# Enter the Collected Data
years = [1860, 1880, 1890, 1900, 1920, 1931, 1940, 1950, 1960, 1970, 1980, 1989];
adoption = [1, 7, 13, 15, 20, 51, 60, 71, 87, 96, 98, 100];

# Define Solution to Bass Model
function F(t, p, q)
    e = exp(-(p+q)*t)
    return (1 - e)/(1 + (q/p)*e)
end

# Transform Data
T = years .- 1860;
Y = adoption / 100; 

# Compute square error sqErr
function sqErr((p, q))
    Fpq = F.(T, p, q) 
    E = sum(Fpq.*Fpq - 2*Fpq.*Y + Y.*Y)
    return E
end

# Minimize the square error
using Optim
results = optimize(sqErr, [0.25, .5])
println(results)

# Extract minimizing parameters from results object
(pMin, qMin) = Optim.minimizer(results)
println("The minimizing parameter values are (p, q) = ($pMin, $qMin).")
println("The ratio q/p = $(qMin/pMin)")

# Plot data and fitted model on same set of axes
using Plots
plot(years, adoption, label="Collected Data")
Ffit = F.(T, pMin, qMin) * 100  
plot!(years, Ffit, label="Fitted Bass Model",
    legend=:right, xlabel="Year", ylabel="Adoption %",
    title="Flushing Toilet Technology Adoption in Society")