{"id":5186,"date":"2021-01-03T19:15:34","date_gmt":"2021-01-04T03:15:34","guid":{"rendered":"https:\/\/portasftpserver.com\/?p=5186"},"modified":"2022-09-16T14:33:00","modified_gmt":"2022-09-16T21:33:00","slug":"simple-linear-regression-models","status":"publish","type":"post","link":"https:\/\/portasftpserver.com\/simple-linear-regression-models\/","title":{"rendered":"Linear Regression Model – Part II"},"content":{"rendered":"\n

A simple linear regression model<\/strong> consists of one predictor variable and one dependent variable. The regression model formula is <\/p>\n\n\n\n

\\( \\hat{Y} \\) = intercept + slope \u22c5 x<\/strong> <\/p>\n\n\n\n

or if you would think in math \\(\\hat{Y} = b_{0} + b_{1}x \\)<\/p>\n\n\n\n

Do not be confused with the equation or the formula. The y-hat (\\( \\hat{y} \\)) is a predicted response variable from the predictor variable or x. The b0 is the intercept (value of y when x is zero). And the b1 is the slope or the rise over run in which a unit change in y based upon a unit change in x and these are referred to as regression coefficients.<\/p>\n\n\n\n

Let\u2019s consider the following dataset for the monthly E-commerce sales<\/strong> (in $1000\u2019s) and online advertising costs (in $1000\u2019s).<\/p>\n\n\n\n

Store<\/th>Monthly E-commerce Sales
(in $1000)<\/th>		Online Advertising Cost
(in $1000)<\/th><\/tr><\/thead>
1<\/td>370<\/td>2.3<\/td><\/tr>
2<\/td>311<\/td>1.7<\/td><\/tr>
3<\/td>620<\/td>3.0<\/td><\/tr>
4<\/td>910<\/td>5<\/td><\/tr>
5<\/td>500<\/td>2.9<\/td><\/tr>
6<\/td>520<\/td>2.5<\/td><\/tr>
7<\/td>600<\/td>3.4<\/td><\/tr>
8<\/td>830<\/td>4.3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

So if we execute the code<\/p>\n\n\n\n

Sales<-c(370, 311, 620, 910, 500, 520, 600, 830)\nAdvertising.Cost<-c(2.3, 1.7, 3.0, 5, 2.9, 2.5, 3.4, 4.3) \nplot(Advertising.Cost, Sales, xlab=\"Advertising Cost (in $1000)\", ylab=\"Monthly E-commerce Sales (in $1000)\", ylim=c(200,1000), pch=16, cex=2, col=\"blue\") \nabline(lm(Sales~Advertising.Cost)) <\/code><\/pre>\n\n\n\n
As you would expect, the scatter plot below seems to just have linear data points that indicate and show a strong positive correlation<\/strong>. This makes sense and appropriate to use a simple linear regression model for the dataset.<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
It is so clear that when advertising costs go up it seems to carry the monthly E-commerce sales up as well. The orange linear regression line is what produce from the equation of a simple linear regression model. <\/p>\n\n\n\n
By using R<\/strong><\/p>\n\n\n\n
mod<-lm(Sales~Advertising.Cost)\nsummary(mod)<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The estimate simple linear regression equation is<\/p>\n\n\n\n
\\( \\hat{y} \\)=-5.192 + 187.352x<\/strong><\/p>\n\n\n\n
3.33e-05 is the p-value which basically means that indicates that the advertising cost significantly affects the monthly E-commerce sales.<\/p>\n\n\n\n
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