¶ … Building and Assumptions Use the Best Subsets approach to refine the predictive models constructed using multiple linear regression

Employ techniques (including residual analysis) to test the assumptions of predictive models obtained through multiple linear regression

The core of predictive modeling is the search for useful predictors. Prediction is centered on a problem that is defined by the size of the data set (the number of cases or observations) and the number or width of potential predictors that can be used to address the problem. A common issue for problem solution is the enormous number of potential predictors that have a weak association with the solution. Computer modeling enables the huge number of models to be fit to subsets of the data and tested across additional data subsets. Each test provides an evaluation of the strength of each individual predictor. The focus, then, of predictive modeling is the search for good subsets of explanatory variables (predictors). Accordingly, models that fit well with the data are desirable, while models that are a poor fit for the data are not desirable. Moreover, generally speaking, simple models are preferred over complex models. The process of predictive modeling is to generate a list of useful explanatory variables and, using the data available, fit many models to the data. The outcome of predictive modeling is achieved by assessing...

Observations
When judging the best subset in a linear regression, the following criteria may be used:

The model with the largest R-squared

The model with the largest adjusted R-squared

The model with the smallest MSE (or S = square root of MSE)

The R-squared criterion and the MSE criterion were used to select the best subset in this activity. [Note: Mallow's Cp-statistic was not used for these observations.]

Step 1. The variables entered in this step include 5 Pre-Test, and the R-Square value is 0.462, and the MSE is 7,440,136.68.

Step 2. The variables entered in this step include 1 Curriculum (CU) and 5 Pre-Test (PT), and the R-Square value is 0.803, and the MSE is 6,469,609.65.

Step 3. The variables entered in this step include 1 Curriculum (CU), 4 Readiness Test (RT), and 5 Pre-Test (PT). And the R-Square value is 0.863, and the MSE is 4,637,852.14.

Step 4. The variables entered in this step include 1 Curriculum (CU), 2 Household Income (IN), 4 Readiness Test (RT), and 5 Pre-Test (PT), and the R-Square value is 0.884, and the MSE is 3,563,385.51.

Step 5. The variables entered in this step include 1 Curriculum (CU), 2 Household Income (IN), 3 Teacher Experience (TE), 4 Readiness Test (RT), and 5 Pre-Test…