Creating Equation Based on Data Set of x,y Values

In summary, the individual is looking for a way to project a trend beyond the current data set of (10) values. They recall learning how to derive an equation to represent the data, but need assistance with the process. They are open to suggestions and mention that the trend may not be linear and could potentially be logarithmic or exponential. They inquire about possible models for a logarithmic trend, such as y=c*log(x), y=c*log(x+d), or y=c*log(x+d)+e. They also mention the possibility of using regression or creating a polynomial expression to fit the data.
  • #1
Zarathuztra
36
0
I'm attempting to reclaim lost knowledge... hopefully this works. I would like to take a data set I have x,y values and project the trend beyond the (10) values I currently have. For example, I have a graph with (10) values for x and y, but would like to graph the trend created by values 1-10 to values 11-15.

I recall learning how to derive an equation to represent the data set but how no idea how I used to to it. Need some help on this one. I'm sure there are other ways to do this that I haven't thought of and wouldn't mind suggestions.

PS, I know I could create a simple linear equation by eyeballing the best fitting slope, but would like to be more accurate as the trend is not always linear.
 
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  • #2
If the trend is not linear and you want to extrapolate beyond the outermost data points, you'll need some other model ("it is linear" is a model as well). There are many possible models, the best one will depend on your data source. A parabola, an exponential function, a square root, a logarithm, some combination of those, ...
 
  • #3
In that case I would say the tendency is for logarithmic and exponential. Could you suggest an example model for logarithmic?
 
  • #4
y=c*log(x)?
y=c*log(x+d)?
y=c*log(x+d)+e?
 
  • #5
Zarathuztra said:
I'm attempting to reclaim lost knowledge... hopefully this works. I would like to take a data set I have x,y values and project the trend beyond the (10) values I currently have. For example, I have a graph with (10) values for x and y, but would like to graph the trend created by values 1-10 to values 11-15.
As usual, it depends. If the data set is a set of measurements, I would use a form of regression (linear, quadratic, exponential...). If the data is a set of calculated values, you can create a polynomial expression that passes exactly through your data points (but that expression is usually useless in predicting values outside the original data set). I suggest you peruse https://en.wikipedia.org/wiki/Curve_fitting.
 

Related to Creating Equation Based on Data Set of x,y Values

1. How do I create an equation based on a data set of x,y values?

To create an equation based on a data set of x,y values, you can use a method called linear regression. This involves finding the line that best fits the data points by minimizing the distance between the line and each data point. The equation for this line is y = mx + b, where m is the slope and b is the y-intercept. You can use software such as Microsoft Excel or R to perform linear regression on your data set.

2. What is the importance of creating an equation based on a data set of x,y values?

Creating an equation based on a data set of x,y values allows you to model and predict relationships between variables. This can be useful in fields such as economics, physics, and engineering, where understanding the relationship between different factors can help make predictions and inform decision-making.

3. How do I know if the equation I have created accurately represents the data set?

One way to determine if the equation accurately represents the data set is by calculating the coefficient of determination (R²). This value measures the proportion of the variation in the data that is explained by the equation. A higher R² value indicates a better fit between the data and the equation.

4. Can I use an equation based on a data set of x,y values to make predictions outside of the data set?

Yes, you can use an equation to make predictions for values outside of the data set, but the accuracy of these predictions may vary depending on the quality of the data and the assumptions made in creating the equation. It is important to validate the accuracy of your predictions by testing them against new data.

5. Are there any limitations to creating an equation based on a data set of x,y values?

One limitation is that the equation may only be valid within the range of values in the data set. Extrapolating beyond this range may result in inaccurate predictions. Additionally, the quality of the data and the assumptions made in creating the equation can affect its accuracy. It is important to carefully evaluate the data and assumptions before using the equation to make predictions.

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