Simple linear Regression | Simple Linear Regression Mode | Simple Linear Regression and Correlation.

Simple Linear Regression is a statistical method used to model the relationship between a dependent variable and a single independent variable. It assumes that there is a linear relationship between these two variables. The best-fitting straight line that predicts the dependent variable based on the independent variable. #simplelinearregression #SLRM Mathematical Formulation: Y = a + b X + € Where: Y is the dependent (response) variable. X is the independent (predictor) variable. a is the intercept (the value of when ). b is the slope (the change in for a one-unit change in ). € is the error term or residual (captures random noise or unobserved factors). Assumptions of Simple Linear Regression: For the model to be valid, certain assumptions must hold: 1. Linearity: The relationship between and is linear. 2. Independence: The observations are independent of each other. 3. Homoscedasticity: The variance of the residuals (errors) is constant across all levels of . 4. Normality of Errors: The residuals (errors) should be approximately normally distributed. Limitations of Simple Linear Regression: Assumes linearity: If the relationship between the variables is non-linear, simple linear regression may not perform well. Outliers: Outliers can heavily influence the regression line. Only one predictor: It doesn't account for multiple factors affecting the dependent variable (for multiple predictors, you would use Multiple Linear Regression). In this chapter we discuss in detail... #UseofcalculatortosolveRegressionandcorrelation #correlationandassosiation #Scatterplot #causation #propertiesofregressionline #propertiesofcorrealtioncoefficient #Deterministicandprobabilisticmodel #SimplelinearRegressionModel #PropertiesofRegressionlines #StandardError #regressioncoefficientvscorrelationcoefficient #Coefficientsofdetermination #SLRMbyusingMethodofLeastsquares #SLRMbyusingCramerRule #SLRMbyusingInversemethod #DerivationofModelYonXandXonY #CorrelationandCorrelationCoefficients #TypesofCorrelation #DerivationsofcorrelationCoefficient #Derivationofrankcorrelationcoefficient #CauseandeffectCorrelation #CorrelationforBivariatefrequencyDistribution #Covariance #curvefitting #methodofleastsquares #plausiblevalues #rankcorrealtion #tiedrankcorrelation #PropertiesofCorrelationcoefficient #Coefficientofconcordance #NonlinearRegression #MethodsofestimatingnonlinearRegression SolvedExercisechapter10BookSherMuhammadch https://youtu.be/UnQvNbdMwnI?si=6SuqhzDeb1KD4bZs https://youtu.be/BgCHJT5u-pE?si=RoHr3OC2WAU9Dwli https://youtu.be/2DjhvCMcYnM?si=FRWGerDnuJDmipol https://youtu.be/8eEzCUh9ykQ?si=57WVNsCgC8ZlUWJ5 https://youtu.be/y6AZnd24-_c?si=FKLjqD2HfosdMTpy https://youtu.be/NvqEoVS86ls?si=ZNgAcbZPO24gHc6N https://youtu.be/rS0DHtNYBa8?si=O9ASwHCj6lVpcl0p https://youtu.be/fJgdWqe0iqI?si=ha3Zjmo8qtNAz2Xk https://youtu.be/eFuBAcz18RQ?si=wM4VjBX2uq7kQhSn https://youtu.be/FAbOEnDcLZE?si=ta2VdIb_qTXoRICx https://youtu.be/T4MG6NcmXsY?si=TGvJOBFC3MA0AGAB Links Play List https://youtube.com/@Mstatistics?si=g4WZatoeiGtGxE2Y https://youtube.com/playlist?list=PLE6FeA-mAm2cw0QJvkmDtXSuFMOcyR22k&si=cFZMBQXx3-NsxEFs https://youtube.com/playlist?list=PLE6FeA-mAm2ckQ2g3PbZa3JFcS7Dch6zH&si=d8tX6T5bikR9ZOvT https://youtube.com/playlist?list=PLE6FeA-mAm2fC2vBS9Tsm1pNq0jrHRBRN&si=Z1xXtYnu3ZLghz2L https://youtube.com/playlist?list=PLE6FeA-mAm2cTiJSRpFQXUXxnwPRnMYd2&si=fwbLBOwb9OZ7KvcT https://youtube.com/playlist?list=PLE6FeA-mAm2cJBSS7MFtY_qNt0S98LrUf&si=xeKv_QM2eETnFtHs https://youtube.com/playlist?list=PLE6FeA-mAm2fN6DP_jOvUmd-Vz7JRCCju&si=APcCUnxh3-09A1vK https://youtube.com/playlist?list=PLE6FeA-mAm2enYtyM0hNZwwkeiDk9_U-n&si=WsmS9fHwFAHWUc9m https://youtube.com/playlist?list=PLE6FeA-mAm2c09AkhYm67o80t3QmDFlUe&si=cUux7KQiJtMm_zqf https://youtube.com/playlist?list=PLE6FeA-mAm2f8b5z-TB-Xa2LaVW-4RlOB&si=xg0ykFRadIZ9ROSi https://youtube.com/playlist?list=PLE6FeA-mAm2e2W1skwNMXb-pAIabRg87w&si=qZ2syfTp0o7mVQjF https://youtube.com/playlist?list=PLE6FeA-mAm2ep0-7j0_5rUjOiO5khbIMe&si=YJ9fRiDw9c_0kQv1 https://youtube.com/playlist?list=PLE6FeA-mAm2eOw--_Qx6fI74O30PdHgOR&si=WLTgwi1S5RY7EuCO https://youtube.com/playlist?list=PLE6FeA-mAm2fPYYT9uC7OJW_qLiDaQRru&si=8bzkAdH1r9FNlJVT https://youtube.com/playlist?list=PLE6FeA-mAm2ePUb5xru9NFGVvT8rYV-KB&si=5ePtgzTDDaxwb1RZ https://youtube.com/playlist?list=PLE6FeA-mAm2elLeIiEJRKDXhQhYQ2GKgg&si=5QXO6vckhfVLejYL https://youtube.com/playlist?list=PLE6FeA-mAm2fyU7Rjk_B4nHMw-jzzf_1A&si=qNftTMbZ137sz5L3 https://youtube.com/playlist?list=PLE6FeA-mAm2c6lj4Fh08DgfZd6YirTqcA&si=-4wtZjdZrbE6vGqK https://youtube.com/playlist?list=PLE6FeA-mAm2csE5-qXt-MHRlmDzsC3E1m&si=YgOCBQq_gQyEQ4Cj https://youtube.com/playlist?list=PLE6FeA-mAm2fszoMIzaEtjqDZgWrxG2Ff&si=DJSuWXIJldNeBxLy https://youtube.com/playlist?list=PLE6FeA-mAm2d7nig0ltxb7c9RhtVnVLVE&si=6JvgcHLtHPysO_Cc https://youtube.com/playlist?list=PLE6FeA-mAm2fwvWmbbgjwuJ2krHcUV4uF&si=7WcT2fYG8Bo11NnB