Question

1. 5.232608753	51.33997	1
   4.559347708	3.047033	0
   4.550088246	11.71957	1
   3.386566659	28.04548	1
   0.989064618	0.202602	0
   4.555668273	67.83218	1
   4.186405129	53.06328	1
   1.207150769	78.43352	0
   3.445792543	14.46725	1
   2.962975266	23.10411	0
   0.173612404	65.70817	0
   2.768815371	65.28198	1
   2.747367434	97.82201	1
   4.486882933	77.4523	1
   4.824678695	0.743551	0
   5.586206724	48.65186	1
   2.755386381	73.45392	1
   1.787901977	97.36504	1
   5.951385802	90.85691	1
   2.737556923	15.44293	0
   5.408894983	4.157112	0
   1.715859824	0.937882	0
   1.278844906	74.59771	0
   2.514277044	97.32341	1
   3.187058008	38.67714	1
   4.949777159	87.91089	1
   5.948802076	99.45704	1
   4.58854855	73.22006	1
   4.944593251	2.002865	0
   4.095092929	30.82503	1
   1.580255616	81.42979	1
   5.582168688	77.37155	1
   1.409875297	73.8556	1
   4.173571574	10.78412	0
   3.405384527	76.08957	1
   5.303746588	91.13028	1
   2.646338619	30.76739	0
   5.648448558	24.47563	0
   5.460162608	6.448907	1
   2.530400279	92.75311	1
   5.282410782	26.05696	1
   4.798709185	42.12116	1
   4.300055705	57.20119	1
   4.729502404	6.523547	0
   2.476612604	55.6309	1
   3.190133005	67.05927	1
   1.021463153	77.07357	1
   0.733750098	95.86227	1
   2.724156232	4.533329	0
   4.232730005	96.12467	1

   For a column of data x and a column of data y, there is an equation that relates the slope of the line of best fit (m) with the correlation coefficient (r). That equation is:

m = r * std(y)/std(x)

In the equation above, std(y) represents the standard deviation of the y column of data and std(x) is the standard deviation of the x column of data.

Use the Pandas .corr() and .std() methods to compute the slope of the line of best fit between Diameter and Pigment（first & second col）.

Next, use compute the y-intecept of the line of best fit using:

b = ybar – m*xbar

         Lastly, plot the line of best fit using matplotlib.pyplot.

Answer 1

Assuming the data is already stored in data.csv by the column names of x and y

Code

#importing pandas as pd

import pandas as pd

#importing matplotlib,pyplot as plt

import matplotlib.pyplot as plt

from matplotlib import pylab

#making data frame from the csv file

df = pd.read_csv("data.csv)

#calculating the correlation

r = df.corr(method = 'pearson')

#calculating the standard deviation of all the variables in the dataset where axis = 0 calculation #column wise correlation and axis = 1 calculation row wise

sr = df.std(axis = 0, skipna = True)

#calculating the standard deviation of the specific column

stdy = df.loc[:,"y"].std()

stdx = df.loc[:,"x"].std()

m = r*stdy/stdx

#calculating mean of the y values

ybar = df.loc[:,"y"].mean()

xbar = df.loc[:,"x"].mean()

b = ybar – m*xbar

Y_pred = m*x + b

fig = plt.figure()
ax = plt.axes()

ax.plot(x, Y_pred,linestyle = '-')

plot.show()

Output

r = -0.18959

std(y) = 33.68728

std(x) = 1.55705

m = -0.18959*33.68728 / 1.55705= -4.1019

ybar = average of y values = 51.32871

xbar = average of x values = 3.54132

b = ybar – m*xbar = 51.32871 - (-4.1019)*3.54132 = 65.85485