LsqFit seems to be more general and conveniently provides the confidence intervals for the parameters estimated.
A correlation coefficient might also be obtained from the approximation of the covariance matrix. An attempt below, r formula to be confirmed.
PS: in your case it is possible and better to work with a log-log scale.
using LsqFit, Plots, Printf
# input noisy data
t = 0.01:0.01:1
y = 420*t.^(-0.13 .+ 0.02*rand(length(t)))
# LsqFit
m(t, p) = p[1] * t.^(-p[2])
p0 = [0.5, 0.5]
fit = curve_fit(m, t, y, p0)
# fit parameters and confidence interval
p = fit.param
confidence_interval(fit, 0.1) # 10% confidence intervals
# correlation coefficient = covariance of 2 variables / product of their standard deviations
cov = estimate_covar(fit)
r = cov[1,2]/sqrt(cov[1,1]*cov[2,2]) # TODO: confirm formula
# plot results
str = @sprintf("%.1f",p[1])*"*t^(-" * @sprintf("%.3f",p[2]) * ")" * @sprintf("; r ~ %.2f",r)
scatter(t,y, mc=:reds, ms=3, xlabel="t", label="input data")
plot!(t,m(t,fit.param),ly=0.25,lc=:blue, ylabel="y(t)", label="LsqFit: "*str)
julia> p = fit.param
419.2404632519413
0.12214587254371537
julia> confidence_interval(fit, 0.1) # 10% confidence intervals
(418.14933388256867, 420.331592621314)
(0.12055572549189375, 0.12373601959553698)
julia> r = cov[1,2]/sqrt(cov[1,1]*cov[2,2]) # TODO: confirm formula
-0.7431633567883187
