Linear interpolation is the process of estimating an unknown value of a function between two known values.
Given two known values (x1, y1) and (x2, y2), we can estimate the y-value for some point x by using the following formula:
y = y1 + (x-x1)(y2-y1)/(x2-x1)
The following example shows how perform linear interpolation in R.
Example: Linear Interpolation in R
Suppose we have the following data frame with x and y values in R:
#define data frame df <- data.frame(x=c(2, 4, 6, 8, 10, 12, 14, 16, 18, 20), y=c(4, 7, 11, 16, 22, 29, 38, 49, 63, 80)) #view data frame df x y 1 2 4 2 4 7 3 6 11 4 8 16 5 10 22 6 12 29 7 14 38 8 16 49 9 18 63 10 20 80
We can use the following code to create a scatterplot to visualize the (x, y) values in the data frame:
#create scatterplot plot(df$x, df$y, col='blue', pch=19)
Now suppose that we’d like to find the y-value associated with a new x-value of 13.
We can use the approx() function in R to do so:
#fit linear regression model using data frame model <- lm(y ~ x, data = df) #interpolate y value based on x value of 13 y_new = approx(df$x, df$y, xout=13) #view interpolated y value y_new $x  13 $y  33.5
The estimated y-value turns out to be 33.5.
If we add the point (13, 33.5) to our plot, it appears to match the function quite well:
#create scatterplot plot(df$x, df$y, col='blue', pch=19) #add the predicted point to the scatterplot points(13, y_new$y, col='red', pch=19)
We can use this exact formula to perform linear interpolation for any new x-value.
The following tutorials explain how to perform other common tasks in R:
How to Solve a System of Equations in R
How to Predict Values in R Using Multiple Regression Model