Lecture 17 Flashcards
What do statistical procedures look at between two samples?
The relationships rather than differences between 2 ratio-interval scale variables
Purpose of simple linear regression?
Looking for a causal relationship between two variables where one affects the other
What is the purpose of a simple linear correlation?
Used when looking for a relationship between two ratio-interval scale variables where no causal relationship is implied
How is the change in the dependent variable assessed for a given change in the independent variable?
Find the equation for slope that relates to our variables (x,y)
How is the strength of the relationship determined between two variables?
Test with normal hypothesis techniques
In the simple linear equation, what is alpha?
The population y-intercept
In the simple linear regression equation, what is ß?
The population slope
In the simple linear regression line, what is E?
The residual value
What is residual?
Between the expected Y and the actual Y; comparable to error in ANOVA
Where is the best-fit line used in?
Sample statistics = no greek letters
Why is there no residual component to the best-fit line?
Each data point is expected to fall directly on the line
How is the best-fit line determined?
Using the least squares method
What is the least squares method?
The residuals are squared and then summed
What are the sources of variation in simple linear regression?
Total, regression, and residual
In simple linear regression, what is the total variation?
All the variation in the Y-variable
In simple linear regression, what is the regression variation?
(Relationship) the variation in Y that is due to its relationship with X; the most of interest we are looking at
In simple linear regression, what is the variation in residuals?
The variation in Y due to all other things other than its relationship with X
What is conclusive if the regression line perfectly fit the data (all data points fell on the line)?
No residual deviations = regression explains all of the total variation in the dependent variable Y
What is conclusive if the data points were spread very widely?
The regression line will not fit the data therefore residual deviations would account for more of the variation in the Y variable
What does the hypothesis test for a simple linear regression?
Tests for a significant relationship between the two variables
What is the coefficient of determination? (r^2)
The proportion of the total variation in the dependent variable Y that is explained by the regression
What does regression mean?
The relationship to the independent variable X
What does a an r^2 value closer to 1 indicate?
A closer relationship
What is the standard error of the estimate? (Syx)
The standard deviation of the Y values about the regression line, Syx = 0 = perfect relationship
