# Linear_regression_week_14 - Linear regression Linear...

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Linear regression Linear regression modelLeast Squares coefficientsStandard error of the estimate Residual analysist-test for the slopeUsing the model for prediction
A linear regression model is a straight line probabilistic relationship between two variablesWhereis the response variable for observation iis the explanatory variable for observation i0 is called the intercept (value of y when x=0)1 is the slope, or the amount of change in y for every unit of change in xi= random error in Yfor observation iLINEAR REGRESSION MODELiiiXY10iYiX
LINEAR REGRESSION EXAMPLEFor the data above, what can we conclude from the scatterplot? Is the dataset a good candidate for a linear regression model?Obs. No.Hydrocarbon LevelPurityX (%)Y (%)10.9990.0121.0289.0531.1591.4341.2993.7451.4696.7361.3694.4570.8787.5981.2391.7791.5599.42101.493.65111.1993.54121.1592.52130.9890.56141.0189.54151.1189.85161.290.39171.2693.25181.3293.41191.4394.98200.9587.33Purity of oxygen produced in a chemical distillation process vs. the percentage of hydrocarbons that are present in the main condenser of the distillation unit0.80.911.11.21.31.41.51.6020406080100120Hydrocarbon level X (%)Purity Y (%)
For the slopeLEAST SQUARE REGRESSION COEFFICIENTSFor the interceptSSXSSXYb1nYXYXYYXXSSXYniiniiniiiniii1111nXXXXSSXniiniinii211212XbYb10nYYnii1nXXnii1
LEAST SQUARE REGRESSION COEFFICIENTS
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