Regression and Correlation of Data Summary

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Presentation transcript:

Regression and Correlation of Data Summary Procedures for regression: 1. Assume a regression equation. 2. If the equation is simple linear form, use least squares method to determine the coefficients. If not, convert it to the form linear in coefficients and then use least squares method. Or use Excel functions such as Solver, Trendline or Linest. 3. Evaluate the regression by statistical analysis

Regression and Correlation of Data Summary Simple Linear Regression: Method of Least Squares: a and b are determined by minimizing the sum of the squares of errors (SSE), deviation, residuals or difference between the data set and the straight line that approximate it.

Regression and Correlation of Data Summary Centroidal point:

Regression and Correlation of Data Summary Procedures for regression: 1. Assume a regression equation. 2. If the equation is simple linear form, use least squares method to determine the coefficients. If not, convert it to the form linear in coefficients and then use least squares method. Or use Excel functions such as Solver, Trendline or Linest. 3. Evaluate the regression by statistical analysis

Regression and Correlation of Data Summary Forms transformable to linear in coefficients: e.g. Other forms linear in coefficients: e.g. Use least square method to determine the coefficients. Convert the equation to the form containing the original variables.

Regression and Correlation of Data Summary Procedures for regression: 1. Assume a regression equation. 2. If the equation is simple linear form, use least squares method to determine the coefficients. If not, convert it to the form linear in coefficients and then use least squares method. Or use Excel functions such as Solver, Trendline or Linest. 3. Evaluate the regression by statistical analysis

Regression and Correlation of Data Summary Statistical analysis of the regression: Sum of the squares of errors (SSE), Estimated variance of the points from the line: Estimated standard deviation or standard error of the points from the line: The degrees of freedom=n data points – the number of estimated coefficients

Regression and Correlation of Data Summary Correlation Coefficient: r =1: the points (xi,yi) are in a perfect straight line and the slope of that line is positive; r =-1: the points (xi,yi) are in a perfect straight line and the slope of that line is negative; r close to +1 or -1: X and Y follow a linear relation affected by random errors. r=0: there is no systematic linear relation between X and Y.

Regression and Correlation of Data Summary Coefficient of determination: The coefficient of determination is the fraction of the sum of squares of deviations in the y-direction from is explained by the linear relation between y and x given by regression.

Regression and Correlation of Data Summary Statistical analysis of the regression: Residuals (also used for graphical checks): Percentage Error: Absolute Percentage Error: