Linear Regression Flashcards
What does regression involve?
Modelling and estimating the relationship between two variables
What is simple linear aggression used for?
To predict the value of one variable based on the value for the other variable
What is the independent variable?
The one that is used to predict the values of the other variable, it is plotted along the x axis
What is the dependent variable?
The one whose values are predicted by the independent variable, it is plotted along the y axis
What is the only relationship that can be examined using linear regression?
A straight-line linear relationship
What is the equation for a straight line?
y = a + bx
What is a?
The y intercept - the point where the line crosses the y axis when x = 0
What is b?
The gradient or slope of the line and is the amount by which y increases for an increase of one unit in x
What does the line of best fit determine?
If the points on a scatter diagram follow a linear pattern - the straight line that bets models the relationship between two variables
What is a residual?
The distance between each point on the scatter diagram and the line of best fit
What is the least squares regression line (or the regression line of y on x)?
The line that minimises the residuals
What is the equation of the regression line?
y = a + bx
- b = Sxy/Sxx
- Sxy= ∑xy - ∑x∑y / n
- Sxx= ∑x2 - (∑x)2/n
- a = y-bx
What is interpolation?
When the given value of the independent variable, x, is within the range of the sample data
Reliable
What is extrapolation?
When the given value of the independent variable, x, is outside the range of sample data
Not reliable
