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No, simple linear regression is a straightforward approach for predicting Y on the basis of a single

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predictor variable X.

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So if you take only one predictor variable, it is called simple linear regression.

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If we assume linear relationship between X and Y.

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Mathematically, it can be written as Y is approximately equal to be zero plus between X. It is nearly

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equal to because the value of Y that model will give may not be exactly equal to the value in our observation.

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Will come back to the thought later.

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Here, let us select only one variable from the dataset to predict price of the house.

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Let's say I choose the average number of rooms for this simple model so we will regress house price

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onto the number of rooms by putting the model price is nearly equal to the zero plus bedevilling times.

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Room number error zero and B1 are the unknown terms which are known as model coefficients or model parameters

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for the particular case of simple linear regression between is the slope and which is the intercept.

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Once we use the training data to estimate these two parameters because it won't be the one, you'll

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be using this heart symbol to denote estimated parameters from our data.

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So we will raise prices are going to be zero plus between cap times number of rooms.

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So for estimating the values of what parameters, we will be using the data points in our dataset.

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If you remember, our house pricing data set has 506 observations.

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This number of data points for general-purpose will be denoted by an smolan.

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So Smolan is 506 for our dataset.

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What this means is we have five hundred six pairs of X and Y values and that goal is to obtain coefficient

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estimate, zero cap and we have UNCAP such that the linear model fits the available data such as Vivint

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cap is equal to zero plus one cap X one, and if you generalize it for any eye, it is Y is nearly equal

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to be zero.

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Karplus be the one cap ex.

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In other words, we want our estimate in line to be as close to this point as possible.

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One method for measuring this closeness of our line is called the least squared method, which will

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discuss now.

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Once we done the model and get a line, the line will be predicting a value of by at each point I.

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This predicted value will be denoted by a gap.

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Now, we do have the actual values of where each of these points, the difference between these actual

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values and the predicted value is that, Miss, this is the residual and it is denoted by, as you can

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see in the graph, using the training data that we had, we have the line using the Betaseron be the

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one that we calculated.

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And this line is drawn here in the blue color.

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Each of these points is also plotted.

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Some of these points are exactly on the line, but most of them are missing the distance of that point

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from the line you need, as it will at some point, this residual is positive.

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At some point this is negative.

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When we are taking out the total residual of the sample, we cannot straight away from the map because

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some are positive and negative, therefore will define a new quantity called residual sum of squares.

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Now, since Odyssey's is something the root of each residual, it is representing the total error in

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this formula.

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You can see that for each of the point.

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We are subtracting the actual observed value from the predicted value and then squaring it.

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And we are doing this for all of the points.

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Now we have the total error of our predicted line and we want to minimize this error.

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So using calculus and matrix algebra, we will get these formulas for Betaseron be the one for which

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this error is minimized.

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So this approach is called Lee Square Meter, because we are minimizing the squared error squared sum

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of errors.

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So this Odyssey's value we are trying to minimize by differentiating and putting it to zero will get

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these values of between carbon zero.

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Got what this value, what these values are zero.

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And B, the one the calculated sum of squares will be minimum.

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So we this summation of X minus X, but if you remember, what is the meaning of the sample.

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So for each data point we will find out this different of each point from each mean and then will multiplied

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with the difference of each y y variable with X mean, you'll sum this product for all the points and

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will divide it by the difference of X from its mean squared I all points.

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Similarly, what does it mean.

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Value of Y minus beta one group times mean value of X.

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So we have mean value of X and Y.

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We first need to calculate the value.

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When we put between value and this formula, we will get to be the zero value.

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So using these formulas for simple linear regression, you can get the Beatles, you know, and be the

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one values.

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For our model, where we selected House Price as Y and Bromium as X environ this morning, this thought

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assortment, I get this result.

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I have highlighted the the values in this bluebox.

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This intercept is zero and room number is the X variable.

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And this is giving the confusion of this variable.

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So this is Beethoven.

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So Beethoven is coming out as nine point zero nine and intercept is coming is minus thirty one point

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six nine.

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In other words, this means that if I increase the number of rooms by one unit, the price of house

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will increase by nine units.

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What is the meaning of all these other values that will be learning in the coming reduce funding to

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NOTARIS?

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You do not need to remember these formulas because these software packages will be doing it for you.

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As you saw in this video and you will see in the coming videos, we'll be telling you the mathematical

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concept behind the theory and discussing those mathematical formulas.

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Also, keep in mind that you do not need to remember these formulas.

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You just need to understand the concept behind them.

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The indication that I tell you that will help you interpret the result.

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That understanding of result is very important.

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But you do not need to memorize these formulas since you will be using a software package which will

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be applying all these formulas and getting the results for you to preparing the data is important for

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running a model is important and interpreting the data accurately is the most important.

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Remembering formula is not important in machine learning, nor also even if you do not understand the

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mathematical part of this.

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Don't be worried.

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You can still run a machine learning model and you can use the results in your professional life.

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But I highly recommend that you go through all the lectures very carefully to understand the core concepts

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behind all these machine learning methods.