Data Modeling

Question 1

When is linear regression the correct choice for data model?

Answer 1

When there is a linear relationship between the dependent and independent variable.

Question 2

What are two ways you can check a linear regression model is the correct choice as a data model?

Answer 2

Run np.corrcoef(x, y1), a linear relationship is indicated by a result close to 1 or - 1.
Run plt.scatter(x, y1) and see if a linear relationship exists.

Question 3

What is linear regression with multiple independent variables called?

Answer 3

A multiple (or multivariate) linear regression model

Question 4

What is the definition of a “cost function”?

Answer 4

A cost function is a function that takes in the regression model and outputs a number indicating the quality of the fit. Lower costs are better than higher costs.

Question 5

What is a common measure of cost function?

Answer 5

Sum of squared errors.

Question 6

Outline workflow up until linear regression?

Answer 6

1. Collect data
2. Data study (EDA) and cleaning.
3. Isolate and study relationships, how do independent variables (features) relate to dependent variables (scatter plots etc).
4. Modelling

Question 7

What is the convention to import statsmodel

Answer 7

import statsmodels.formula.api as smf

Question 8

What is the syntax for running a linear regression analysis using statsmodels?

Answer 8

diamond_reg = smf.ols(“price ~ carat + depth + table”, data=diamonds).fit()
diamond_reg.summary()

Question 9

What are the areas of interest in the summary obtained after running a linear regression analysis using statsmodels?

Answer 9

The “coeff” for each independent variable.
The “p” value for each independent variable (if large > 0.05 or so) the variable is not useful.
The R squared value (closer to 1 is better).

Question 10

How can I use the Linear Regression analysis from statsmodels to make predictions on the data?

Answer 10

This creates a new column with the predicted price. Beware that the column names of “new_diamonds” in this case, must match the order of the independent variables passed into the linear regression analysis (.ols)
new_diamonds[‘predicted’] = diamond_reg.predict(new_diamonds)

Question 11

What is residual?

Answer 11

The difference between a measurement and it’s model prediction.

Question 12

Discuss the x axis in regression analysis.

Answer 12

The thing we are trying to explain.
The independent variable
Explanatory variable.

Question 13

Discuss the Y axis in regression analysis

Answer 13

The dependent variable

Response variable

Question 14

What is the gradient called on a regression analysis chart?

Answer 14

The regression coefficient.

Question 15

What is the relationship between the Pearson coefficient, and the standard deviations of the variables and gradient (regression coefficient)?

Answer 15

If the standard deviations of the variables are the same, the gradient and the Pearson coefficient is the same.

Question 16

What are the two main components of a statistical model?

Answer 16

A mathematical formula that expresses a deterministic, predictable components. And the residual error.

Question 17

What is logistic regression?

Answer 17

A form of regression developed for proportions which ensures a curve which cannot go above 100% or below 0%.

Question 18

What is n and p when describing a data set?

Answer 18

n is the number of records

p is the number of attributes (parameters)

Question 19

What is a 1 dimensional vector?

Answer 19

A column.

If it contains the outcomes that we are trying to predict by convention it is called ‘y’.

Question 20

What is a matrix of features?

Answer 20

The columns of data that will help us predict the vector ‘y’.
The number of rows should equal the rows of ‘y’,

Question 21

What is a binary classification?

Answer 21

Predicting the outcome of one of two possibilities.

Usually these two will be classified as 1 and 0, or positive vs. null.

Question 22

What is a Gini Impurity?

Answer 22

It measures the quality of a split in a decision tree.
Perfect splits provide a Gini Impurity of 0.

When training a decision tree, the best split is chosen by maximizing the Gini Gain, which is calculated by subtracting the weighted impurities of the branches from the original impurity.

Question 23

What are the steps involved in training a decision tree?

Answer 23

First determine the root node (the first feature to split on), this is done by trying each split and determining the best Gini Gain (every feature and every unique threshold), the best gain should be the root node.
Repeat this for each node until they are equally good or have a Gini Gain of 0, then they become a leaf node.

Question 24

Explain RMSE in regression modeling

Answer 24

Root Mean Squared Error
The standard deviation of the residuals
Ranges from 0 to infinity, with 0 being a perfect fit and the larger the number the more error
Absolute measure of goodness of fit, and therefore cannot be used to compare across different data sets, but between models with the same dataset
Same units as the dependent variable.
Predictions farther away have a greater impact on the RMSE and is therefore sensitive to outliers

Question 25

Explain MAE in regression models

Answer 25

Mean Absolute Error
The average absolute values of the errors between the true value and the predicted value
Similar to RMSE, Ranges from 0 to infinity with 0 being a perfect fit and is an absolute measure of fit
Predicted values father away contribute proportionally to the MAE and is therefore more robust to outliers than RMSE
Relatively intuitive and simple to explain regression metric.

Question 26

Explain R2 in regression models

Answer 26

Coefficient of Determination
Proportion of variance in the dependent variable that is predicted by the independent variables
Typically ranges from 0 to 1, with 1 being a perfect fit and 0 being no better than predicting the dependent variable with its mean
Relative measure of goodness of fit

Question 27

What is the “feature” and “target” in machine learning?

Answer 27

Features (y) are things that we are using to predict the target (X).

Question 28

When should you use a train/test split when fitting a model?

Answer 28

Always.