Simple Linear Regression Flashcards
What are three different names for the Predictor Variable?
●Independent Variable
●Explanatory Variable
●Predictor Variable
What are three different names for the Outcome Variable?
●Dependent Variable
●Criterion Variable
●Outcome Variable
What is the difference between Correlations and Regression?
Correlations assess the strength and direction of a relationship between variables. Regression extends this concept to make predictions about how much Y will change if X changes by one unit.
What two pieces of information can be gained from the Regression Line?
●The slope (steepness/angle)
●The intercept (where the regression line crosses the Y-axis)
What is the Regression Line also known as, and what does it do?
The regression line is also known as the line of best fit. It predicts the best-fitting straight line through the data by minimizing the distance between all data points and the line.
What does R^2 stand for, what does it represent, and what is it also known as?
R^2 stands for the coefficient of determination and represents the variance explained by the model. It is also known as variance.
What outputs are obtained when running a regression?
R, R^2, and the model table.
What does the R-value tell us, and what is its range?
The R-value indicates the strength of the relationship between variables and ranges from 0 to 1. The direction of the relationship is found elsewhere in the output (beta values).
What is the relationship between R and Pearson’s r in simple linear regression?
When only dealing with two variables, R is equivalent to Pearson’s r (correlation coefficient)
What are Beta values, and what do B0 and B1 represent?
Beta values represent the coefficients of the regression equation.
●B0 is the intercept (also called the constant on SPSS).
●B1 is the slope, which indicates the direction of the relationship.
What is Model Fit, and what does it assess?
Model Fit, assessed through the ANOVA table, determines how well the data fits the model. It assesses the usefulness of the line of best fit, indicating whether regression is more accurate or if using the mean and descriptive statistics to predict the Y value is better.
What are the two equations for simple regression?
Outcome = (model) + error
Y = (b_1X_1 + b_0) + ε_i
What does the ANOVA table tell us about the error in simple regression?
The ANOVA table helps determine if the error makes the model useful for making good predictions.
List four important statistics in simple regression.
●Correlation coefficient (R) - standardized measure of relationship strength (ranges from 0 to +1)
●Coefficient of Determination (R^2) - proportion of variance explained by the model
●Beta coefficient (b1) - change in outcome for a one-unit change in the predictor (slope)
●Intercept (b0) - constant term (the value of Y when X is 0)
What are the assumptions of simple linear regression?
●Variable type: The outcome variable must be interval (continuous), and predictors should ideally be interval (continuous) but can be nominal with two levels.
●Non-zero variance: There must be variability in scores (participants should have different scores from each other).
●Sufficient power: Enough participants are needed to provide sufficient data (40+ k(10), where K is the number of predictors).
●Linear Relationship: The relationship between variables should be linear, which can be visually assessed using a scatter plot.
●Normally distributed residuals (errors): Residuals/errors should be random and normally distributed with a mean of zero, with most scores falling close to zero.
●Homoscedasticity: The error should be roughly the same as we move along the predictor variable.
●Independence of errors: All values of the outcome should come from different individuals (also known as auto-correlation), which can be checked using the Durbin-Watson statistic (ideally between 1.5 and 2.5).
