|  AUG 1993

Using Multiple Regression Analysis by Jack Karczewski

Using Multiple Regression Analysis by Jack Karczewski Happily, today's spreadsheets enable traders and investors to measure the relationships between any times series of data. In this article, a linear regression technique is explained for analyzing the relationship between interest rates, the yield on the S&P 500 and the S&P 500 price/earnings ratio. Time series analysis is simply a tool for measuring the relationships, if any, among various sets of data. One statistical method for data analysis is the linear regression technique, which is used to measure the relationships among variables. The regression is referred to as linear because a straight line that best fits the data can be approximated. thereby explaining the relationship. Once you have a formula for the line that best fits the data, you have then created a model for future reference. Here, we will focus on using the least-squares method for measuring linear relationships of interest rates as well as a popular stock market indicator. CHOOSING THE COMPONENTS Traders and investors routinely look at a host of indicators that includes valuation measures and intermarket relationships for planning their next trade or investment. One popular intermarket relationship is the effect of interest rates on the stock market. I have often wondered about the impact of these changing interest rates on the stock market. However, instead of looking at the relationship between interest rates and the stock market, I decided to explore the relationship between interest rates and a very popular valuation tool — the price/earnings ratio (P/E) of the Standard & Poor's (S&P) 500. I also included the yield on the S&P 500 as an input because I was curious about this indicator's association with the P/E ratio. It appears that interest rate changes have an impact on the market's P/E ratio and therefore on one of the basic valuation measures of the stock market. To explore this question, let's construct a rudimentary model of this economic phenomenon and analyze the results. We'll use short- and long-term interest rates and stock market yields as our model components and then determine their association with the price/earnings multiple of the S&P 500 index. Gathering the data and arranging it in a spreadsheet helps understand the relationship of the variables. Viewing the data graphically is also useful. Figure I illustrates the S&P 500 index as a graph. While it is useful to examine and compare the other charts to the S&P 500, bear in mind that it is the P/E ratio (Figure 2) that we are interested in exploring.

by Jack Karczewski