Linear regression - accelerate framework in Swift

Question

My first question here at Stackoverflow... hope my question is specific enough.

I have an array in Swift with measurements at certain dates. Like:

var myArray:[(day: Int, mW: Double)] = []
myArray.append(day:0, mW: 31.98)
myArray.append(day:1, mW: 31.89)
myArray.append(day:2, mW: 31.77)
myArray.append(day:4, mW: 31.58)
myArray.append(day:6, mW: 31.46)

Some days are missing, I just didn't take a measurement... All measurements should be on a line, more or less. So I thought about linear regression. I found the Accelerate framework, but the documentation is missing and I can't find examples.

For the missing measurements I would like to have a function, with as input a missing day and as output a best guess, based on the other measurements.

func bG(day: Int) -> Double {
    return // return best guess for measurement
}

Thanks for helping out. Jan

Answer 1

My answer doesn't specifically talk about the Accelerate Framework, however I thought the question was interesting and thought I'd give it a stab. From what I gather you're basically looking to create a line of best fit and interpolate or extrapolate more values of mW from that. To do that I used the Least Square Method, detailed here: http://hotmath.com/hotmath_help/topics/line-of-best-fit.html and implemented this in Playgrounds using Swift:

//  The typealias allows us to use '$X.day' and '$X.mW',
//  instead of '$X.0' and '$X.1' in the following closures.
typealias PointTuple = (day: Double, mW: Double)

//  The days are the values on the x-axis.
//  mW is the value on the y-axis.
let points: [PointTuple] = [(0.0, 31.98),
                            (1.0, 31.89),
                            (2.0, 31.77),
                            (4.0, 31.58),
                            (6.0, 31.46)]

// When using reduce, $0 is the current total.
let meanDays = points.reduce(0) { $0 + $1.day } / Double(points.count)
let meanMW   = points.reduce(0) { $0 + $1.mW  } / Double(points.count)

let a = points.reduce(0) { $0 + ($1.day - meanDays) * ($1.mW - meanMW) }
let b = points.reduce(0) { $0 + pow($1.day - meanDays, 2) }

// The equation of a straight line is: y = mx + c
// Where m is the gradient and c is the y intercept.
let m = a / b
let c = meanMW - m * meanDays

In the code above a and b refer to the following formula from the website:

a:

b:

Now you can create the function which uses the line of best fit to interpolate/extrapolate mW:

func bG(day: Double) -> Double {
    return m * day + c
}

And use it like so:

bG(3) // 31.70
bG(5) // 31.52
bG(7) // 31.35