Chapter 13 Flashcards
A group of techniques to measure the relationship between two variables
Correlation analysis
The variable that is being predicted or estimated
dependent variable
The dependent variable is measured on which axis
Y-axis
A measure of strength of the linear relationship between two variables of interval or ratio scale
Correlation coefficient
6 characteristics of a correlation coefficient
- Designated with letter r
- Between -1 and 1
- Shows direction and strength of linear relationship between two variables
- Closer to 0 means less of a correlation
- Near 1 shows strong correlation
- near -1 shows strong correlation
an equation that expresses the linear relationship between two variables
Regression equation
A mathematical procedure that uses the data to position a line with the objective of minimizing the sum of the squares of the vertical distances between the actual y-values and the predicted values of y.
Least squares principle
What is the symbol y hat
The estimated y value for a given x
What is the y hat formula for linear regression equation
y hat = a+bx
The difference between the actual y values and the predicted y values, known as the error values
Residuals
A measure of dispersion, or scatter, of the observed values around the line of regression for a given value of x
Standard error of estimate
What does a small standard error mean
The data is close to the regression line
Predicted Y will have small error
The proportion of the total variation in the dependent variable Y that is explained by the variation in x
The coefficient of determination
Assumptions for linear regression
- Corresponding y values are normally distributed
- The means of the distributions lie on the regression line
- The standard deviations are the same.
- Y values are statistically independent
If the standard error of estimate is large, what would you expect for the coefficient of determination
It would be small
