What do R and R represent?

What does the TM symbol mean?

The TM symbol placed next to a mark is meant to put the public on notice that the owner considers that particular mark to be proprietary. In other words, the owner is claiming rights to that mark even if a trademark application has not been filed. As discussed further below, a circle R symbol may be used only when a trademark is registered.

Not all marks are protectable, and the fact that a company placed a TM symbol next to a term or slogan does not necessarily mean that they have the right to stop others from using the term. Nonetheless, it is useful to know where a competitor is coming from if you see the TM symbol next to an unregistered mark. If you’re thinking of using or applying for a similar mark, you may want to reconsider unless you have strong arguments for making fair use of the term.

Does the TM symbol mean that a trademark application has been filed?

No, the TM symbol does not necessarily signify that a trademark application is pending. In fact, it is entirely lawful to use the TM symbol to signify unregistered common law rights to a mark for which federal registration has not been applied.

What is the difference between TM and SM symbols?

Both TM and SM symbols serve the same purpose: providing notice that a owner considers a particular mark to be proprietary. When a mark is used in connection with services, the mark is technically called a service mark. So the SM symbol can be applied to for marks for services while the TM symbol can be applied marks for goods.

What does the circle R symbol (®) mean?

The circle R symbol (®) means that a mark is federally registered with the US Patent and Trademark Office, either on the Principal Register or Supplemental Register.

When is it OK to use the circle R symbol?

Do not use the ® symbol if you have not yet secured a federal registration of your mark. Filing a trademark application alone does not entitle you to use the circle R symbol.

If you are launching new products under a new mark and need to file a Statement of Use for an Intent-To-Use application, make sure the mark shown on the product or packaging omits the circle R symbol. In filing a Statement of Use, it would be acceptable to submit specimens showing the TM or SM symbol.

How to use the ® symbol

The ® symbol is typically placed in the upper right hand corner or lower right hand corner of a mark that is registered with the USPTO.

Need help protecting a trademark?

Contact US patent and trademark attorney Vic Lin by email or call (949) 223-9623. We can help you determine the right type of trademark application to file and search for similar trademarks before filing. Save time and money by avoiding common mistakes made by do-it-yourself trademark filers.

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R-squared is a measure of how well a linear regression model fits the data. It can be interpreted as the proportion of variance of the outcome Y explained by the linear regression model.

It is a number between 0 and 1 (0 ≤ R2 ≤ 1). The closer its value is to 1, the more variability the model explains. And R2 = 0 means that the model cannot explain any variability in the outcome Y.

On the other hand, the correlation coefficient r is a measure that quantifies the strength of the linear relationship between 2 variables.

r is a number between -1 and 1 (-1 ≤ r ≤ 1):

  • A value of r close to -1: means that there is negative correlation between the variables (when one increases the other decreases and vice versa)
  • A value of r close to 0: indicates that the 2 variables are not correlated (no linear relationship exists between them)
  • A value of r close to 1: indicates a positive linear relationship between the 2 variables (when one increases, the other does)

Here are 3 plots that show the relationship between 2 variables with different correlation coefficients:

  • The left one was drawn with a coefficient r = 0.80
  • The middle one with r = -0.09
  • And the right one with r = -0.76:
What do R and R represent?

Below we will discuss the relationship between r and R2 in the context of linear regression without diving too deep into the mathematical details.

We start with the special case of a simple linear regression and then discuss the more general case of a multiple linear regression.

R-squared vs r in the case of a simple linear regression

We’ve seen that both r and R-squared measure the strength of the linear relationship between 2 variables, so how do they relate in the case of a simple linear regression?

When we’re dealing with a simple linear regression:

Y = β0 + β1X + ε

R-squared will be the square of the correlation between the independent variable X and the outcome Y:

R2 = Cor(X, Y) 2

R-squared vs r in the case of multiple linear regression

In simple linear regression we had 1 independent variable X and 1 dependent variable Y, so calculating the the correlation between X and Y was no problem.

In multiple linear regression we have more than 1 independent variable X, therefore we cannot calculate r between more than 1 X and Y.

When dealing with multiple linear regression:

Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + … + ε

R-squared will be the square of the correlation between the predicted/fitted values of the linear regression (Ŷ) and the outcome (Y):

R2 = Cor(Ŷ, Y) 2

Note that in the special case of the simple linear regression:
Cor( X, Ŷ) = 1
So:
Cor( X, Y ) = Cor( Ŷ, Y )

Which is why, in that special case:
R2 = Cor( Ŷ, Y ) 2 = Cor( X, Y ) 2

Further reading

  • What is a Good R-Squared Value? [Based on Real-World Data]
  • 7 Tricks to Get Statistically Significant p-Values
  • P-value: A Simple Explanation for Non-Statisticians

What does R and R means?

R & R. abbreviation. Britannica Dictionary definition of R & R. rest and recreation; rest and recuperation; rest and relaxation. We rented a cottage in the country to get a little R & R.

What did R stands for?

Republican. R. Registered Trademark (usually written ®) R.

What is R&R mean in business?

R&R. Roles & Responsibilities. Responsibility, Management, Projection. Responsibility, Management, Projection.

What does R and R mean in a budget?

Research and Development (R&D) Expenses Definition. Fundamental Analysis.