week 8 Flashcards
Correlations
whether two variables change together or covary
The value of correlation coefficient can vary from -1 to +1
Regression
uses correlation to predict values of one variable from another
The prediction is done by finding a regression line that best represents the data
X axis
predictor
Y axis
outcome
regression equation
Y=bo+b1x+e
Y
outcome
bo
intercept
b1
slope of the line
X
predictor
e
error
Intercept
The point at which the regression line crosses the Y-axis
The value of Yi when X=0
Slope
a measure of how much Y changes as X changes
Regardless of it’s sign the larger the value of b1, the steeper the slope
For 1 unit of change on the X axis, how much change is there on the Y axis
Residual or prediction error
the difference between the observed value of the outcome variable and what the model predicts
Lines of best fit
a line that best represents the data
a line that minimises residuals
residual sum of squares
residuals can be positive or negative. If we add the residuals, the positive ones will cancel out the negative ones, so we square them before we add them up. We refer to this total as the sum of squared residuals or residual sum of squares
SSr is a gauge of how well the model fits the data
Total sum squares
Using the sample mean of observed Y as a baseline model assuming no relationship Y and X
The sum of squared differences between the Yobs and the sample mean total sum squares
Model sum of squares
sum of squared differences between the Yobs and the sample mean. It represents the improvement from the baseline model to the regression model
SSt
total variance in the outcome variable can be partitioned into two parts
SSm
variance explained by the model more variance
SSr
variance not experienced by the model residual or error variance
R2
this provides the proportion of variance accounted for by the model
F ratio
f is the ratio of the explained variance to the unexplained variance
Overall test
the hypothesis in regression can be phrased in various ways
can the scores on x and the regression line
does the model explain significant amount of variance in the outcome variable
Unstandardised beta
the value of the slope b1
for every one unit change in x, the change in the value of Y. In units of measurement. Important to look at whether b1 is positive or negative
If b1 is 0 there is no relationship between X and Y
