I have a dataset of real data, for example looking like this:
# Dataset 1 with known data known <- data.frame( x = c(0:6), y = c(0, 10, 20, 23, 41, 39, 61) ) plot (known$x, known$y, type="o")
Now I want to get an aswer to the question
"What would the Y value for 0.3 be, if all intermediate datapoints of the original dataset, are on a straight line between the surrounding measured values?"
# X values of points to interpolate from known data aim <- c(0.3, 0.7, 2.3, 3.3, 4.3, 5.6, 5.9)
If you look at the graph: I want to get the Y-Values, where the ablines intersect with the linear interpolation of the known data
abline(v = aim, col = "#ff0000")
So, in the ideal case I would create a "linearInterpolationModel" with my known data, e.g.
model <- linearInterpol(known)
… which I can then ask for the Y values, e.g.
(which should in this case give "3")
abline(h = 3, col = "#00ff00")
How can I realize this? Manually I would for each value do something like this:
- What is the closest X-value smaller
Xsmalland the closest X-value larger
Xlargethan the current X-value
- Calculate the relative position to the smaller X-Value
relPos = (X - Xsmall) / (Xlarge - Xsmall)
- Calculate the expected Y-value
Yexp = Ysmall + (relPos * (Ylarge - Ysmall))
At least for the software Matlab I heard that there is a built-in function for such problems.
Thanks for your help,