# Trend in data - determining according to angle between regression line and vertical line?

This question is a little bit referring to this question How to determine trend strength from linear regression slope? but I found a another solution so I am creating new question to confirm my idea. In my previous question I need to determine how is a trend in dataset steep. I were trying to do it with slope parameter from linear regression equation. I have a another idea and I would like to consult it.

According to linear regression equation I can determine two points that lie on this regression line. Next I can create a line that crosses one of these two points and is collinear with x-axis. Now I can compute degree between this horizontal line and regression line. Maximum value of this angle is 90°. So I can compute my angle (e.g. 48°) and divide it with 90°.

Trend strength = 48 / 90 = 0.53


what means 53% of its maximum value and with this I can work in my application.

Question: Is my idea correct from statistical perspective?

• Technically, you describe a nonlinear re-expression of the estimated slope (that is, you have converted a slope into an angle measure in grads). What you ought to focus your attention on, then, is not "correctness" but on its potential usefulness and on its statistical properties. – whuber Mar 27 '13 at 13:19
• I am wondering if a method I mentioned is not nonsense, because its part of my school project and I don't want to incorporate some stupid things. – Artegon Mar 27 '13 at 13:27
• It makes sense, but in most applications it would not have good properties. As an example, when you change how your data are measured (such as changing from meters to kilometers or pounds to ounces), the slope in the linear regression changes in a simple predictable way. That will not be the case for the angle that you compute. As such, unless there is a unique or conventional choice of units for both the x and y variables and there is a natural interpretation of that angle, the angle is likely a poor choice for a numerical representation of the slope. – whuber Mar 27 '13 at 13:32

## 1 Answer

The angle with the x axis is linked to the slope of your regression line by $a = tan(angle)$. The angle doesn't bring more information than the slope itself...

If you want a cheap method for observing trends which will be easily understand by everyone: Spotting trends in time based data

• Thank you. I am solving a problem how to define trend in my dataset in one number (moving averages are great but I need one number). Indicator needs to be simple and easy to understand. As I mentioned in my original question, I get one number (0.53) and with this value I can work in my application. – Artegon Mar 27 '13 at 13:49
• But you get 1 number from the regression coefficient; 1 number from the angle; and 1 number from the angle/90...and all of these numbers are easily transformed into one another, so there is really no difference between them. – D L Dahly Mar 27 '13 at 13:52
• If you read the link you will see in my answer a cheap and easily understandable methode: comparing a short term mean to a long term mean. – lcrmorin Mar 27 '13 at 14:01
• @DLDahly - there is a difference for me, because when I divide an angle value with maximum value of 90 degrees I normalize it (unfortunately I don't know a maximum slope value for normalization - it's about my previous question). I can use it in ordinal scale and define a steep of trend in data (0 - 0.1. slow trend etc.). – Artegon Mar 27 '13 at 14:09
• @Imorim - thanks, I misunderstand it, I will read it again. – Artegon Mar 27 '13 at 14:10