Python

Question 1

Import all libraries.

Answer 1

import numpy as np
import scipy as sp
import scipy.stats as stats
import pandas as pd
from pandas import DataFrame
import matplotlib.pyplot as plt
import statsmodels.formula.api as smf

Question 2

Create a dictionary and turn it into a dataframe.

Answer 2

dict1 = { ‘Age’:[23,45,17,64,57,32],
‘Height’:[1.7,1.9,1.55,1.8,1.75,1.65],
‘Names’:[‘Aoife’,’Brian’,’Catherine’,’Daniel’,’Eamonn’,’Fiona’],
‘Weight’:[82,88,55,101,75,67]}
df = DataFrame(dict1)

Question 3

Use pandas to read a csv file.

Answer 3

df = pd.read_csv(‘file_name.csv’)

Question 4

What does df.iloc[a, b] do?

Answer 4

Returns the ath row and bth column entry.

Question 5

What does df.iloc[3:5, :2] do?

Answer 5

Returns the 3rd row to the 4th row and returns the 0 and 1 column.

Question 6

What does .tail() and .head() do?

Answer 6

.tail() prints the last five rows and .head prints the first five rows.

Question 7

How can a summary description be created?

Answer 7

data.describe()

Question 8

How is the mean calculated for (a) a single column (b) all numeric columns? How would these calculations change to calculate standard deviation and maximum?

Answer 8

data[“ColumnName”].mean()
data.mean(numeric_only=True)

Replace mean with std or max.

Question 9

How is the loc function used? How can the id of the maximum be found?

Answer 9

data.loc[id, ‘columnnamewithid]
data[‘columnnamewithmax’].idxmax()

Question 10

Code to create a scatterplot?

Answer 10

plt.figure()
plt.scatter(data.Coursework,data.Exam)
plt.xlabel(‘Coursework grade’)
plt.ylabel(‘Exam grade’)
plt.axis([0,100,0,100])

Question 11

Code to create a histogram?

Answer 11

plt.figure()
plt.hist(data.Coursework,bins=10,alpha=0.5,label=’Coursework’)
plt.hist(data.Exam,bins=10,alpha=0.5,label=’Exam’)
plt.xlabel(‘Grade’)
plt.ylabel(‘Number of students’)
plt.legend()

Question 12

Code to create a boxplot?

Answer 12

plt.figure()
data.boxplot()
plt.ylabel(‘Grade’)
plt.ylim(0,100)

Question 13

How to get the number of times each outcome in a row occurs sorted by the outcome and not the number of times?
How to seed the random value?
How to select a random value from a column?

Answer 13

dataFrameName.ColumnName.value_counts(sort=False)
np.random.seed(seedNum)
np.random.choice(dataFrameName.ColumnName)

Question 14

What does the .unique() function do?

Answer 14

Print the unique values in a column.

Question 15

Simulate a binomial trial, where a coin is flipped ten times, use a sample size of 15.

Answer 15

stats.binom.rvs(n=10, p=0.5, size=15)

Question 16

Calculate the probability of observing heads 40 times out of 60 on an unbiased coin?

Answer 16

stats.binom.pmf(40, n=60, p=0.5)

Question 17

Calculate the probability of observing 10 or less heads when an unbiased coin is flipped 30 times?

Answer 17

stats.binom.cdf(10, n=30, p=0.5)

Question 18

Simulate a hypergeometric trial. Calculate probability of hypergeometric trial.

Answer 18

stats.hypergeom.rvs(N,s,n,size=10420)
stats.hypergeom.pmf(x,N,s,n)

Question 19

Simulate a poisson trial with a rate of 100, and sample size 10. Calculate the probability of 60 occurring with the same rate. Calculate the probability of 60 or less occuring with the same rate.

Answer 19

stats.poisson.rvs(100, size=10)
stats.poisson.pmf(60, 100)
stats.poisson.cdf(60, 100)

Question 20

Code for normal distribution.

Answer 20

x = np.linspace(-5,5,100)
plt.figure()
plt.plot(x,stats.norm.pdf(x,loc=0,scale=1))
plt.axis([-5,5,0,0.41])
plt.xlabel(‘$x$’,fontsize=16)
plt.ylabel(‘$f(x)$’,fontsize=16)
plt.xticks(fontsize=14)
plt.yticks([0,0.1,0.2,0.3,0.4],fontsize=14)
plt.title(‘Standard Normal Distribution’,fontsize=16)

Question 21

Simulate a standard normal distribution. Calculate probability of less than 0.5 occuring on a standard normal distribution.

Answer 21

stats.norm.rvs(loc=0,scale=1,size=100)
stats.norm.cdf(0.5,loc=0,scale=1)

Question 22

Code for exponential graph.

Answer 22

x = np.linspace(0,15,100)
plt.figure()
plt.plot(x,stats.expon.pdf(x,scale=4))
plt.axis([0,15,0,0.25])
plt.xlabel(‘iPad lifetime (years)’,fontsize=16)
plt.ylabel(‘Probability density’,fontsize=16)
plt.xticks(fontsize=14)
plt.yticks(fontsize=14)

Question 23

Simulate an exponential distribution with rate 4 and sample size 50. Calculate the probability of less than or equal to 5 occuring with the same rate.

Answer 23

stats.expon.rvs(scale=4,size=50)
stats.expon.cdf(5,scale=4)

Question 24

How do you sqrt n?

Answer 24

np.sqrt(n)

Question 25

How do you calcuate a sample std deviation as opposed to population s.d.?

Answer 25

np.std(X, ddof=1)

Question 26

Code to perform two-sided t-test?
Code to perform two-sample t-test?

Answer 26

t_statistic, p_value = stats.ttest_1samp(X,mu0)
stats.ttest_ind(data A, data B)

Question 27

Code to calculate correlation coefficent.

Answer 27

df.corr()

Question 28

How to print out summary data for linear regression?

Answer 28

import statsmodels.formula.api as smf
model = smf.ols(formula=’Y~X’,data=df).fit()
print(model.summary())

Question 29

What function is used to predict values?

Answer 29

model.predict({‘ColumnName’: Value})

Question 30

Code to plot data with fitted regression line.

Answer 30

xrange = np.linspace(140,200,100)
plt.plot(xrange,model.params.Intercept+model.params.Height*xrange)
plt.scatter(df.Height,df.Weight)
plt.xlabel(‘Height (cm)’)
plt.ylabel(‘Weight (kg)’)

Question 30

Code to plot residuals and check assumptions.

Answer 30

residuals = model.resid
plt.figure()
plt.hist(residuals)
plt.axis([-20,20,0,20])
plt.xlabel(‘Residuals’)
plt.ylabel(‘Frequency’)
plt.figure()
plt.scatter(df.Height,residuals)
plt.axis([142,195,-20,20])
plt.xlabel(‘Height’)
plt.ylabel(‘Residuals’

Question 31

Syntax for printing a variable within a string to 4 decimal places.

Answer 31

print(f”{variable:.4f}”)