Task 6 Flashcards
What is the least square regression line?
Line with least errors / that fits best: y (hut)
Minimized distances of the observed y-values from the regression line
Name 3 characteristics of the least squares regression line
- always goes through point (mean of x, mean of y)
- changes of 1 standard deviation in X corresponds to change of r standard deviation in Y
- correlation is 0, if slope of line is 0
b=0 = r=0
What is the intercept?
Starting point of the line
(Y-achsenabschnitt)
Where independent variable (x) is equal to 0
What is the slope?
The slope determines the direction of the line
if we increase our independent variable by 1 unit the dependent variable will go up by b (the slop)
which two regression coefficients do you know?
slope b
intercept a
When do you use regression?
- regression line predicts Y value for an X value
- Extrapolation: predicting far outside the X range of our data (should be avoided)
Which 2 variables do you have? Which one is on which axis?
Dependent/ Response/ Explains variable
-is on the y-axis
Independent/ Predictor / Explanatory variable
- is on the x-axis
What is the prediction error / the residual?
Which variation is it?
The difference between the observation (y) and the fitted line (y hut)
Unexplained variation
If we square and add up all residuals we get the unexplained variation
What is the regression?
the difference between the line (y hut) and the mean (mean of y)
explained variation
Name 5 characteristics of a residual plot
- Scatterplot of regression residuals (Y) against explanatory variable X
- Helps assessing the fit of regression line
- Shows deviations and outliers
- If random: linear regression is appropriate
- If Non-random: It doesn’t make sense to use linear regression!
How does the residual plot looks like if its random?
the residuals are spread around the 0 line as a random cloud
How does the residual plot look like if its non-random?
the residuals are organized in some sort of pattern around the 0 line (eg. curvilinear correlation)
