最佳拟合线与散点图不匹配

Question

Below is my scatter plot with a regression linear. Just by looking at how the markers are distributed on the plot, I feel like the linear is not covering them correctly. From what i see, it is supposed to be more of a diagonal and a more straight line instead of a curve. here is my code producing the plot:

for i in range (len(linkKarmaList)):
    plt.scatter(commentKarmaList[i], linkKarmaList[i], marker="o", s=len(clearModSet[i])*1.0*0.9)
x = numpy.asarray(commentKarmaList)
y = numpy.asarray(linkKarmaList )
plt.plot(numpy.unique(x), numpy.poly1d(numpy.polyfit(x, y, 1))(numpy.unique(x)))
plt.xlabel('Comment Karma ')
plt.ylabel('Link Karma')
plt.title('Link and comment Karma of most popular Forums on reddit')
plt.xscale('log')
plt.yscale('log')
plt.legend()
plt.show

Am I interpreting that correctly? What am I missing?

Answer 1

You're trying to fit a straight line y = a*x + b , which doesn't look like a straight line in log-space. Instead, you should be plotting a straight line in log-space.

This comes down to log(y) = a * log(x) + b Which we can then rewrite to log(y) = log(x^a) + b If we then take the exponent of this, we find: y = x^a * 10^b or just y = C * x^a , where C (=10^b) and a are the fitting parameters and x and y are your data. This is the function that makes a straight line in log-log space, which is the function you should try to fit against your data.

Answer 2

From what you show, I'd say the problem is that in the log-log plot the scatterplot looks more or less like a line.

The problem is that you're fitting against natural values and then plotting in a log-log plot.