5.5.A—Calculate the coefficients for the least-squares regression line model

Calculate the coefficients for the least-squares regression line model.

• The simple linear regression model is fit to the data by minimizing the sum of the squares of the residuals. Because of this, the resulting equation is often called the least-squares regression line (LSRL) and is calculated using technology. This regression line will pass through the point ()xy, .
• The slope of the regression line, b, is calculated using technology.
• The y-intercept of the regression line, a, is calculated using technology.
• In simple linear regression, the correlation coefficient, r, is calculated using technology.
• In simple linear regression, the square of the correlation coefficient, r2 , is called the coefficient of determination. The value of r2 is the proportion of variation in the response variable that is explained by the linear relationship with the explanatory variable.