1. GRA 6020 Multivariate Statistics The regression model OLS Regression Ulf H. Olsson Professor of Statistics

2. Ulf H. Olsson Variance, Covariance and Correlation

3. Ulf H. Olsson Covariance Matrix; Correlation Matrix

4. Ulf H. Olsson Regression Analysis One of the objectives of regression analysis is to develope an equation that will allow the investigator to predict the response for given values of the predictor variables. Thus it is necessary to ”fit” the ”model” to the observed response, yi, to the known values 1, x1i, x2i, ……xki for all i. That is, we must determine the values of the regression coefficients and the error variance. The ”fitting method” is called OLS

5. Ulf H. Olsson Regression Analysis

6. Ulf H. Olsson Regression analysis OLS Regression parameter St.error T-value P-value Confidence interval R-sq R-sq.adj F-value The error term

7. Ulf H. Olsson Regression Analysis The error term has constant variance The error term follows a normal distribution with expectation equal to zero The x-variables are independent of the error term The x-variables are linearly independent The dependent variable is normally distributed

8. Ulf H. Olsson Econometric Model Klein’s Model (1950 )

9. Ulf H. Olsson Making Numbers (OLS and TSLS) CT = 16.237+0.193*PT+0.0899*PT_1+0.796*WT, R² = 0.981 (1.303) (0.0912) (0.0906) (0.0399) 12.464 2.115 0.992 19.933 CT = 15.324+0.0763*PT+0.186*PT_1+0.828*WT, R² = 0.979 (1.453) (0.138) (0.146) (0.0439) 10.546 0.553 1.275 18.844

10. Ulf H. Olsson Assignment You need the LISREL software USE the File: NPV.PSF 1) Do a data screening. Do the variables “follow” a normal distribution? 2) Estimate the sample covariance- and correlation matrix