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Project 1(b)
Descriptive Statistics

The following example has been taken from the Book and is Problem No. P3_82.
The data contains information on monthly interest rates on bonds that pay money a year after the day they are bought, and the changes in the interest rates at different intervals. The data pertains to 96 months, and prevailing interest rates on bonds and changes in the rates over the previous month.


The summary measures in respect of two variables viz. Bond Rates (FYGT1) and Changes in interest rates (Changes) is as under:


Summary measures for selected variables
FYGT1 Change
Count 97.000 96.000
Mean 6.898 -0.058
Median 7.050 -0.070
Standard deviation 1.614 0.309
Minimum 3.180 -0.720
Maximum 9.860 0.640
Range 6.680 1.360
Variance 2.603 0.095

The above summary shows that there are 97 observations in respect of FYGT1 and 96 in respect of changes.

The scatter plot shown here as under, draws the correlation between the FYGT1 and changes in the rates over the previous month.

Table of correlations
FYGT1 Change
FYGT1 1.000 0.172
Change 0.172 1.000

Table of covariances (variances on the diagonal)
FYGT1 Change
FYGT1 2.603 0.084
Change 0.084 0.095

The above scatter plot shows that maximum variation observations are located around FYGT1 of 8 and between FYGT1 of 6 and 8, whereas the highest FYGT1 is 9.860 and lowest value is 3.180.The observations are less between FYGT2 to FYGT14.They are centered around FYGT1 of 6 and 8The time series presentation of this observation is as under:

Thus it can be inferred that the volatility in interest rate is high when the rates are moderately high and not at the highest level.