A linear regression is one

of the easiest algorithm in machine learning. It is a statistical model that attempts to

show the relationship between two variables. with the linear equation. Hello everyone. This is Atul from Edureka

and in today’s session will learn about

linear regression algorithm. But before we drill down

to linear regression algorithm in depth, I’ll give you a quick overview

of today’s agenda. So we’ll start a session with a quick overview

of what is regression as linear regression

is one of a type of regression algorithm. Once we learn about regression, it’s use case the various

types of it next. We’ll learn about the algorithm

from scratch where I’ll teach you it’s mathematical

implementation first, then we’ll drill down

to the coding part and Implement linear

regression using python in today’s session will deal with linear regression algorithm

using least Square method check its goodness of fit or how close the data is to the fitted regression line

using the R square method. And then finally, what will do will optimize

it using the Gradient descent method in the last part

on the coding session. I’ll teach you to implement

linear regression using Python and the coding session

would be divided into two parts. The first part would consist of linear regression

using python from scratch where you will use

the mathematical algorithm that you have learned

in this session. And in the next part

of the coding session will be using scikit-learn

for direct implementation of linear regression. All right. I hope the agenda is clear

to you guys are like so let’s begin our session

with what is regression. Well regression analysis is a form of predictive

modeling technique which investigates

the relationship between a dependent

and independent variable a regression analysis

involves graphing a line over a set of data points that most closely fits

the overall shape of the data or regression shows the changes

in a dependent variable on the y-axis to the changes in the explanatory variable

on the x-axis fine. Now you would ask

what are the uses of regression? Well, they are major

three uses of regression. Let’s has the first

being determining the strength of predictors, ‘s the regression might be used to identify

the strength of the effect that the independent variables

have on the dependent variable. For example, you

can ask question. Like what is the strength

of relationship between sales and marketing spending or what

is the relationship between age and income second is forecasting and effect in this

the regression can be used to forecast effects

or impact of changes. That is the regression analysis

helped us to understand how much the dependent variable

changes with the change in one or more

independent variable fine. For example, you

can ask question like how much additional sale income will I get for each thousand

dollars spent on marketing. So it is Trend forecasting

in this the regression analysis to predict Trends

and future values. The regression analysis can

be used to get Point estimates in this you can ask questions. Like what will be

the price of Bitcoin in next six months, right? So next topic is linear

versus logistic regression. By now, I hope

that you know, what a regression is. So let’s move on

and understand its type. So there are various

kinds of regression like linear regression logistic

regression polynomial regression and others early, but for this session will be focusing on linear

and logistic regression. So let’s move on and let me tell

you what is linear regression. And what is logistic regression then what we’ll do

we’ll compare both of them. All right. So starting with

linear regression in simple linear regression, we are interested in things

like y equal MX plus C. So what we are trying to find

is the correlation between X and Y variable this means that every value of x has

a corresponding value of y in it if it is continuous. All right, however

in logistic regression, we are not fitting our data

to a straight line like linear regression instead

what we are doing. We are mapping Y versus X to a sigmoid function

in logistic regression. What we find out is is y 1 or 0

for this particular value of x That’s we are essentially

deciding true or false value for a given value of x fine. So as a core concept

of linear regression, you can see that the data is

model using a straight line. We’re in the case

of logistic regression. The data is model using

a sigmoid function. The linear regression is used

with continuous variables on the other hand

the logistic regression. It is used with categorical

variable the output or the prediction

of a linear regression is the value of the variable on the other hand the output of prediction of a logistic

regression is the probability of occurrence of the event. Now, how will you

check the accuracy and goodness of fit in case of linear regression

are various methods like measured by loss r squared

adjusted r squared Etc while in the case

of logistic regression you have accuracy precision

recall F1 score, which is nothing but

the harmonic mean of precision and recall next is Roc curve for determining the probability

threshold for classification or the confusion Matrix Etc. There are many. All right, so

Rising the difference between linear and logistic

regression you can say that the type of function you are mapping to is

the main point of difference between linear and logistic

regression a linear regression Maps a continuous X2 a continuous fi

on the other hand a logistic regression

Maps a continuous x to the binary why so we can use logistic

regression to make category or true false decisions from the data find so let’s move on ahead next is linear

regression selection criteria, or you can say when will

you use linear regression? So the first is classification and regression capabilities

regression models predict a continuous variable such as

the sales made on a day or predict the temperature of a city their Reliance

on a polynomial like a straight line

to fit a data set poses a real challenge when it comes towards building

a classification capability. Let’s imagine that you fit

a line with the train points that you have to imagine you add

some more data points to it. But in order to fit it

what you have to do, you have to change

your existing model. That is Maybe. Between the threshold itself. So this will happen

with each new data point you are to the model hence. The linear regression is not

good for classification models. Fine. Next is data quality

each missing value removes one data point that

could optimize the regression in simple linear regression. The outliers can significantly disrupt the outcome

just for now, you can know that if you

remove the outliers your model will become very good. All right. So this is about data quality

next is computational complexity a linear regression is often

not computationally expensive as compared to the decision tree or the clustering algorithm

the order of complexity for n training example and X features usually Falls

in either Big O of x square or bigger of xn

next is comprehensible and transparent the

linear regression are easily comprehensible

and transparent in nature. They can be represented by

a simple mathematical notation to anyone and can be

understood very easily. So these are some

of the criteria based on which you will select

the linear regression algorithm. Alright next is where is linear regression

used first is evaluating Trends and sales estimate. Well linear regression

can be used in business to evaluate Trends

and make estimates or focused. For example, if a company sales have

increased steadily every month for past few years, then conducting a linear

analysis on the sales data with monthly sales on the y axis

and time on the x axis. This will give you a line that predicts the upward Trends

in the sale after creating the trendline the company

could use the slope of the lines to focus

sale in future months. Next is analyzing. The impact of price changes

will linear regression can be used to analyze

the effect of pricing on consumer behavior. For instance. If a company changes the price on a certain

product several times, then it can record the quantity

itself or each price level and then perform

a linear regression with sold quantity as a dependent variable and price

as the independent variable. This would result in a line

that depicts the extent to which the Reduce

their consumption of the product as the price is increasing. So this result would help us

in future pricing decisions. Next is assessment of risk

in financial services and insurance domain for linear regression

can be used to analyze the risk, for example health insurance

company might conduct a linear regression algorithm how it can do it can do it

by plotting the number of claims per customer against its age

and they might discover that the old customers then to make more

health insurance claim. Well the result of such analysis might guide

important business decisions. All right, so by now you

have just a rough idea of what linear regression

algorithm as like what it does where it is used when you should use

it early now, let’s move on and understand

the algorithm and depth So suppose you have independent

variable on the x-axis and dependent variable

on the y-axis. All right suppose this is

the data point on the x axis. The independent variable

is increasing on the x axis. And so does the dependent

variable on the y-axis? So what kind of linear

regression line you would get you would get a positive

linear regression line. All right as the slope would

be positive next is suppose. You have an independent

variable on the x-axis which is increasing and on the other hand the

dependent variable on the y-axis that is decreasing. So what kind of line

will you get in that case? You will get

a negative regression line. In this case as the slope

of the line is negative and this particular line that is line of y equal MX plus C is a line

of linear regression which shows the relationship

between independent variable and dependent variable and this line is only known

as line of linear regression. Okay. So let’s add some data

points to our graph. So these are some observation

or data points on our graphs. Let’s plot some more. Okay. Now all our data points

are plotted now our task is to create a regression line

or the best fit line. All right. Now once our regression

line is drawn now, it’s the task

of production now suppose. This is our estimated value

or the predicted value and this is our actual value. Okay. So what we have to do our main

goal is to reduce this error that is to reduce the distance

between the estimated or the predicted value

and the actual value. The best fit line would be the

one which had the least error or the least difference

in estimated value and the actual value. All right, and other words we

have to minimize the error. This was a brief understanding of linear regression

algorithm soon. We’ll jump towards

mathematical implementation. All right, but for then

let me tell you this. Suppose you draw a graph

with speed on the x-axis and distance covered on the y axis with the time

demeaning constant. If you plot a graph

between the speed travel by the vehicle and the distance traveled

in a fixed unit of time, then you will get

a positive relationship. All right. So suppose the equation

of line as y equal MX plus C. Then in this case Y is

the distance traveled in a fixed duration of time x is the speed of vehicle m

is a positive slope of the line and see is

the y-intercept of the line. All right suppose

the distance remaining constant. You have to plot a graph

between the speed of the vehicle and the time taken

to travel a fixed distance. Then in that case

you will get a line with a negative relationship. All right, the slope

of the line is negative here the equation of line changes

to y equal minus of MX plus C where Y is the time taken

to travel a fixed distance X is the speed of vehicle m is

the negative slope of the line and see is

the y-intercept of the line. All right now, let’s get back

to our Independent variable. So in that term why is

our dependent variable and X that is

our independent variable. Now, let’s move on and see the mathematical implementation

of the things. Alright, so we have x equal 1 2 3 4 5 let’s plot

them on the x-axis. So 0123456 alike

and we have y as 34245. All right. So let’s plot 1 2 3 4 5 on the y-axis. Now, let’s plot our coordinates 1 by 1 so x

equal 1 and y equal 3, so we have here x equal 1 and y equal 3, so there’s a point

1 comma 3 so similarly we have 13243244 and 55. Alright, so moving on ahead. Let’s calculate the mean of X

and Y and plot it on the graph. All right, so mean of X is 1 plus 2 plus 3 plus 4

plus 5 divided by 5. That is 3. All right. Similarly mean of Y

is 3 plus 4 plus. 2 plus 4 plus 5 that is 18. So 18 divided by 5. That is nothing but 3.6 aligned. So next what we’ll do

we’ll plot R Min that is 3 comma 3 .6

on the graph. Okay. So there’s a point 3 comma 3 .6 see our goal is to find

or predict the best fit line using the least Square

Method All right. So in order to find that we first need to find

the equation of line, so let’s find the equation

of our regression line. All right. So let’s suppose this is our regression line

y equal MX plus C. Now, we have

an equation of line. So all we need to do is

find the value of M and see where m equals summation of x minus X bar X Y minus y bar

upon the summation of x minus X bar whole Square

don’t get confused. Let me resolve it for you. Alright, so moving on

ahead as a part of formula. What we are going to do

will calculate x minus X bar. So we have X as 1 minus X bar

as 3 so 1 minus 3 It is minus 2 next we have x

equal to minus its mean 3 that is minus 1 similarly. We have 3 minus 3 is 0 4 –

3 1 5 – 3 2. All right, so x minus X bar. It’s nothing but the distance

of all the point through the line y equal 3 and what does this y minus y bar implies

it implies the distance of all the point from the line x equal 3 .6 fine. So let’s calculate the value

of y minus y bar. So starting with y equal 3 – value of y bar

that is 3.6. So it is three minus 3.6

how much – of 0.6 next is 4 minus 3.6

that is 0.4 next to minus 3.6 that is – of 1.6. Next is 4 minus 3.6

that is 0.4 again, 5 minus 3.6 that is

one point four. Alright, so now we are done

with Y minus y bar. Fine now next we will calculate

x minus X bar whole Square. So let’s calculate x

minus X bar whole Square so it is minus 2 whole square. That is 4 minus 1 whole square. That is 1 0 squared is

0 1 Square 1 2 square for fine. So now in our table we have x

minus X bar y minus y bar and x minus X bar whole Square. Now what we need. We need the product of x

minus X bar X Y minus y bar. Alright, so let’s see

the product of x minus X bar X Y minus y bar that is minus

of 2 x minus of 0.6 that is 1.2 minus

of 1 multiplied by zero point 4 that is

minus of 0 point 4 0 x minus of 1.6. That is 0 1 multiplied

by zero point four that is 0.4. And next 2 multiplied

by 1 point for that is 2.8. All right. Now almost all the parts

of our formula is done. So now what we need

to do is get the summation of last two columns. All right, so the summation of X minus X bar

whole square is 10 and the summation of x minus X bar X Y minus y bar is 4

so the value of M will be equal to 4 by 10 fine. So let’s put this value

of m equals zero point four and our line y equal MX plus C. So let’s fill all the points

into the equation and find the value of C. So we have y as 3.6 remember

the mean by Ms. 0.4 which we calculated just now X

as the mean value of x that is 3 and we have the equation as 3 point

6 equals 0 point 4 x 3 plus C. Alright that is 3.6 equal

1 Point 2 plus C. So what is the value of C

that is 3.6 minus 1 Point 2. That is 2 point 4. All right. So what we had we had m

equals zero point four see as 2.4 and then finally when we calculate the equation

of the regression line what we get is y equal

zero point four times of X plus two point four. So this is the regression line. All right, so there is how you

are plotting your points. This is your actual point. All right. Now for given m equals

zero point four and SQL 2.4. Let’s predict the value of y

for x equal 1 2 3 4 & 5. So when x equal

1 the predicted value of y will be zero point 4 x one

plus two point four that is 2.8. Similarly when x equal

to predicted value of y will be zero point 4 x 2 + 2 point 4 that equals

to 3 point 2 similarly x equal 3 y will be 3 point 6 x equal 4 y will be 4 point 0 x equal 5 y will be

four point four. So let’s plot them on the graph and the line passing through

all these predicting point and cutting y-axis

at 2.4 as the line of regression now your task

is to calculate the distance between the actual and the predicted value and your job is

to reduce the distance. Like or in other words, you have to reduce the error

between the actual and the predicted value the line with the least error will be

the line of linear regression or regression line and it will also be

the best fit line. Alright, so this is

how things work in computer. So what it do it performs

n number of iteration for different values of M

for different values of M. It will calculate

the equation of line where y equals MX plus C. Right? So as the value

of M changes the line is changing so iteration

will start from one. All right, and it will perform

a number of iteration. So after every iteration what it will do it will

calculate the predicted value according to the line and compare the distance

of actual value to the predicted value and the value of M

for which the distance between the actual and the predicted value is

minimum will be selected as the best fit line. Alright now that we have calculated the best

fit line now it’s time to check the goodness

of fit or to check how good our

model is performing. So in order to Do that. We have a method

called R square method. So what is this R square? Well r-squared value is

a statistical measure of how close the data are to the fitted regression

line in general. It is considered that a high r-squared

value model is a good model, but you can also have a lower squared value

for a good model as well or a higher squared

value for a model that does not fit at all. All right. It is also known as

coefficient of determination or the coefficient

of multiple determination. Let’s move on and see

how a square is calculated. So these are our actual values

plotted on the graph. We had calculated

the predicted values of Y as 2.8 3.2 3.6 4.0 4.4. Remember when we calculated

the predicted values of Y for the equation Y

predicted equals 014 X of X plus two point four for every x

equal 1 2 3 4 & 5 from there. We got the predicted

values of Y. All right. So let’s plot it on the graph. So these are point

and the line passing through these points are nothing

but the regression line. All right. Now what you need to do is you have to check and compare

the distance of actual – mean versus the distance

of predicted – mean. Alright. So basically what you are doing

you are calculating the distance of actual value to the mean

to distance of predicted value to the mean I like so there is nothing

but a square in mathematically you can represent

our Square as summation of Y predicted values

minus y bar whole Square divided by summation of Y minus

y bar whole Square where Y is the actual value y p is the predicted value

and Y Bar is the mean value of y that is nothing but 3.6. So remember, this

is our formula. So next what we’ll do

we’ll calculate y minus y bar. So we have y is 3y bar as

3 point 6 so we’ll calculate it as 3 minus 3.6 that is nothing but

minus of 0.6 similarly for y equal 4

and Y Bar equal 3.6. We have y minus y bar as

zero point 4 then 2 minus 3.6. It is 1 point 6 4 minus

3.6 again zero point four and five minus 3.6 it is 1.4. So we got the value

of y minus y bar. Now what we have to do we

have to take it Square. So we have minus of 0.6 Square

as 0.36 0.4 Square as 0.16 – of 1.6 Square as 2.56 0.4 Square

as 0.16 and 1.4 squared is 1.96 now is a part

of formula what we need. We need our YP

minus y BAR value. So these are VIP values and we have to subtract

it from the mean. No, right. So 2 .8 minus 3.6

that is minus 0.8. Similarly. We will get 3.2 minus 3.6 that is 0.4 and 3.6 minus 3.6

that is 0410 minus 3.6 that is 0.4. Then 4 .4 minus 3.6 that is 0.8. So we calculated the value

of YP minus y bar now, it’s our turn to calculate

the value of y b minus y bar whole Square next. We have –

of 0.8 Square as 0.64 – of 0.4 Square as 0.160 Square

zero zero point four square as again 0.16 and

0.8 Square as 0164. All right. Now as a part of formula what it suggests it suggests

me to take the summation of Y P minus y bar whole square and summation of Y minus

y bar whole Square. All right. Let’s see. So in submitting y minus y bar whole Square

what you get is five point two and summation of Y P minus y bar whole Square you

get one point six. So the value of R square

can be calculated as 1 point 6 upon 5.2 fine. So the result which will get

is approximately equal to 0.3. Well, this is not a good fit. All right, so it suggests that the data points are far

away from the regression line. Alright, so this is how your graph will look

like when R square is 0.3 when you increase the value

of R square to 0.7. So you’ll see that the actual value would like

closer to the regression line when it reaches

to 0.9 Atkins more clothes and when the value

of approximately equals to 1 then the actual values lies

on the regression line itself, for example, in this case if you get a very low value

of R square suppose 0.02. So in that case what will see

that the actual values are very far away from the regression

line or you can say that there are too

many outliers in your data. You cannot focus

anything from the data. All right. So this was all about

the calculation of R square now, you might get a question

like are low values of Square always bad. Well in some field it

is entirely expected that I ask where

value will be low. For example any field that attempts to predict human

behavior such as psychology typically has r-squared values

lower than around 50% through which you can conclude that humans are simply harder to predict on the physical

process furthermore. If you ask what value is low, but you have statistically

significant predictors, then you can still

draw important conclusion about how changes in the predicator values

associated with the changes in the response value regardless of the r-squared the significant coefficient

still represent the mean change in the response for one unit

of change in the predicator while holding other predicate is

in the model constant, obviously this type of information can be

extremely valuable. All right. All right. So this was all about

the theoretical concept now, let’s move on to the coding part and understand the

code in depth. So for implementing

linear regression using python, I’ll be using Anaconda with jupyter notebook

installed on it. So I like there’s

a jupyter notebook and we are using python 3.01 it alright, so we are going

to use a data set consisting of head size and human brain

of different people. All right. So let’s import our data set

percent matplotlib and line. We are importing numpy as NP pandas as speedy

and matplotlib and from a totally we are importing

pipe lot of that as PLT. Alright next we will import

our data head brain dot CSV and store it

in the database table. Let’s execute the Run button

and see the output. So this task symbol, it symbolizes that

it still executing. So there’s a output

our dataset consists of two thirty seven rows

and 4 columns. We have columns as

gender age range head size in centimeter Cube and brain weights

and Graham fine. So there’s our sample data set. This is how it looks it consists

of all these data set. So now that we

have imported our data, so as you can see they are

237 values in the training set so we can find a linear. And Chip between the head size

and the Brain weights. So now what we’ll do

we’ll collect X & Y the X would consist

of the head size values and the Y would consist

of brain with values. So collecting X and Y.

Let’s execute the Run. done next what we’ll do

we need to find the values of b 1 or B naught

or you can say m and C. So we’ll need the mean of X

and Y values first of all what we will do will calculate

the mean of X and Y so mean x equal NP dot Min X. So mean is a predefined function

of Numb by similarly mean underscore y equal

NP dot mean of Y, so what it will return if you’ll return

the mean values of Y next we’ll check

the total number of values. So m equal length of X. Alright, then we’ll use the formula

to calculate the values of b 1 + B naught or MNC. All right, let’s execute the Run button and see

what is the result. So as you can see here on the screen we have got

d 1 as 0 point 2 6 3 and be not as three twenty

five point five seven. Alright, so now

that we have a coefficient. So comparing it with

the equation y equal MX plus C. You can say that brain weight

equals zero point 2 6 3 x head size plus 3 Seven so you can see that the value of M

here is zero point 2 6 3 and the value of C. Here is three twenty

five point five seven. All right, so there’s

our linear model. Now, let’s plot it and see

graphically let’s execute it. So this is how our plot looks

like this model is not so bad, but we need to find out

how good our model is. So in order to find it

there are many methods like root mean Square method

the coefficient of determination or the a square method. So in this tutorial, I have told you

about our score method. So let’s focus on that and see

how good our model is. So let’s calculate

the R square value. All right here SS underscore

T is the total sum of square SS underscore R

is the total sum of square of residuals and R square as the formula is

1 minus total sum of squares upon total sum

of square of residuals. All right next

when you execute it, you will get the value

of R square as 0.63 which is pretty Good now that you have implemented

simple linear regression model using least Square method. Let’s move on and see

how will you implement the model using machine learning

library call scikit-learn. All right. So this scikit-learn is a simple

machine learning library in Python welding machine

learning model are very easy using scikit-learn. So suppose there’s

a python code. So using the scikit-learn

libraries your code shortens to this length like so let’s execute

the Run button and see you will get the same are

to score as Well, this was all for today’s

discussion in case you have any doubt. Feel free to add your query

to the comment section. Thank you. I hope you have enjoyed

listening to this video. Please be kind enough to like it and you can comment any

of your doubts and queries and we will reply them at the earliest. Do look out

for more videos in our playlist and subscribe to Edureka

channel to learn more. Happy learning.

## 94 Comments

## edureka!

Got a question on the topic? Please share it in the comment section below and our experts will answer it for you. For Edureka Python Machine Learning Course curriculum, Visit our Website: http://bit.ly/2FBUtO7

## Binayak G Shankar

Best channel

## VEERESH NB

Thankyou very much

## Technical World

Thanku sir

## Anshuman Singh

how the formulas will be modified if y depends on more than one variable ?

## Manoj Kumar

nice video sir

## Mustafa Bohra

Best in this world!

## Amritha raj herle

The presentation is great. May I know how you created these presentations (is it power point presentation or something else?)

## Suravi Mahanta

Sir, could you please help me with the source from where you had downloaded that hairbrain dataset?

## Akshay Pandey

how should i start with ml?

## Abhishek Singh

awesome.. got it in one go!!!

## Hari Babu Sompalli

Excellent Session. Could you please share the data set used in this practice.

## tashu s

Can you please share the code which has been used in demo

## ranveer singh

An awesome session can you please share dataset and code?

## sidddiqui farheen

Great session. Will be greatfull if data set could b shared

## Megtuti

I get TypeError: 'numpy.float64' object cannot be interpreted as an integer from numer to print(b1,b0)which is annoying

## Joshua John

According to the formula for r-square, there is no subtraction from one… but in the implementation via coding, i noticed you subtracted from 1. why is that?

## Jyothi Koushik

can u post a video predicting bitcoin values using linear regression?

## Prabu Venkatesan

Great. Thanks edureka! ..

## AtomH

TNX FROM MEXICO

## manisha agale

Thank You I'm very well understand it

## Dipendra Sha

What is weight of a variable? how to calculate?

## Arun Thakur

Can anyone tell how to plot the least squared value ??

## Lucky Lucky

Good explanation

## Lucky Lucky

How to find the best value of m and c

## Aaliyah Kaltsum

great video! but please improve the sound quality 🙂 thank you very much

## Manish rajput

Can you please share the code which has been used in demo

## jakirajam khan

Very nice Explaination about LINEAR regression with PPTS

## Chats

I have a question

## Sangeet

Wonderful work…please share the code and data set

## Jerry Auvagha

Wonderful. Thanks.

## bharath bhimshetty

That last twist of scikit learn saved me from that for loop… thank you so much for this presentation…

## Karthikeyan S

really a great work.kindly explain the code slowly

## Donovan Chiazzese

Wow… the quality of this video and explanation is insanely good. Good job sir! Very appreciated

## Akhil Krishnan

Good tutorial

## Ujjwal Raj Shah

An awesome session can you please share dataset and code?

## Anumolu Kumar

Excellent explanation and so far the best video i have seen.

it will be very helpful if you share the ppts too

## Younus Ansari

Awesome video…made a complex understanding to a very simple understanding..trust me I was struggling to understand the Liner Regression for more then 1 month and my struggle ends just in 38 min of this video.. the explanation was superb Thank you is a little word.. God Bless you..

## Uday jagtap

Nice Sir….

## Divya Sampathirao

it was a nice session. Can you please share code and dataset?

## Ashmit Dwivedi

Sir your voice is so clear thanks to explain

## Ishwar Kurwade

Awesome explanation. Thax for the sharing video. Can you please share the dataset files so that we all can practice. Thanks in Advance.

## Amr Elsayed

Great session, keep on 🙂

## amrendra kumar

I got it. thanks. great jobs edureka.

## Akshay Rupnar

Literally such helpful video sir ….keep uploading such type of videos thanx ….👍👌

## vikas rajput

My Question is there, I have seen lots of videos on youtube but i didn't get way how to use machince learning in real life..

## Aisha Shabbir

Is there any acceptable range for R^2???

As for the inclusion and exclusion criteria of a dependent variable the p-value of linear regression has a range..

## Kina cute

This was the best one amongst all the videos I went through.. nice.. I need data set too…

## snehal sakhare

Can u plz explain more about scikit learning

## Vijay Ajarla

alright 🙂

## CS Mania

Awesome, It's a great explanation.

I got it, thanks a lot.

Quality Unmatched, A Vigorous teacher.

## G Caira

Great video man 🙂

## Sunitha A S

I got an error while finding root square…nymph.float64 object cannot be interpreted as integer

## Md. Akhtaruzzaman Adnan

Awesome lecture brother!thanks so much. can you share the code and data set please : [email protected]

## Perumal S

Very well Explained!

## Tushar Agarwal

Awesome

## Rubyat -Ul-Hasnat

29 mints just clear my one week confusions

## Ashwin A.J

Can we split data in train and test and analyze the data

## Abhishek 98

maaan thanks alllot your voice and you content was awesome much power to you

## Kiran Edupuganti

Very Good , looking for Mathematical understanding for prediction and code implementation. Very Much satisfied to understand prediction derivation. Thanks much.

## sourav Saha

Well explained…

## Siphesihle Y

Wow this helped me a lot! great video!!!

## Akshita Bhatnagar

May I get this dataset.. Or can u plz send me the link for this dataset

## proddutoori saikiran

Residual plots and VIF were not explained pls upload it as well

## Probal Das

plc.rcParams['figour.figoursize'] = [20.0,10.0] what is this ?

## Ganesh Raj

Awesome Video!… Very nicely explained and easy to understand.

## Jaisha Kakkoth

How the value of R- square can be used to predict the future values for a given input?

## Aishu Tk

The video was very amazing. It helped a lot! Thanks!

## akshat saxena

The only video that helped me in calculating the best fit line in so much detail and plain english. Thanks for the same.

## Ravi Kumar

Awesome explanation . Thank you edureka. Explanation is Very understandable manner to even poor mathematical background people. I need clarification. When R(square) is very less how to increase R(square) to make best fit of line. Is there any formula or mathematical procedure. Kindly clarify me.

## Karthik Dhanabal

Very well explained. Awesome tutorial Bro.

## Deojeet Sarkar

CODING AT 24:00

## Swastik Singh

deserves more views

## RAJU DEBNATH

👌

## Nick Thomson

24:20 – Programming part

## naveen kumar

Great Learning session , Could you please let us know how to get csv file which you used in your video , e.g. headBrain.csv

## Raminta Stankutė

You are awesome. It is wonderful video ! I wish all lecturers be so simple sometimes when needed.

## Mahesh S

where can get headbrain.csv ???????

## Digwijoy Mandal

Very good basic understanding delivered. Good refresher. Thanks for this video.

## sc13nt1st

Thanks edureka!.

## Kushwanth Kapa

can we have plot that line in python

## gaganutube2k8

How we know which is best fit algo in regression i.e. Mean sqaure error, measure by loss or R Squared? Can we use any one of them.

## siva chaitanya prasad

Excellent 😍

## Shikha Majumder

Excellent video. Would it be possible to share the data set and the code. Many thanks.

## Sunilk Kumar

Really superb ..

## Kamalakannan kk

The best Linear Regression tutorial i have ever seen!! Thank you edureka!!!

## R Sivaranganayakulu

very nice explanation

## Sombra47

dataset can be downloaded off from here- https://www.kaggle.com/jemishdonda/headbrain or https://github.com/mubaris/potential-enigma/blob/master/headbrain.csv

## Abirami

Very clear, neat and fantastic explanation to the linear regression.. Very well done!!… Thank you…

## Ikbal Nayem

Excellent explanation it was.

## Keyway Shao

Hello sir, I used Pycharm but it shows it is invalid syntax of the first line %matplotlib inline for the %, how to solve it?

## kishore kumar

It is very good!

## Tejaswini Reddy

May I get this dataset.. Or can u plz send me the link for this dataset ?

## Naveed Bhuiyan

Amazing video….really cleared out a lot of confusions. Will it be possible to get the data set?..