Chapter 3: Correlation and Regression Flashcards
What are the five characteristics of a good theory?
- Explanatory power (your theory explains something and it makes you smarter)
- broad scope
- systematic (Internally consistent statements)
- generative
- parsimonious (Simple is better, occam’s razor)
What is a scatterplot (scatter diagram)? How does it work?
One variable on X axis and one on Y axis
Make a least-squares regression line/ line of best fit
Useful for: Showing linear/curvilinear relationships, Detecting outliers, Detecting restricted range problems
What is the Correlation Coefficient? With what concept should correlation not be confused?
a value between -1 and +1. A correlation coefficient of +1 indicates a perfect positive correlation. As variable x increases, variable y increases
Understand and be able to differentiate and plot positive, negative, and 0 correlation
I can do this
What is the principle of least squares? How does it relate to the regression line?
getting the sum of the squares of the errors a minimum value, the most probable values of a system of unknown quantities can be obtained upon which observations have been made.
the process of finding a regression line
Define covariance
just the direction, NO MAGNITUDE
Degrees to which two variables vary together
How much COvariance do they share?
As one changes, the other changes as well IN THE SAME DIRECTION
Correlations need variation
What is the Pearson product moment correlation? What meaning do the values -1.0 to 1.0 have?
measure of the strength and direction of association that exists between two variables measured on at least an interval scale
Define residual
Difference between each individual point to the least-squares regression line
What is the standard error of estimate? What is its relationship to the residuals?
Square the residuals, find the standard deviation of the residuals, predicted points can vary around the line of best fit, standard deviation around the line of best fit
What is shrinkage?
the situation in which the strength of a correlation coefficient or regression equation decreases when it is applied to a new data set
What is restricted range? To what does it lead?
Restriction of range occurs when a variable has less variability in a study sample than in the full population. The restricted range can be present for observed variables (dependent or independent variables) or in other variables that were not measured
What is factor analysis?
to estimate a model which explains variance/covariance between a set of observed variables by a set of unobserved variables and weightings
What is the co-efficient of determination? What is the purpose of the co-efficient of determination?
a number between 0 and 1 that measures how well a statistical model predicts an outcome (R squared)
What is the regression formula? Understand the different components of the formula and how they are applied.
One variable predicting another
Y’ = a + bx
What is the difference between simple linear regression and multiple regression?
Two or more predictor variables (ACT AND class range AND spirituality…)
