Lesson 4.1: Intro to Regression

Question 1

density curve in Excel

Week 3 Homework

Answer 1

1. In Column ‘A’, generate series of numbers from -3 to 3 with an increment of 0.1 (z-values)
2. In Column ‘B’, compute ‘Individual p-value’ by using NORM.S.DIST(z-value,FALSE) function.
   - ‘TRUE’ = cumulative p-value, ‘FALSE’ = individual p-value.
3. Select column ‘A’ and ‘B’. Create scatter plot with column ‘A’ on x-axis, and column ‘B’ on y-axis.

Question 2

density curve in R

Week 3 Homework

Answer 2

1. x <- seq(-3, 3, 0.01)
2. y <- dnorm(x)
3. curve <- plot(x, y, type = ‘l’)

Question 3

linear regression

Answer 3

• equation that fits into given observations
• y = mx + b OR y = β1x + c

2 Variable Regression
- How a response variable “y” changes as the predictor (explanatory) variable “x” changes

Multiple Regression
- How a response variable “y” changes as the predictor (explanatory) variables “x1”, “x2”, … “xn” change

Question 4

single-variable polynomial regression

Answer 4

y may curve - not linear when polynomial

• 𝑦=𝑐+𝑎1𝑥
• 𝑦=𝑐+𝑎1𝑥+𝑎2𝑥²
• 𝑦=𝑐+𝑎1𝑥+𝑎2𝑥²+𝑎3𝑥³ 𝑦=𝑐+𝑎1𝑥+𝑎2𝑥²+𝑎3𝑥³+𝑎4𝑥⁴
• 𝑦=𝑐+𝑎1𝑥+𝑎2𝑥2+𝑎3𝑥3+𝑎4𝑥4+⋯𝑎𝑛𝑥𝑛

Question 5

Ordinary Least Squares
(OLS)

Answer 5

The least squares regression line of y and x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible

Question 6

OLS

residual

Answer 6

• distance from the perfect line to the given point
• compute and square that distance
• doesn’t work well with high-dimensional data (many independent variables)

Question 7

machine-learning methods

2

Answer 7

1. supervised - response variable
2. unsupervised - no response variable

Question 8

supervised machine learning

Answer 8

Model development, Model verification, Model deployment

1. split data into training and test data (eg. 80/20)
2. Model Development: take training data, use modeling technique (eg. regression) to build model (equation)
3. Model verification: test the model on test data with known response value

• Subject to training and test/generalization errors

Question 9

supervised machine learning

generalization error

Answer 9

• Single split model assessment methodology
• The model is tested on hold out sample
• Only the hold out sample accuracy is reported