Simple Regression 1 Flashcards
What it the line of best fit?
A line which goes through the scatterplot which shows the regression line
What is another way of saying line of best fit?
The least squares criterion
What is the least squares criterion?
The line with the lowest sum of squares residuals is the line of best fit.
How can we satisfy the least squares criterion?
By finding the line with lowest SSR
What is the slope?
The regression coefficient (b).
The number of units that the regression moves on the y axis for each unit it moves along the x axis.
What is intercept?
Regression constant (a). The point at which the regression line cuts the y axis. So the value of x=0.
When reading the Coefficients table in SPSS. Where do you find the intercept (a) and slope (b)?
Unstandardised coefficients the look under B. The top number (the (constant))is the intercept and the one below is the slope.
What is the equation for linear regression?
Y = a + b*x.
How does the linear regression equation look like when concerning a population rather than the sample?
In Greek letters.
What does a little i mean in the regression equation? Yi = a +bx
The i indicates that there is a particular case.
What the a ^ (hat) symbol above the Y is a regression equation mean?
That the y we are talking about is the predicted y.
What does the symbol epsilon (reversed 3).
That our model is not perfect, y might not be exactly at a+bx but somewhere near because of some inevitable error.
What is the goodness of fit?
Assessing the regression line to see if the regression line is the best line available for fitting the data.
It basically assess how well the regression line fits the data.
How can we calculate the goodness of fit?
Fitting the data using a line based on the mean value of y.
The intercept is equivalent to the mean value and the slope is 0 (flat).
How do we asses goodness of fit?
By looking at how much more variability in the outcome variable (y) the regression line is able to explain by comparing it with the line based on the mean. Then divide this amount by the variance unexplained by the regression line.
