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Regression Analysis

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 +. Least Square Method.

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Regression Analysis

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1. 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 +

2. Least Square Method • Minimizes the sum of squared differences between observed and values from the regression line. • : slope of the line and • = Ssxy SSx • Look for the short cut formula on page 731 • o: y intercept = y- - x- • Residual: yi - Y^

3. Regression continued • R2 = SSR/SST • Proportion of the total variation in Y explained by the regression line • R2 = 1, all scatter points on the regression line • R2 = 0 no scatter point on the regression line • Square root of R2 is called coefficient of correlation

4. 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.

5. 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.

6. 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 • R2 =1, all scatter points fit on the regression/least square line • R2 = 0, non of the scatter points lie on the regression line. • Explains the proportion of the total deviation explained by the regression line.

7. Apply t-test because standard deviation of the population is unknown H0: = 0 Ha:  0 t= (^ - )/S^ S^ is the standard deviation of the slope and =Se /SSx 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. Inference on Slope

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