Numpy Statistics

Question 1

What is the standard import procedure for numpy?

Answer 1

import numpy as np

Question 2

How do you generate a list of 10000 random normalized data points, centered at “x” with standard deviation of “y”.

Answer 2

list_name = np.random.normal(x,y,10000)

Question 3

How do you get the mean of a numpy list?

Answer 3

list_mean = np.mean(list_name)

Question 4

How do you get the median of a numpy list?

Answer 4

list_median = np.median(list_name)

Question 5

How do you generate a list of 10000 random integers, ranging from “x” to “y”?

Answer 5

list_name = np.random.randint(x,y,10000)

Question 6

How do you get the mode of a numpy list (remember the import statement)?

Answer 6

from scipy import stats

list_mode = stats.mode(list_name)

Question 7

How do you get the standard deviation of a numpy list?

Answer 7

list_std = list_name.std()

Question 8

How do you get the variance of a numpy list?

Answer 8

list_var = list_name.var()

Question 9

How do you generate a list of 10000 random uniform data points, ranging from “x” to “y”?

Answer 9

list_name = np.random.uniform(x,y,10000)

Question 10

How do you generate an evenly-spaced list of numbers from x to y with a spacing of “gap”?

Answer 10

list_name = np.arange(-3, 3, 0.001)

Question 11

How do you visualize the probability density function with a given list (include necessary import statements)?

Answer 11

from scipy.stats import norm
…
plt.plot(list_name, norm.pdf(list_name))

Question 12

How do you visualize the exponential probability density function with a given list (include necessary import statements)?

Answer 12

from scipy.stats import expon
…
plt.plot(list_name, expon.pdf(list_name))

Question 13

How do you visualize the binomial probability mass function with a given list (include necessary import statements)?

Answer 13

from scipy.stats import binom
import matplotlib.pyplot as plt

n, p = 10, 0.5
list_name = np.arange(0, 10, 0.001)
plt.plot(list_name, binom.pmf(list_name, n, p))

Question 14

How do you visualize the Poisson probability mass function with a given list (include necessary import statements)?

Answer 14

from scipy.stats import poisson
import matplotlib.pyplot as plt

mu = 500
list_name = np.arange(400, 600, 0.5)
plt.plot(x, poisson.pmf(list_name, mu))

Question 15

How do you calculate the nth percentile of a numpy list?

Answer 15

per = np.percentile(list_name,n)

Question 16

What is a statistical moment?

Answer 16

A quantitative measure of the shape of a probability density function.

Question 17

Give the first four moments that were discussed.

Answer 17

First moment: mean.
Second moment: variance.
Third moment: skew.
Fourth moment: kurtosis.

Question 18

What is the scale of the skew value (what does it mean to have negative, zero, or positive skew)?

Answer 18

A longer tail to the left represents negative skew.
A longer tail to the right represents positive skew.
A perfectly normal model has zero skew.

Question 19

What is kurtosis?

Answer 19

It represents the shape of the tail and peak.

Question 20

What is the scale of the kurtosis value (what does it mean to have low or high kurtosis)?

Answer 20

A sharp peak represents high kurtosis.

Normal models have zero kurtosis.

Question 21

How do you get the skew of a numpy list?

Answer 21

import scipy.stats as sp

sp.skew(list_name)

Question 22

How do you get the kurtosis of a numpy list?

Answer 22

sp.kurtosis(list_name)

Question 23

What is covariance?

Answer 23

The measure of how two variables vary in tandem with their means. A near-zero covariance implies a low correlation, while a large covariance implies a high correlation.

Question 24

What is correlation?

Answer 24

The measure of a relationship between two variables.

Question 25

How do you get the correlation of two numpy lists?

Answer 25

np.corrcoef(x_list, y_list)

This returns a 2x2 array with the correlation at (0,1) and (1,0).

Question 26

How do you get the covariance of two numpy lists?

Answer 26

np.cov(x_list, y_list)

This returns a 2x2 array with the covariance at (0,1) and (1,0).

Question 27

What is Bayes’ Theorem?

Answer 27

P(A|B) = P(A) * P(B|A) / P(B)

Question 28

How do you get a linear regression from two variables?

Answer 28

from scipy import stats

slope, intercept, r_value, p_value, std_err = stats.linregress(x_list,y_list)

Question 29

How do you generate two lists of data that have varying linearity?

Answer 29

import numpy as np
from pylab import *

pageSpeeds = np.random.normal(3.0, 1.0, 1000)
purchaseAmount = 100 - (pageSpeeds + np.random.normal(0, 0.1, 1000)) * 3

scatter(pageSpeeds, purchaseAmount)

Question 30

When is a polynomial regression appropriate?

Answer 30

If the data is clearly non-linear.

Question 31

How do you perform an nth degree polynomial regression?

Answer 31

import numpy as np
x = np.array(x_list)
y = np.array(y_list)

pn = np.poly1d(np.polyfit(x, y, n))

Question 32

Does a high degree polynomial regression necessarily improve things? (Y/N)

Answer 32

No.

Question 33

How is multivariate regression written?

Answer 33

y = A + B1var_1 + B2var_2 + …

Question 34

How do you grab an Excel file at a specific link (don’t forget the import statement)?

Answer 34

import pandas as pd

df = pd.read_excel(‘link_name’)

Question 35

How do you show a few lines from an Excel file “df”?

Answer 35

df.head()

Question 36

How do you create a multivariate regression summary?

Answer 36

import statsmodels.api as sm

df['Model_ord'] = pd.Categorical(df.Model).codes
X = df[['Mileage', 'Model_ord', 'Doors']]
y = df[['Price']]

X1 = sm.add_constant(X)
est = sm.OLS(y, X1).fit()

est.summary()

Question 37

What is a multi-level model?

Answer 37

A model that contains a hierarchy of interdependent events.