Linear Regression

Question 1

Types of regression

Answer 1

Simple linear regression
Multiple linear regression
Ridge regression
Logistic regression

Question 2

What type of model is linear regression

Answer 2

Linear regression is one of the regressive prediction model

Question 3

type of output of linear regression model

Answer 3

This model gives the output in a continuous value format (-∞ to ∞)

Question 4

Linear regression model is supervised/ unsupervised learning model

Answer 4

supervised learning

Question 5

Linear regression model is used to ______

Answer 5

Linear regression model is used to calculate the unknown value based on the known value

Question 6

Regression definition
general equation

Answer 6

Regression is statistical technique used to model the relationship b/w the dependent variable and independent variable (one or more)
y = f(x, θ)
here θ denotes the set of parameters of the models i.e. m₁, m₂…mₙ, c

Question 7

Types of linear regression

Answer 7

Simple linear regression
Multiple linear regression

Question 8

Simple linear regression (definition)

Answer 8

This regression shows the relationship between the dependent variable and one independent variable.

Question 9

What is used to make prediction in simple linear regression

Answer 9

Straight line equation is used as best fit line to make prediction.

Question 10

equation used in simple linear regression

Answer 10

Question 11

Multiple linear regression (definition)

Answer 11

This regression model shows the relationship between the dependent variable and 2 or more independent variables.

Question 12

What is used to make prediction in multiple linear regression

Answer 12

predicted best fit line

Question 13

Goal of linear regression

Answer 13

Goal of a linear regression is to find out the best fit line which minimises the error between the predicted output and actual output based on the historical data (training data set).

Question 14

Another name of error (2)

Answer 14

Cost function or residual

Question 15

Assumptions in linear regression

Answer 15

1.) Linearity
2.) Homoscedasticity
3.) No multicolinearity

Question 16

Linearity

Answer 16

Data points are represented in the scatter plot in a linear order.

Question 17

Homoscedasticity (and also opposite of Homoscedasticity)

Answer 17

Homoscedasticity: Distance between the data points in the scatter plot is less

Question 18

No multicolinearity
(Also explain multicollinearity)

Answer 18

All the i/p variable or attributes are independent in the data set.

Multicolinearity means interdependency between the i/p variables.
Ex: x1 ∝ x2 (directly proportional)
Here no need to train the model with x1 and x2 attributes because Both are dependent. So drop any one attribute to make the independent attributes in the data set.

Question 19

How we know this as best fit line

Answer 19

We use the prefromance matrics to calculate the error.
If the error is low then fix the line as best fit line

Question 20

Slop of best fit line

Answer 20

slope(m) = Δy / Δx

Question 21

Graph of best fit line

Answer 21

Question 22

What is performance metrics

Answer 22

A system or standard of measurement

Question 23

Types of performance metrics

Answer 23

1.) R² measure
2.) Adjusted R² measure
3.) Mean square error (MSE)
4.) Root mean square error (RMSE)
5.) Mean absolute error (MAE)
6.) Mean absolute percentage error (MAPE)

Question 24

R² measure formula

Answer 24

Question 25

R² range

Answer 25

[0 to 1]

Question 26

Two special points about R²

Answer 26

If R² value is 1 means no error (error is zero) in the model. 100% accuracy. If R² value is close to zero then more errors are present in model. Error is high. Re-training required.

Question 27

Adjusted R² measure

Answer 27

Question 28

SSE

Answer 28

sum of square error

Question 29

MSE

Answer 29

MSE : Mean square Error

Question 30

RMSE

Answer 30

RMSE: Root mean square error RMSE = sqrt(MSE)

Question 31

MAE

Answer 31

MAE: Mean absolute error

Question 32

MAPE

Answer 32

MAPE: Mean absolute percentage error MAPE = MAE * 100

Question 33

How to calculate m and c in straight line equation which is best prediction line of simple linear regression

Answer 33

2 methods are used to calculate m and c 1.) Straight line method 2.) Ordinary least square method

Question 34

regression coefficient

Answer 34

m (slope)

Question 35

Straight line method

Answer 35

Question 36

Compare straight line method and ordinary least square method

Answer 36

In the straight line method, we considered only the first and last sample to calculate the slope. Therefore most is food for 1st and last samples only and bad for the rest of the samples. So, alternative required i.e.ordinary least square method. This take the mean value of all the data points to give the best prediction.

Question 37

m and c in terms of mean

Answer 37

ȳ = m.x̄ - c

Question 38

Ordinary least square method

Answer 38

m = covariance(x,y)/var(x) c = ȳ - m.x̄

Question 39

Which equation uses multiple linear regression

Answer 39

B = (XᵀX)⁻¹XᵀY

Question 40

How to find multiple linear regression (Explain whole method)

Answer 40