Working out the equation for coordinates on a graph

In summary, the conversation discusses finding an equation for a trend line based on a series of data points on a graph. The method suggested is to do a linear least-square fit, which would result in a straight line for the trend. However, it is also mentioned that if there is an underlying model, an exponential curve could be used instead. To calculate the equation for the trend line, the averages and sum of squares need to be calculated. It is recommended to use existing software, such as Matlab, to do this.
  • #1
Saints-94
63
1
I have a series of data points for X and Y points on a graph. The data is quite random and I am trying to work out a trend line so I can then form an equation for the line. How would I go about working out the equation for the data below.
(0, 580)
(6.7, 495)
(13.4, 445)
(18.7, 365)
(22.8, 350)
(27, 340)
upload_2017-3-6_20-7-31.png
 
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  • #2
Unless there is an underlying model that would suggest otherwise, I would consider that to be a straight line and do a linear least-square fit.
 
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Likes jedishrfu
  • #3
I'm not sure how I can apply that to the data that I have. Where would I start with working out an equation?
 
  • #4
You need to first calculate the averages, ##\bar{x}## and ##\bar{y}##. Then use eqs. (16) and (20) in the link I gave you to get ##\mathrm{ss}_{xx}## and ##\mathrm{ss}_{xy}##. You then get the slope from eq. (27) and the intercept from eq. (28).
 
  • #5
I was expecting to get a trend line that looked like an exponential curve. Is it possible to work out an equation that would give me an exponential curve?
 
  • #6
Saints-94 said:
I was expecting to get a trend line that looked like an exponential curve. Is it possible to work out an equation that would give me an exponential curve?
The problem with the non-linear case is that you can't get a direct answer. It becomes a multidimensional minimization problem.

The best is to use existing software to do this. Most graphing programs can do this, as well as other software such as Matlab.
 
  • #7
Ok, thanks. I have the Matlab software, but am unsure how to programme my data.
 

Related to Working out the equation for coordinates on a graph

1. What is the purpose of working out the equation for coordinates on a graph?

The purpose of working out the equation for coordinates on a graph is to determine the relationship between two variables and to represent that relationship visually on a graph. This allows for a better understanding of the data and can help with making predictions and drawing conclusions.

2. How do you work out the equation for coordinates on a graph?

To work out the equation for coordinates on a graph, you need to identify the two variables being represented on the x and y axes. Then, plot the given points on the graph and connect them with a straight line. Next, determine the slope of the line by calculating the change in y over the change in x. Finally, use the slope and one of the plotted points to write the equation in the form y = mx + b, where m is the slope and b is the y-intercept.

3. What is the significance of the slope in the equation for coordinates on a graph?

The slope in the equation for coordinates on a graph represents the rate of change between the two variables. It shows how much the dependent variable (y) changes for every unit change in the independent variable (x). A positive slope indicates a direct relationship between the variables, while a negative slope indicates an inverse relationship.

4. Can you solve for the equation of a curved line on a graph?

Yes, it is possible to solve for the equation of a curved line on a graph. This type of equation is known as a nonlinear equation and it involves a higher degree of complexity compared to a linear equation. The process involves using the points on the curve to create a system of equations and using algebraic methods to solve for the unknown variables.

5. How can working out the equation for coordinates on a graph be useful in real life?

Working out the equation for coordinates on a graph has several practical applications in real life. It can help in predicting trends and making forecasts, such as in financial or economic analyses. It can also be useful in engineering and scientific experiments to understand the relationship between different variables. Additionally, it can aid in decision-making processes by providing a visual representation of data and helping to identify patterns and correlations.

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