We use regression analysis frequently in our energy engineering analysis, but results can be less than ideal for many cases. In this and following posts, I will provide you with the building blocks to understand this aspect of energy analysis. So, the next time you run a regression analysis on energy data, calculate its CV(RMSE) to understand the model’s predictive accuracy. In addition to being able to flaunt your expertise on the subject, you will also significantly reduce your workload when the time for Measurement & Verification rolls around. If you’d like to dive deep into your energy use data and need help identifying opportunities for energy savings, contact us any time.

In Europe, butter prices have spiked forty percent, and pork prices in China are up twenty percent. By 2025, according to Runge and Senauer, rising food prices caused by the demand for ethanol and other biofuels could cause as many as 600 million more people to go hungry worldwide. The most seductive myth about ethanol is that it will free us from our dependence on foreign oil. But even if ethanol producers manage to hit the mandate of 36 billion gallons of ethanol by 2022, that will replace a paltry 1.5 million barrels of oil per day — only seven percent of current oil needs. Even if the entire U.S. corn crop were used to make ethanol, the fuel would replace only twelve percent of current gasoline use. Like believing we can replace gasoline with ethanol, the much-hyped biofuel that we make from corn.

Moving beyond regression analysis

For the dataset given above, The CV(RMSE) was found to be 6%, implying that the model is reliably predictive. The R-squared value does not paint an optimistic picture by itself (some sources suggest 0.75 as a lower threshold). However, when combined with other metrics, it can provide us an insight into what is actually happening under the hood. Last December the Energy Information Administration (EIA) released its latest estimate of U.S. Although natural gas reserves rose, the real story was crude oil reserves. In 2021 the average Henry Hub natural gas spot price was $3.89/MMBtu, which was the highest annual average since 2014.

A common theme is a “path to zero”, which defines how, and how quickly, a company will reach net zero carbon emissions. This means either that the company has taken steps to ensure that carbon emitted while doing business is cumulative dividend definition key features and formula eliminated or offset through projects that sequester carbon. Going by the popular opinion, of wanting an R-squared value of at least 0.75 or higher, one would deem this model as ‘bad’ and rush to discard its summary output.

Essentially, an R-squared value of 0.9 would indicate that 90% of the variance of the dependent variable being studied is explained by the variance of the independent variable. For instance, if a mutual fund has an R-squared value of 0.9 relative to its benchmark, this would indicate that 90% of the variance of the fund is explained by the variance of its benchmark index. So, if the R2 of a model is 0.50, then approximately half of the observed variation can be explained by the model’s inputs. There are a lot of different applications for regression models and r-squared, and financial analysts often try to determine how different metrics influence each other.

If you knew the scale was consistently too high, you’d reduce it by an appropriate amount to produce a weight that is correct on average. In this blog post, I look at five reasons why your R-squared can be too high. This isn’t a comprehensive list, but it covers some of the more common reasons. Select Setup Monitors and you would see a host of already prepared monitors. Click the link to open your Arize space where the model and data have been logged. Once successful, you will get a prompt like an image below that contains the link to the model and the data in Arize.

Hands-On Exercise of a Linear Regression Model Using R-squared Metric

The correlation observed in the five samples would then be misleading if we were to use it as the basis of our energy savings calculations. To gauge the predictive capability of the model, we could use it to predict the energy use of building and compare those predictions against the actual energy use. The statistical measure that allows us to quantify this comparison is the Coefficient of Variation of Root-Mean Squared Error, or CV(RMSE).


Some processes can have R-squared values that are in the high 90s. These are often physical process where you can obtain precise measurements and there’s low process noise. In finance, R-squared can be used to evaluate the performance of asset pricing models. In marketing, R-squared might be used to measure the effectiveness of advertising campaigns. In engineering, R-squared can be used to evaluate the accuracy of predictive maintenance models. This helps to identify models that have high predictive power without adding unnecessary parameters that do not contribute significantly to the explanation of variance in the data.

What Is Goodness-of-Fit for a Linear Model?

At its core, the p-value attempts to clarify whether the correlation between the variables as seen in the sample is purely chance, or if an actual relationship exists. We can see that while model’s R-squared value is quite low, it captures most of the energy consumption behavior of the facility, and so can be safely used for energy use prediction. As per ASHRAE Guideline 14, a CV(RMSE) of and below 25% indicates a good model fit with acceptable predictive capabilities.

What do different r-squared values mean?

You can get a sense of this by looking at it, but the best way to know how well the model explains the relationship is with the r-squared number. R-squared enters the picture because a lower R-squared indicates that the model has more error. However, you can’t use R-squared to determine whether the predictions are precise enough for your needs. In general, a model fits the data well if the differences between the observed values and the model’s predicted values are small and unbiased. Even when you meet the sample size guidelines for regression, the adjusted R-squared is a rough estimate.

R squared energy blog

We know that prices of sandwiches vary, or they differ based on 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. Or in other words, the sole reason that prices differ at Jimmy’s, can be explained by the number of toppings.

With a multiple regression made up of several independent variables, the R-squared must be adjusted. The first is that a high value of R-squared implies that the regression model is useful for predicting new observations. The accuracy of R-squared as an estimate of the population proportion is affected by the technique used to select terms for the model.

However, the population mean is unlikely to exactly equal the sample mean. A confidence interval provides a range of values that is likely to contain the population mean. Narrower confidence intervals indicate a more precise estimate of the parameter. In both cases, the relationship between consumption and its driving factor is imperfect.

But the biggest problem with ethanol is that it steals vast swaths of land that might be better used for growing food. In a recent article in Foreign Affairs titled “How Biofuels Could Starve the Poor,” University of Minnesota economists C. Ford Runge and Benjamin Senauer point out that filling the gas tank of an SUV with pure ethanol requires more than 450 pounds of corn — roughly enough calories to feed one person for a year. I’ve written about R-squared before and I’ve concluded that it’s not as intuitive as it seems at first glance. It can be a misleading statistic because a high R-squared is not always good and a low R-squared is not always bad.

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