t-tests and partial F-tests; interaction; Durbin-Watson statistic
1. What do the regression coefficients in a multiple regression represent? The
coefficient attached to a particular x is a partial slope and indicates the change in y for
each one unit chan
Lack of Autocorrelation Structure
The following shows that there is essentially no autocorrelation structure remaining in
the residuals (the lag 15 result may be a false positive). There is perhaps some
remaining seasonal and trend structure, though.
It is easy to use the JMP Formula Editor to obtain numerical values for the js. The
last model fit involves r = 1, p = 2, the first case above. We have
St = (1 0.965412B + 0.205023B2)1(0.549964 0.3447B)At +
= ( 0 + 1B + 2B2 + )At.
Group By Option
The Group By option allows one to look for interactions graphically at the start of an
analysis. However, there is a better way to fit a model with interaction and perform the
required statistical analysis. It leads to the same two fitted
We begin by fitting a distributed lag model with geometric decay,
where B is the backward shift operator. Recall that this formulation is equivalent to
In this model the contemporaneous effect of advertising is , the cumulative effect afte
If the residual lag correlation is above 0.25, then the model is not acceptable. To make
the model a better fit, we need to add more lags, because lags are what captures the
correlation. Thus, we had one more lag, called lag2sales.
The Durbin-Watson statistic is used to test the null hypothesis of uncorrelated errors in a
time series regression model, against the alternative that the errors follow a first-order
autoregression with positive lag one correlation. The time
Weekly Garbage Deposits
The data analyzed are weekly garbage deposits, in tons, at a Delaware Solid Waste
Authority facility. There are three years of data, beginning with the week of 12/30/84
and ending with the week of 12/13/87 (each date listed is a Su
The standard breakup formula is:
St = (1 + 1B + + pB ) (0 + 1B + + r B )At +
= ( 0 + 1B + 2B2 + )At .
Then we have
0 + 1B + + rB r = (1 + 1B + + pB p)( 0 + 1B + 2B2 + ).
Equating coefficients of B j on both sides, j = 1, 2, ., we c
Best Fit Formula
An example of a best fit can be written
St = 1084.509 + (1 0.965412B + 0.205023B2)1(0.549964 0.3447B)At
+ terms in Indit (i=1,2,3)
= 1084.509 + 0.5500(At + 0.3385At1 + 0.1219At2 + 0.0483At3 + )
+ terms in Indit (i=1,2,3).
This suggests a