High School Creating Equation Based on Data Set of x,y Values

[Zarathuztra]

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.

 

[mfb]

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, ...

 

[Zarathuztra]

In that case I would say the tendency is for logarithmic and exponential. Could you suggest an example model for logarithmic?

 

[mfb]

y=c*log(x)?
y=c*log(x+d)?
y=c*log(x+d)+e?

 

[Svein]

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.