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# R-Squared Definition, Interpretation and Tutorial for Finance

A scale from 0 to 1 makes this difficult-to-calculate measure, easy to interpret.
1. Define - Define R-squared for Finance.
2. Context - Use R-squared in a sentence.
3. Video - See the charts in Excel.
4. Script - Follow along with the transcript below.
5. Quiz - Test yourself. by Paul Alan Davis, CFA
Updated: February 18, 2021
Many in Finance race to interpret R-Squared without thinking about its context. Here we review it more deeply below.

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## How to Interpret R Squared for Investment Modeling

Intermediate

R-Squared is a measure of the strength of the relationship between two data sets, often called variables. With investments it is used for statistical interpretations, most commonly for single-variable linear regressions.

The R refers to Pearson's R, sometimes just r, from correlation and is calculated by squaring the correlation. between a pair of securities. This transforms the correlation scale, of -1 to +1, to an easily interpreted scale of 0 to 1. On the one end, 0 indicates no relationship and 1 indicates a perfect linear relationship between the variables.

Synonym: coefficient of determination, r2, R Squared

For context, since the range is from 0 to 1, or 0.01 to 1.00, or 0% to 100%, it's easy to assume the pattern is linear, when it isn't. Recall R-Squared comes from squaring correlation, so the pattern is curved. So the way we naturally interpret the percentile scale doesn't exactly work the same here.

Also, the interpretation depends on which branch of the sciences you're analyzing. In the hard sciences or earth sciences high R-Squared measures may be above 0.90, whereas for the social sciences like economics, an R-Squared of 0.70 may represent a high reading.

### In a Sentence

Doc:  Who remembers why it is important to review R-Squared with beta.
Mia:  Even a random shotgun pattern has a line of best fit.

### Video

This video can be accessed in a new window or App , at the YouTube Channel or from below.

R-Squared definition for investment modeling (4:31)

### Video Script

The script includes two sections where we visualize and demonstrate the concept of R-squared.

#### Visualize

We're sitting right here in Excel and this is a snippet from our boot camp course.

This is one depiction of R-squared, from a scatterplot of returns for one stock Merck versus a basket of stocks, the Market, for 60 periods. Think about each dot here as returns for the Market on the x-axis and Merck on the y-axis, for each month.

So if stocks exhibit co-movements, as they appear to here, then a pattern will look linear. A random shotgun pattern would have low R-squared.

Once we square correlation, the direction of the line goes away, and we can only interpret the goodness of fit of the line versus the data points.

The best way to understand R-squared is with an example, so let's head there now.

#### Demonstrate

We'll walk all the way through a calculation for two stocks, Microsoft and eBay.

We have six monthly returns for each stock from April to September 2003. Column F is the return on Microsoft, eBay is in column G.

Next we compute the average of each, here 2.38% and 3.98%. Then we move those over to columns H and I.

In column J take the return minus this average which gives us 3.24%. That's 5.62% minus 2.38%. For eBay it is 8.91% minus 3.98% or 4.93%. Carry that formula down, and let's call these demeaned returns.

Next, in column L, multiply these together. As you notice, when the stocks move together, like in April, the product is negative. And when they move in opposite directions, the product is negative.

Next, using the =SUM function, add up the products to get -0.0037 for the pair of stocks. Next, divide by 6 observations for a covariance of -0.0006 for the pair of stocks. This isn't interpretable as the units are returns-squared, so we translate to correlation by dividing by the product of the two standard deviations.

So to interpret, the R-squared explains what percentage of the total errors is explained by the x-variable.

### Quiz

To calculate R-squared divide the covariance between a pair of assets by the product of their standard deviations and then square the result. | True or False?

True. The first part is correlation.

The R-Squared for a scatterplot that looks close to a shotgun pattern would be closest to what number? | -0.85 or -0.15 or 0.25 or 1.0?

0.25. R-Squared are positive numbers.

Still unclear on R-squared? Leave a question in the comments section on YouTube or check out the Quant 101 Series, specifically How to interpret Correlation and R-squared.

### Related Terms

Our trained humans found other terms in the category statistics for finance you may find helpful.

## What's Next?

• To see all Glossary terms, click Outline.
• To learn time-series Rolling Regression measures, click Back.
• For a few tidbits about the statistical term Sample, click Next.

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