of variance to covariance
Regression coefficient (b)
It is the slope of regression line
Regression coefficient (b)
It is the sum of squared deviation around the mean
Sum of squares
It is the relationship of two random variables and how the scores vary
Covariance
It is the difference of the predicted value (Y) from the regression equation and observed value (X) or the vertical distance of the two
Residuals
It is the SD of regression obtained from regression equation
Standard error of Estimate
What is the mutlivariate analysis?
It studies 2 or more variables
What are the three methods of mutivariate?
Multiple regression, Discriminant analysis and Factor analysis
What is multiple regression?
It is one criterion versus 2 or more predictor variables
What is discriminant analysis?
It is one categorical criterion vs 2 or more predictors
What is factor analysis?
Reducing the larger set of variables into smaller set of variables
Interrelationship of two set of variables without a reference of criterion
Who is the founder of regression?
Francis Galton
He is continue to study the regression to create a new statistical method
Karl Pearson
It a measurement of strength (magnitude) and direction of the relationship of two variables
Pearson correlation coefficient or correlation coefficient
What is positive correlation?
Both variable increases
What is negative correlation?
One variable increase, One variable decreases
What is no correlation?
Variables has no relationship
One variable increase nor one variable decreases
It refers to the number of independent observations in a set of data.
Degrees of Freedom (Df)
It used to estimate population parameters when the sample size is small and/or when the population variance is unknown.
T - Distribution or Student’s T - Distribution
T distribution is determined by ___>
Degrees of Freedom (Df)
In regression analysis, It is data point that diverges greatly from the overall pattern of data is called ____
Outlier
It refers to the distributions of data that have many more observations on one side of the graph than the other.
Skewness
Distributions with one clear peak are called ___
Unimodal
Distributions with two clear peak are called ___
Bimodal
It is an attribute used to describe the shape of a data distribution. What are the two kinds?
Symmetry
Symmetrical and asymmetrical
It is a categorical variables with two categories or levels. Example is head or tails
Dichotomy variables
It is a sub-type of dichotomous variable
The variables assigned either a 0 or a 1.
For example Male (0) and female (1).
Binary variable
He was the first person to measure correlation, originally termed “co-relation,”
Francis Galton
He used “Coefficient of Correlation” in his two papers.
Karl Pearson
A special case of Pearson correlation coeffient which measures the continuous/ true and discrete/artificial variable
Biserial Correlation
Dead or alive is example of ___ dichotomy variable
passed or failed is example of ___ dichotomy variable
discrete/ true
continous/artificial variable
A special case of Pearson correlation coeffient between two dichotmous variables
Phi coefficient
It measure rater agreement for binary data.
A binary data is data with two possible answers—usually right or wrong.
This tells you how strong (or weak) the association is between ratings for two raters.
tetrachoric coefficient
It is the relationship of each variable to the underlying factor
Factor loading
It is transformation method used to rotate the axes created by factors
Methods of rotation
- It remove the unit of measurement of predictor and outcome variables. They are sometimes called betas.
- They serve as standardized effect size statistics.
- They allow you to compare the relative effects of predictors measured on different scales.
Standardized Regression Coefficients (B’s)
How to make a standardized Regression Coefficients? (B’s)
Convert the units into Z scores
It is unstandarized coeffiecients which describes the relationship between the predictor and dependent variable in terms of original or raw units of measurement.
Raw regression coefficients (b’s)
How to make a Raw Regression Coefficients? (B’s)
Do not make z scores
He got the factors of trust
Rotter
What are three factors of trust?
Institutional trust, Sincerity Trust, and Caution Trust
.70+
very strong correlation
.40 - .69
Strong correlation
.30 - . 39
Moderate correlation
.20 - . 29
Weak correlation
.01 - .19
no or neglible correlation
0
Zero correlation
