Topics in simple linear regression

Examining lack of fit

• A) residual plots
• B) SS pure experimental error

Calibration: predicting x for a given y value

• Example: calibrating a speed gun

Use of SSP_exp to study lack of fit

When we have more than one observation per x_i value, we can partitiion SSE:

SSE = SSP_exp + SS_lack = SS for pure error + SS for lack of fit

which leads to an F test of lack of fit: F = MS_lack / MSP_exp

Multiple regression

Often a simple linear regression model is not sufficient as a model for y .

Other possibilities are:

y_i = b₀ + b₁x_i + b₂x_i² + e_i (polynomial in x)

y_i = b₀ + b₁x_1i + b₂x_2i+ e_i (linear in two variables x₁ and x₂ )