Simple regression ( 1-independent variable) Flashcards
Sample correlation coefficient
Testing significance of the correlation coefficient
Simple Linear Regression (unique topics only…everything else in multiple applies to simple)
- Correlation coeffcient (r)
- Assumptions
- Confidence Interval for predicted Y value
Correlation & Regression
Terminology - Define the following:
- Coefficient
- Correlation coefficient
- Coefficient of Determination
- Confidence interval
- P-value
Coefficient - a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y). It is usually a number, but may be any expression. In the latter case, the variables appearing in the coefficients are often called parameters, and must be clearly distinguished from the other variables.
Correlation coefficient, r, for a sample and ρ for a population, is a measure of the strength of the linear relationship (correlation) between two variables.
Coefficient of determination is R2
A confidence interval is an interval of values that we believe includes the true parameter value, b1, with a given degree of confidence. To compute a confidence interval, we must select the significance level for the test and know the standard error of the estimated coefficient.
P-value is the smallest level of significance for which the null hypothesis can be rejected. An alternative method of doing hypothesis testing of the coefficients is to compare the p-value to the significance level:
- P-value < less than significance level, reject null
- P-value > greater than significance level then cannot rejcect null
- Remember: small Ps and big Ts to reject the null!
SEE - Standard error of the estimate (smaller SEE indicatesbetter fi t of regression model)
Prediction interval around the predicted value of the dependent variable
For a linear regression model with one independent variable, the standard error of estimate (SEE) is the square root of:
<span> </span>(sum of squared residuals)
(n-2)
