Lecture 3 HSPM J716

New spreadsheet layout Coefficient Standard error T-statistic – Coefficient ÷ its Standard error

Standard error of coefficient Shows how near the estimated coefficient might be to the true coefficient.

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.

Standard error of the regression Should be called standard residual – But it isn’t

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

Durbin-Watson statistic Serial correlation – For clinic 2

Confidence interval for prediction The hyperbolic outline

Formal outlier test? Using confidence interval of prediction

Multiple regression 3 or more dimensions 2 or more X variables Y = α + βX + γZ + error Y = α + β 1 X 1 + β 2 X 2 + … + β p X p error

Fitting a plane in 3D space Linear assumption – Now a flat plane – The effect of a change in X 1 on Y is the same at all levels of X 1 and X 2 and any other X variables. Residuals are vertical distances from the plane to the data points floating in space.

β interpretation in Y = α + βX + γZ + error β 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 β more than you would expect from what Z is.

β -hat formula in Y = α + βX + γZ + error – See pdf file

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