2. Regression Analysis Deterministic model No chance of an error in calculating y for a given x Probabilistic model chance of an error First order linear probabilistic model  0 +  x + 

3. Least Square Method Minimizes the sum of squared differences between observed and values from the regression line.  : slope of the line and = Ss xy  SS x Look for the short cut formula on page 731  o : y intercept = y - -  x - Residual: y i - Y ^

4. Regression continued R 2 = SSR/SST Proportion of the total variation in Y explained by the regression line R 2 = 1, all scatter points on the regression line R 2 = 0 no scatter point on the regression line Square root of R 2 is called coefficient of correlation

5. Regression continued When Coefficient of correlation is positive, there is direct relationship between variables When Coefficient of correlation is negative, y value increases when x decrease and vice versa When Coefficient of correlation is zero, there is no linear relationship.

6. Regression SST=SSR+SSE Formulae for predicted interval and expected interval are on page 756 To infer on the population coefficient of correlation, use t -test, formula on page 761 To find t-value from t-table, you must know –degree of freedom –the level of significance For two tailed test, divide the level of significance by 2.

7. Assessing the Model Standard error of the estimate –Divide the standard error of the estimate by the average of y –Smaller its value, better the fit Coefficient of determination –Closer its value to 1, better the fit –R 2 =1, all scatter points fit on the regression/least square line –R 2 = 0, non of the scatter points lie on the regression line. –Explains the proportion of the total deviation explained by the regression line.

8. Inference on Slope Apply t-test because –standard deviation of the population is unknown H 0 :  = 0 H a :  0 t= (  ^ -  )/S  ^ S  ^ is the standard deviation of the slope and =S e /  SS x use level of significance and the degree of freedom = (n-2) to derive a conclusion based on the data. Predicting a value of Y for a given value of x use the formula on page 756 or use the Excel print- out under PI Estimating expected value Use the formula on page 756 or use the computer print out under confidence interval.