Flashcards
linear regression
Cards in this deck (23)
- 1Regression =The prediction of one variable from knowledge of one or more other variables.
- 2Linear regression =Linear regression is regression when the relationship between two variables is linear i.e. a constant increase or decrease in one leads to a constant increase or decrease in the other.
- 3Simplest casejust one predictor variable. When this is true the standardised regression co-efficient beta is the same as the pearson’s r correlation co-efficient
- 4Equation for lrY^ = bX + a
- 5Y^predicted value of Y (dependent variable)
- 6bco-efficient is the slope of the regression line (the amount of change in Y associated with a 1- unit change in X).
- 7ais the intercept: the predicted value of Y when X is 0
- 8Xis value of the predictor variable (independent)
- 9Standard error of estimatesquare root of (Y-Y^)sq divided by N
or Square root of the variance between Y and predicted value of Y - 10standard error of estimate in wordsSo the standard error of estimate = standard deviation of Y values around the predicted regression line.
- 11If all the values of Y fitted the line perfectlythe standard error would be 0 – perfect fit.
- 12b (relative to Beta)is an unstandardized regression co-effcient. It is based on actual values of Y and is useful for predicting actual values of Y.
- 13Beta isthe standardized regression co-efficient and happens when we standardize X and Y values to have a mean of 0 and a standardized deviation of 1.
- 14b and B are the same whenthere is only one predictor variable
- 15Beta is equal topearson’s r correlation coefficient
- 16Beta squaredis equal to r squared
- 17R squared expressesthe amount of variability in Y that is accounted for by X
- 18Beta-squared x100 =percentage of variability in Y scores accounted for by X
- 19Testing the significance of the b-co-efficientThe regression co-efficients (b or beta) only indicate the degree of relationship between X and Y variables, i.e. the strength of the relationship.
They don’t indicate whether the relationship is a statistically significant one.
However, a simple t-test on the b co-efficient will test its significance. - 20constant in SPSSis the intercept and is only useful with interval level data
- 21Linear Regressionis used to determine the strength and significance of the relationship between one predictor (independent) and one predicted (dependent)variable.
- 22The regression equation can be used toplot a line of best fit through the scatterplot of data – and can be used to predict scores on Y from knowledge of X.
- 23When standardised, the regression co-efficient is equal tothe pearson correlation between the two variables, and has the same interpretation.
Information
- Description
- whiffy bum RM2 Flashcards on linear regression, created by James Rowland on 31/03/2016.
- Created by
- James Rowland · Mar 2016
- Updated
- Apr 26, 2016
- Views
- 0
- Rating
More on Simple Linear Regression