HSPM J716

1
Lecture 3

• HSPM J716

2
New spreadsheet layout

• Coefficient
• Standard error
• T-statistic
• Coefficient its Standard error

3
Standard error of coefficient

• Shows how near the estimated coefficient might be
  to the true coefficient.

4
Confidence interval for a coefficient

• Coefficient its standard error t from table
• 95 probability that the true coefficient is in
  the 95 confidence interval?
• If you do a lot of studies, you can expect that,
  for 95 of them, the true coefficient will be in
  the 95 confidence interval.

5
Standard error of the regression

• Should be called standard residual
• But it isnt

6
Assumptions

• Required for using linear least squares model
• Illustrated in assignment 2

7
Durbin-Watson statistic

• Serial correlation
• For clinic 2

8
Confidence interval for prediction

• The hyperbolic outline

9
Formal outlier test?

• Using confidence interval of prediction

10
Multiple regression

• 3 or more dimensions
• 2 or more X variables
• Y a ßX ?Z error
• Y a ß1X1 ß2X2 ßpXp error

11
Fitting a plane in 3D space

• Linear assumption
• Now a flat plane
• The effect of a change in X1 on Y is the same at
  all levels of X1 and X2 and any other X
  variables.
• Residuals are vertical distances from the plane
  to the data points floating in space.

12
ß interpretation

• in Y a ßX ?Z error
• ß is the effect on Y of changing X by 1, holding
  Z constant.
• Often, there is a linear relationship between X
  and Z. When X is one unit bigger than you would
  predict it to be, based on what Z is, then we
  expect Y to be ß more than you would expect from
  what Z is.

13
ß-hat formula

• in Y a ßX ?Z error
• See pdf file

14
LS

• Spreadsheet as front end
• Word processor as back end
• Interpretation of results
• Coefficients
• Standard errors
• T-statistics
• P-values
• Prediction