Example from book: Multiple Correlation and regression--interaction term
Are Auction Prices of Clocks related to Number of Bidders and age of clocks?
Is there an interaction between these two factors?
There is a Comma-delimited ASCII files of the data as CXA11_01.prn
which you can download to your disk by shift-click or right click. Bring
it into EXCEL and immediately do a
SaveAs to your A: disk, specifying
file type EXCEL before you start on the project. It's not enough
to add the .xls extension on the file.
Comment on the results of each analysis. This might work well if you put
the analyses down the page next to the data, and then short comments to
the right of each analysis. Answer the questions by typing the answers
down at the bottom of the sheet or by the relevant data.
generate a scatter plot of price vs. age of clock with trendline, equation
and r-squared. don't force intercepts to zero. comment on the appearance
of the plot and the significance of r-squared.
do the same for price vs. number of bids
produce a correlation matrix and comment on what it means
produce a multiple regression analysis with alpha =5% for the confidence
intervals on the coefficients. from this table, what is the equation of
the line? referring to Pvalues a t statistics, are the intercept and regression
relationship statistically significant at the 5% level? What does
the P value mean and how does it relate to alpha?
put in another column, multiplying number of bids times age and use this
as a third independent variable. What is the practical significance
of this variable?
repeat the regression anlysis including the NB*Age (interaction) variable.
referring to the t statistics and P values, as well as the reduction in
error mean square by including this variable, does it look like a useful
thing to do? Test this by doing an Ftest on difference in error mean
Square for the full model vs. the reduced model (leaving out the interaction)
dividing this reduction by residual mean square of the full model.
What is the equation for the full model? What practical significance might
this have? Following from your analysis how might you speculate about a
possible "way things work" in clock auctions?