calculate the linear regression equation r2

Mutual fund performance – R-squared is used within the mutual fund industry by investors as a historical measure that represents how a funds movements correlates with a benchmark index. Some of areas within the Financial industry where r-squared is used includes: Usage Explanations and Cautions Who uses R-squared? 9 fund because its performance is most correlated to the S&P 500. Let’s assume the investor can choose between three funds with R2 values of. The closer the value gets to 1, the more correlated it is. The investor would look for a fund that has an r-squared value close to 1. For instance, let’s assume that an investor wants to purchase an investment fund that is strongly correlated with the S&P 500. Investors use the r-squared measurement to compare a portfolio’s performance with the broader market and predict trends that might occur in the future. Like I said before, r-squared is a measure of how well a particular line first a set of observations. These models benefit from continual increases in computational power, as well as, recent developments that provide additional data points like the recent flash crashes and ’08 credit crisis. Specifically, they are designing models to manage risks associated with their portfolios with an emphasis on minimizing risks.

One of the areas where R2 is being used by analysts is in the area of factor risk models. Again, what R2 tells you is that the percent in the variability in Y that is explained by the model. Again, 82% of the prices differences can be explained by the differences in the number of prices. There are other reasons besides the number of toppings why two sandwiches might cost differently. While the model does explain 82% of how the price differed, it doesn’t explain all the price differences. Price = $5 + $0.64(# of toppings) and R2 = 82%.Īt Fozzie’s, it’s a different story. And at the end of the week I went back home, plotted the points on a chart and found that I could explain the price using the following equation. The next day I did the same thing and sat outside Fozzie’s for 7 days and collected another 100 customer’s orders. Again, 100% of the variability in sandwich price is explained by the variability of toppings. Or in other words, the sole reason that prices differ at Jimmy’s, can be explained by the number of toppings. What R2 tells us for Jimmy’s Sandwich shop is that 100% of the differences in price can be explained by the number toppings. We know that prices of sandwiches vary, or they differ based on the number of toppings. When I say variability, you should think of the word “differs.” Now, I’m going to explain to you what r-squared means. To understand what r-square tells us you must understand the word variability. At the end of the week, I plotted these points on a chart and found out that I could explain the price using the following equation Price = $5 + $1.00(# of toppings) and figured out that r-squared = 100%. The third customer, Pat, ordered 5 topics and the price was $10.00. The second customer, Suzie, ordered 4 toppings and the price was $9.00. The first customer, Joe, ordered 3 toppings and the price was $8.00. Now, I sat outside Jimmy’s for 7 days and took a survey from all the customers leaving and asked how many toppings they ordered and what was the total price.

double meat $1.50, double cheese $0.75, or double lettuce $0.50). At Fozzie’s they also charge $5.00 for a sandwich, but different topping prices (i.e. double the meat $1.00, double the cheese $1.00, or double the lettuce for $1.00). At Jimmy John’s they charge $5 for a sandwich and $1.00 for each additional topping (i.e. To help explain what exactly R-squared means, I’m going to tell you about two sandwich shops in my town, Jimmy’s Sandwich Shop and Fozzie’s Sandwich Emporium. Once you have a list of errors, you can add them up and run them through the R-squared formula. Once the line of best fit is in place, analysts can create an error squared equation to keep the errors within a relevant range. There are several steps that you need to calculate before you can get to this point.įirst, you use the line of best fit equation to predict y values on the chart based on the corresponding x values.

Keep in mind that this is the very last step in calculating the r-squared for a set of data point. R-squared = 1 – (First Sum of Errors / Second Sum of Errors)

Calculate the linear regression equation r2