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Simple Linear Regression

The purpose of regression analysis is to:

• Predict the value of the dependent variable as a function of the value(s) of at least one independent variable.
• Explain how changes in an independent variable are manifested in the dependent variable

• The dependent variable is the variable that is to be predicted unexplained.
• An independent variable is the variable or variables that is used to predict or explain the dependent variable

The regression equation: $y=a+bx$

• Dependent variable: $y$:
• Independent variable: $x$:
• Slope: $b=r{\frac {S_{y}}{S_{x}}}$

The slope is the amount of change in units of $y$ for each unitchange in $x$.

• $y$ intercept: $a={\bar {y}}-b{\bar {x}}$: