1. Regression Models First-order with Two Independent Variables
Second-order with One Independent Variable
Second-order with an
Interaction Term
Second-order with
Two Independent
Variables

2. Non-Linear Regression

3. Stepwise Regression:
Add or Remove Variables for the Model One Step at a Time
1) Forward Selection:
Step 1: Put the Variable in the Model with Highest Correlation with Y
Next Step Add the Variable to Model with the Highest Correlation with
the Residuals from the Previous Model
Continue This as Long as the Added Variable Tests Significant
2) Backward Elimination:
Step 1: Put all Independent Variables into the Model
Next Step Remove the Variable from the Model which Tests Least
Significant
Continue This Until all Variables Test Significant

4. Example 1: Quarterback Rating Data
filename qb "QB_2015.txt";
data;
infile qb;
input comp att pct yds yds_a long td tdp int intp sacks rating yds_g;
proc stepwise;
model rating = comp att pct yds yds_a long td tdp int intp sacks yds_g;
run;
SAS Output
The SAS System
The STEPWISE Procedure
Model: MODEL1
Dependent Variable: rating
Number of Observations Read34
Number of Observations Used34
Stepwise Selection: Step 1
Variable yds_a Entered: R-Square = and C(p) =
Analysis of Variance
Source DF Sum of Squares Mean Square F Value Pr > F
Model l <.0001
Error
Corrected Total
Variable Parameter Estimate Standard Error Type II SS F Value Pr > F
Intercept
yds_a <.0001
Bounds on condition number: 1, 1

5. Stepwise Selection: Step 2
Variable intp Entered: R-Square = and C(p) =
Analysis of Variance
Source DF Sum of Squares Mean Square F Value Pr > F
Model <.0001
Error
Corrected Total
Variable Parameter Estimate Standard Error Type II SS F Value Pr > F
Intercept
yds_a <.0001
intp <.0001
Bounds on condition number: ,
Stepwise Selection: Step 3
Variable tdp Entered: R-Square = and C(p) =
Model <.0001
Error
Intercept <.0001
yds_a <.0001
tdp <.0001
intp <.0001
Bounds on condition number: ,

6. Stepwise Selection: Step 4
Variable pct Entered: R-Square = and C(p) =
Analysis of Variance
Source DF Sum of Squares Mean Square F Value Pr > F
Model <.0001
Error
Corrected Total
Variable Parameter Estimate Standard Error Type II SS F Value Pr > F
Intercept <.0001
Pct <.0001
yds_a <.0001
tdp <.0001
intp <.0001
Bounds on condition number: ,
Summary of Stepwise Selection
Step Variable Entered Partial R-Square Model R-Square C(p) F Value Pr > F
yds_a <.0001
intp <.0001
tdp <.0001
pct <.0001

7. Mallows Coefficient C(p) 2014 Data

8. NFL Quarterback Rating Formula: 2016 Rodgers Bradford
Part A: (COMP% - .30)*
Part B: (YDS/ATT - 3)*
Part C: (TD%)*
Part D: ( INTER%)*
Parts A,B,C,&D must be between 0 and 2.375
Rating = ( A + B + C + D )*100/

9. Dummy (Indicator) Variables
Dummy Variables are used to Enter Qualitative Variables into Regression
If the Qualitative Variable has k Values, then k-1 Dummy Variables
are Needed and take values of (0 or 1)
Gender: Xd = 0 ; Female
Xd = 1 ; Male
Class Yr: X1 X2 X3
Freshman 0 0 0
Sophomore 1 0 0
Junior
Senior

10. Example 2: Regress Cost on Mileage, Age, and Make