Machine Learning : Linear regression

 

 

Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. 

 One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable. 

 

 Dependent Variable – Variable who’s values we want to explain or forecast Independent or explanatory Variable that Explains the other variable. Values are independent. Dependent variable can be denoted as y, so imagine a child always asking y is he dependent on his parents.

 

 And then you can imagine the X as your ex boyfriend/girlfriend who is independent because they don’t need or depend on you. A good way to remember it. 

 

Anyways Used for 2 Applications To Establish if there is a relation between 2 variables or see if there is statistically signification relationship between the two variables- • To see how increase in sin tax has an effect on how many cigarettes packs are consumed • Sleep hours vs test scores • Experience vs Salary • Pokemon vs Urban Density • House floor area vs House price Forecast new observations – Can use what we know to forecast unobserved values Here are some other examples of ways that linear regression can be applied. • So say the sales of ROI of Fidget spinners over time. • Stock price over time • Predict price of Bitcoin over time.

 

 Linear Regression is also known as the line of best fit The line of best fit can be represented by the linear equation y = a + bx or y = mx + b or y = b0+b1x You most likely learnt this in school. 

 

So b is is the intercept, if you increase this variable, your intercept moves up or down along the y axis. M is your slope or gradient, if you change this, then your line rotates along the intercept. Data is actually a series of x and y observations as shown on this scatter plot. They do not follow a straight line however they do follow a linear pattern hence the term linear regression Assuming we already have the best fit line, We can calculate the error term Epsilon. Also known as the Residual. And this is the term that we would like to minimize along all the points in the data series. So say if we have our linear equation but also represented in statistical notation. The residual fit in to our equation as shown y = b0+b1x + e