1. Linear Regression Analysis Using MS Excel Tutorial for Assignment 2 Civ E 342

2. The Regression Analysis Procedure Assume Equation Import Data to Excel Correlation Analysis Prepare Data Table Regress Using Excel Quality Analysis No Yes Try More Equ.? Select the Best Equ.

3. Step 1: Import Data to Excel Objective: Import original data to Excel. If it is a text file, open the file in Excel and follow the steps! Label each column - variable names Define (label) independent and dependent variables (x1,x2,...,y) Demo Assume Equation Import Data to Excel Correlation Analysis Prepare Data Table Regress Using Excel Quality Analysis No Yes Try More Equ.? Select the Best Equ.

4. Step 2: Correlation Analysis Objectives: –Important factors? –Correlation between factors? –Factors with non-linear effect - transform into linear if necessary Method 1: Correlation matrix –Excel - “Tools - Data Analysis… - Correlation” –Identify the factors that are correlated - high coefficient of correlation Method 2: Scatter diagram Demo Assume Equation Import Data to Excel Correlation Analysis Prepare Data Table Regress Using Excel Quality Analysis No Yes Try More Equ.? Select the Best Equ.

5. Step 3: Assume a Functional Form Objective –Identify factors and form of relationship Methods: –A trial-and-error process: –Stepwise process (not covered in this tutorial) Assume Equation Import Data to Excel Correlation Analysis Prepare Data Table Regress Using Excel Quality Analysis No Yes Try More Equ.? Select the Best Equ. y =  0 +  1 x 1 y =  0 +  1 x 1 +  2 x 2

6. Step 4: Prepare Data Table Objective –For the assumed equation: y =  0 +  1 x 1 +  2 x 2 Assume Equation Import Data to Excel Correlation Analysis Prepare Data Table Regress Using Excel Quality Analysis No Yes Try More Equ.? Select the Best Equ. Demo

7. Step 5: Regress Using Excel Objective: determine the coefficients that make the equation best fit to the data Method: –Method of Least Squares Demo Assume Equation Import Data to Excel Correlation Analysis Prepare Data Table Regress Using Excel Quality Analysis No Yes Try More Equ.? Select the Best Equ.

8. Step 6: Assess the Adequacy of the Regression Model Objective: Measures: –Coefficient of Determination (R 2 ) –t-tests ti>t , n-k-1,  -level of significance n-sample size k-no of independent variables –Residual plot –Intuitive acceptability Demo Assume Equation Import Data to Excel Correlation Analysis Prepare Data Table Regress Using Excel Quality Analysis No Yes Try More Equ.? Select the Best Equ.

9. Step 7: Select the Best Regression Model Objective: Model Application –Models are valid only for the values of the variables within the range of the original data! Assume Equation Import Data to Excel Correlation Analysis Prepare Data Table Regress Using Excel Quality Analysis No Yes Try More Equ.? Select the Best Equ. y =  0 +  1 x 1 +  2 x 2 t 1 t 2 R 2