demo-lesson-06-starter - (done).ipynb

Kernel: Python 3

##Lesson 05 Demo

%matplotlib inline
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
import seaborn as sns
sns.set_style("darkgrid")

# this is the standard import if you're using "formula notation" (similar to R)
import statsmodels.formula.api as smf

# read data into a DataFrame
data = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)
data.head()

#Checks for Linear Regression. It works best when:

1. The data is normally distributed (but doesn’t have to be)

2. X’s are independent of each other (low multicollinearity)

3. X’s significantly explain y (have low p-values)

Check 1. Distribution

Last time we plotted our data like this

# visualize the relationship between the features and the response using scatterplots
fig, axs = plt.subplots(1, 3, sharey=True)
data.plot(kind='scatter', x='TV', y='sales', ax=axs[0], figsize=(16, 8))
data.plot(kind='scatter', x='radio', y='sales', ax=axs[1])
data.plot(kind='scatter', x='newspaper', y='sales', ax=axs[2])

<matplotlib.axes._subplots.AxesSubplot at 0x1139a98d0>

• TV sales: non stable variance, diminishing returns

Seaborn plotting library

https://stanford.edu/~mwaskom/software/seaborn/index.html

Today we use lmplot https://stanford.edu/~mwaskom/software/seaborn/generated/seaborn.lmplot.html

sns.lmplot('TV', 'sales', data)

<seaborn.axisgrid.FacetGrid at 0x1138d9a20>

sns.lmplot('radio', 'sales', data)
sns.lmplot('newspaper', 'sales', data)

<seaborn.axisgrid.FacetGrid at 0x117be7cc0>

Check 2. Low Multicollinearity

cmap = sns.diverging_palette(220, 10, as_cmap=True)

correlations = data[['TV', 'radio', 'newspaper']].corr()
print(correlations)
print(sns.heatmap(correlations, cmap=cmap))

                 TV     radio  newspaper
TV         1.000000  0.054809   0.056648
radio      0.054809  1.000000   0.354104
newspaper  0.056648  0.354104   1.000000
AxesSubplot(0.125,0.125;0.62x0.755)

Student question:

1. Do these variables have colinearity?

Answer:

Check 3: X’s significantly explain y (have low p-values)

Let's take a look again the the crude model

lm = smf.ols(formula='sales ~ TV', data=data).fit() 

#this is the regression model 
#where sales are what you are trying to predict (dependant variable) and TV is your predictor (independant variable)
#the coefficient is the number that you multiply your predictor by to get your prediction 

#print the full summary
lm.summary()

• interecept: this value is what you would expect (in this case sales) if your predictors are zero, in this case TV = 0.

• TV or the predictor: this value is the amount that what you are trying to predict, in this case sales, would go up by, if TV or the predictor was raised by 1 unit. so sales would go up by .0475 for every unit in crease in TV.

• std err: if you take your coefficient of either the predictor or what you are tryin to predict, and add/subtract the std err x 2, you will be brought to the range of the lower and upper bounds of the curve. it is like the std dev, going out two bands which is 97.5% of the data.

• R squared: this shows significance and can be read as, the amount that the predictor contributes to the prediction. - R^2 of 100% indicates that the model explains all the variability of the response data around its mean.

• meaning R^2 of 100% in this case of TV, would suggest that TV is the sole driver of sales.

• in this case, our model suggests that TV is the driver of 61% of sales. leaving 39% to other variables.

• note that were you to invest 100 dollars in TV your sales would NOT increase by 61%, as they would only increase by 100*.0475, which would be $4.75.

• Important things to look out for when reading the results of a liner regression model:

• R^2: make sure that you have a high value

• P value: make sure it is below .05

• if P value is large, make sure that the confidence interval (aka .025 - .975) does not contain 0 in its range.

Student Model

Now do a full model with TV, Radio and Newspaper

syntax can be found here: http://statsmodels.sourceforge.net/devel/example_formulas.html

#fit model
lm = smf.ols(formula='sales ~ TV + radio + newspaper', data=data).fit()

#print the full summary
lm.summary()

#print summary

#fit model
lm = smf.ols(formula='sales ~ TV + radio', data=data).fit()

#print the full summary
lm.summary()

#print summary

X_variables = data[['TV', 'radio', 'newspaper']]
Y = data['sales']

r_squared = []

from itertools import combinations
    
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score
model = LinearRegression()

for i in combinations(X_variables.columns,2):
    model.fit(data[list(i)], Y)
    preds = model.predict(data[list(i)])
    r_2 = r2_score(Y, preds)
    r_squared.append([i, r_2])

r_squared

[[('TV', 'radio'), 0.8971942610828956],
 [('TV', 'newspaper'), 0.6458354938293271],
 [('radio', 'newspaper'), 0.33270518395032256]]

X_variables = data[['TV', 'radio', 'newspaper']]

from itertools import combinations

for i in combinations(X_variables.columns,2):
    print(i)

('TV', 'radio')
('TV', 'newspaper')
('radio', 'newspaper')

1. Which of the media buys were significantly associated with the sales?

Answer:

2. Controlling for all the other media buys, which media type had the largest association with sales?

Answer:

####3. Given that one of the variables above was not significant do we drop it from our model? Why or why not?

Answer: