class: center, middle, inverse, title-slide # Recap --- layout: true <div class="my-footer"> <span> Dr. Lucy D'Agostino McGowan </span> </div> --- ## Simple linear regression `\(\Huge y = \beta_0 + \beta_1 x + \epsilon\)` --- ## Simple linear regression `\(\Huge \hat{y} = \hat{\beta}_0 + \hat{\beta}_1 x\)` --- ## Simple linear regression .question[ What is the method used to estimate `\(\hat{\beta}_0\)` and `\(\hat{\beta}_1\)`? ] `\(\Huge \hat{y} = \hat{\beta}_0 + \hat{\beta}_1 x\)` --- ## Simple linear regression .question[ What is the method used to estimate `\(\hat{\beta}_0\)` and `\(\hat{\beta}_1\)`? ] .center[  ] --- ## Simple linear regression .question[ What is least squares minimizing? ] .center[  ] --- ## Simple linear regression .question[ What is least squares minimizing? ] * Sum of square errors (SSE) .center[  ] --- ## Simple linear regression .question[ How do we calculate the SSE? ] * SSE: `\(\sum (y-\hat{y})^2\)` .center[  ] --- ## Simple linear regression .question[ How do we calculate the SSE? ] * SSE: `\(\sum (y-\hat{y})^2\)` .center[  ] --- ## Simple linear regression .question[ How do we calculate the a residual? ] --- ## Simple linear regression .question[ How do we calculate the a residual? ] * residual: `\(y - \hat{y}\)` --- ## Simple linear regression .question[ How do we calcualte the regression standard error (residual standard error)? ] --- ## Simple linear regression .question[ How do we calcualte the regression standard error (residual standard error)? ] * `\(\hat{\sigma}_\epsilon = \sqrt{\frac{SSE}{n-2}}\)` --- ## Simple linear regression .question[ How do we interpret the regression standard error? ] * `\(\hat{\sigma}_\epsilon = \sqrt{\frac{SSE}{n-2}}\)` --- ## Simple linear regression .question[ What are the (six) assumptions for simple linear regression? ] --- ## Simple linear regression .question[ What are the (six) assumptions for simple linear regression? ] * Linearity * Zero Mean * Constant Variance * Independence * Random * Normality --- ## Simple linear regression `\(\Huge\epsilon \sim N(0, \sigma_\epsilon)\)` * Linearity * Zero Mean * Constant Variance * Independence * Random * Normality --- ## Simple linear regression .question[ What are the three parameters we estimate with simple linear regression? ] --- ## Simple linear regression .question[ What are the three parameters we estimate with simple linear regression? ] - `\(\Huge\hat{\beta}_0\)` - `\(\Huge\hat{\beta}_1\)` - `\(\Huge\hat{\sigma}_\epsilon\)`