lecture 11 - - Simple Linear Regression Terms Independent...

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Simple Linear Regression Terms Independent Variables Dependent Variables Simple Linear Regression Model Simple Linear Regression Equation Estimated Simple Linear Regression Equation Slope for the Estimated Regression Equation Y-intercept for Estimated Regression Equation Sum of Squares Due to Error Total Sum of Squares Relationship among SST, SSR, SSE Coefficient of Determination Correlation Coefficient Homoscadacity Heteroscadacity Simple linear regression model Simple linear regression focuses on two variables, an independent and a dependent, and their relationship is estimated by a straight line. The equation for a simple linear regression straight line takes the form of: y i = α + βx i + є Alternatively it can be written as: y i = β 0 + β 1 x i + є Where y is the dependent variable, α or β 0 is the y-intercept, β or β 1 is the slope, x is the independent variable, and is the error term For model to be correct the population of error terms have to have a mean of zero, be independent and have a constant standard deviation throughout the range of the x values. The error terms also have to be normally distributed. One additional necessary assumption is that there exist a linear relationship between x and y. As stated, with simple linear regression, the dependent variable is a linear function of the independent variable. When the ‘ x ‘ term changes by 1 the ‘ y ‘ term changes by beta, β. There are several assumptions made about the error term є.
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It is a random variable with an expected mean of zero, E (є) = 0. The variance of the error term, σ 2 , is the same for all values of ‘ x ‘. This is called the assumption of homoscedasticity. Hetero scadasticity is when the error terms are not equal spread around the regression line. The error terms may be increasing or decreasing , but there spread is not constant. It is randomly distributed following a normal distribution
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lecture 11 - - Simple Linear Regression Terms Independent...

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