How to change marker size in caption in seaborn relplot

Question

Following is the working code. I want to have a few changes to following code which I am not sure how to do it.

1) Marker size is too small in the caption. I want marker size in the legend to increase(I tried legend.markersize which doesn't show any effect). 2) Secondly I want to draw a regression line. I tried code given in the last but shrinks the graph so I want the original graph with the regression line labeled with the parameters of regression line.

from matplotlib import pyplot as plt
import pandas as pd
import seaborn as sns
import numpy as np

d = {'x-axis':[71,35,61,253,145,157,218,241,291,277,159,167,171,188,240,254,258,269,277,288,298,347,349,353,360,380,441,443,506,528,530,537,538,566,600,762,815,889],
        'y-axis': [5,5,15,79,75,641,172,867,289,67,75,112,46,150,70,70,897,391,671,54,353,275,191,189,432,526,591,516,507,838,874,934,934,1086,698,913,1717,1482],
        'text':['p1','p2','p3','p4','p5','p6','p7','p8','p9','p10','p11','p12','p13','p14','p15','p16','p17','p18','p19','p20','p21','p22','p23','p24','p25','p26','p27','p28','p29','p30','p31','p32','p33','p34','p35','p36','p37','p38'],
        'size':[4,4,3,54,22,162,3,44,9,0,22,4,12,67,32,32,46,6,159,17,13,3,4,3,11,79,15,12,5,19,22,20,20,34,18,27,50,35],'hue':['good','bad','average','poor','good','bad','average','poor','good','bad','average','poor','poor','poor','poor','poor','poor','poor','poor','good','bad','good','bad','good','bad','good','bad','good','bad','good','bad','average','average','average','average','average','average','average']}
df = pd.DataFrame(d)
with sns.plotting_context(rc={"legend.fontsize":25,"legend.markersize":18,"axes.titlesize":20,"font.weight":'heavy',"legend.labelspacing":20}):
  p1 = sns.relplot(x='x-axis', y='y-axis',hue='hue',size='size',sizes=(300,1450),data=df,height=10, aspect=2 )
ax = p1.axes[0,0]
for idx,row in df.iterrows():
    x = row[0]
    y = row[1]
    text = row[2]
    ax.text(x+.05,y,text, horizontalalignment='left')
p1.set(xticks=[i for i in range(0, max(df['x-axis']) + 50, 50)],
       yticks=[i for i in range(0, max(df['y-axis']) + 500, 500)])

plt.show()

This code I used for drawing regression line.

b, a = np.polyfit(df['x-axis'], df['y-axis'], 1)
xtest = np.linspace(df['x-axis'].min(),df['x-axis'].max(),10)
ax.plot(xtest, a + b* xtest, '--')

Answer 1

from matplotlib import pyplot as plt
import pandas as pd
import seaborn as sns
import numpy as np
import scipy.stats as st


d = {'x-axis':[71,35,61,253,145,157,218,241,291,277,159,167,171,188,240,254,258,269,277,288,298,347,349,353,360,380,441,443,506,528,530,537,538,566,600,762,815,889],
    'y-axis': [5,5,15,79,75,641,172,867,289,67,75,112,46,150,70,70,897,391,671,54,353,275,191,189,432,526,591,516,507,838,874,934,934,1086,698,913,1717,1482],
    'text':['p1','p2','p3','p4','p5','p6','p7','p8','p9','p10','p11','p12','p13','p14','p15','p16','p17','p18','p19','p20','p21','p22','p23','p24','p25','p26','p27','p28','p29','p30','p31','p32','p33','p34','p35','p36','p37','p38'],
    'size':[4,4,3,54,22,162,3,44,9,0,22,4,12,67,32,32,46,6,159,17,13,3,4,3,11,79,15,12,5,19,22,20,20,34,18,27,50,35],'hue':['good','bad','average','poor','good','bad','average','poor','good','bad','average','poor','poor','poor','poor','poor','poor','poor','poor','good','bad','good','bad','good','bad','good','bad','good','bad','good','bad','average','average','average','average','average','average','average']}

df = pd.DataFrame(d)

p1 = sns.relplot(x='x-axis', y='y-axis',hue='hue',size='size',sizes=(300,1450),data=df,height=10, aspect=2 )
p1._legend.remove()
ax = p1.axes[0,0]
for idx,row in df.iterrows():
    x = row[0]
    y = row[1]
    text = row[2]
    ax.text(x+.05,y,text, horizontalalignment='left')
p1.set(xticks=[i for i in range(0, max(df['x-axis']) + 50, 50)],
       yticks=[i for i in range(0, max(df['y-axis']) + 500, 500)])

#Regression part

slope, intercept, r_value, p_value, std_err = st.linregress(df['x-axis'],df['y-axis'])
line_df = pd.DataFrame()
line_df['line'] = slope*df['x-axis']+intercept
p,= plt.plot(df['x-axis'], line_df['line'],label='({:.2f})x+({:.2f})'.format(slope,intercept))

# adding legends for seaborn relplot
lgnd = plt.legend(loc="lower right", numpoints=1, fontsize=20)
for i in range(2,6):
    lgnd.legendHandles[i]._sizes = [300]  # you can change this for suitable size

plt.show()

I just modified your code a little bit, I hope this should do the work.