4: Precision, Statistical Inference and Goodness of Fit

Question 1

assumption 1 CLRM

Answer 1

errors have zero mean

Question 2

assumption 2 CLRM

Answer 2

the errors have constant finite variance, homoscedasticity

Question 3

assumption 3 CLRM

Answer 3

the errors are linearly independent of each other

Question 4

assumption 4 CLRM

Answer 4

there is no relationship between an error and its corresponding x variate
- stronger alternative assumption is that the xt’s are stochastic (fixed in repeated samples)

Question 5

assumption 5 CLRM

Answer 5

error is normally distributed
- required if we want to make inferences about population parameters from sample parameters

Question 6

comments on SE estimators for intercept and slope

Answer 6

• sample size (the larger it is, the smaller the coefficient variances, the greater the sample size, the more information available)
• error variances (the SEs depend on s^2, the greater this is the more dispersed)
• total sum of squares (the larger this is, the smaller the coefficient variances)

Question 7

R squared

Answer 7

measures how well the regression model fits the data
how much of the changes in y are explained by changes in x

Question 8

problems with R squared

Answer 8

• not sensible to compare R squared values for models with different dependent variables
• as R squared never decreases, it cannot tell if a variable should be present in the model