Answer question $1$

Causal Methods: Linear Regression

Demand for oil changes at Garcia's Garage has been as follows:

$\backslash$table$[[$Month$,$Number of Oil Changes$],[$January$,41],[$February$,46],[$March$,57],[$April$,52],[$May$,59],[$June$,51],[$July$,60],[$August$,62]]$

a$.$ Use simple linear regression analysis to develop a forecasting model for monthly demand. In this application, the dependent variable, $Y,$ is monthly demand and the independent variable, $x,$ is the month. For January, let $x=1$; for February, let $x=2$; and so on$.$

b$.$ Use the model to forecast demand for September, October, and November. Here, $x=9,10,$ and $11,$ respectively.

$2.$ At a hydrocarbon processing factory, process control involves periodic analysis of samples for a certain process quality parameter. The analytic procedure currently used is costly and time consuming. A faster and more economical alternative procedure has been proposed. However, the numbers for the quality parameter given by the alternative procedure are somewhat different from those given by the current procedure, not because of any inherent errors but because of changes in the nature of the chemical analysis.

Management believes that if the numbers from the new procedure can be used to forecast reliably the corresponding numbers from the current procedure, switching to the new procedure would be reasonable and cost effective. The following data were obtained for the quality parameter by analyzing samples using both procedures: