Models + Linear Regression

Question 1

what are independant variables?

Answer 1

the inputs, what we manipulate to see how they affect the dependant variables

Question 2

what are dependant variables?

Answer 2

the outputs, what we measure when manipulating the independant variables

Question 3

difference between continuous and discrete data?

Answer 3

discrete data can only take on certain values i.e. half a person? and rolling dice

continuous data can take on any value within a range i.e. height

discete data is counted
continuous data is measured

Question 4

how is a predictive model used and why is it useful?

Answer 4

a predictive model can be used to predict how a change in the independant variables will affect the dependent ones

useful as they are prescriptive: they enable prediction of behavioural outcomes so the interface can be designed accordingly

Question 5

what is the overfitting problem?

Answer 5

• trying to make the model match all observations (super curvy line)
• risks modelling noise
• counters occam’s razor

Question 6

how are a and b calculated in a linear model?

Answer 6

Y = a + bX

b = XYbar - (Xbar x Ybar) / X^2bar - Xbar^2
a = Ybar - b*Xbar

Question 7

describe a method of model validation

Answer 7

coefficient of determination (R^2)
the lower R2, the less variance is explained by the model
if the ratio is 1 then no variance is explained (good)
your ratio is how much variance is explained
R2 = 1 - SSerror/SStotal

SSerror is the sum of (y - y’)2 where y’ is the model’s estimate and y is the actual value
SStotal is the sum of (y - ybar)2

or

SSerror is how much you were off the model by and
SStotal is how much you were off the avg by

Question 8

how to calculate SStotal?

Answer 8

SStotal is the sum of (y - ybar)2

Question 9

how to calculate SSerror?

Answer 9

SSerror is the sum of (y - y’)2 where y’ is the model’s estimate and y is the actual value