BasicRegression Package

ScatterPlot[xdata, ydata] produces a scatterplot of the data whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata. ScatterPlot[data] will also produce such a plot, where data is a list of x-y pairs of the form {{x1,y1},{x2,y2},...}. ScatterPlot can accept any options that ListPlot accepts.

LinearFit[xdata, ydata] gives the equation of the least-squares regression line, the value of r-squared, and a scatterplot (with the regression line superimposed) of the data whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata. LinearFit[data] will also produce this output, where data is a list of x-y pairs of the form {{x1,y1},{x2,y2},...}. LinearFit can accept any options that ListPlot accepts.

LinearResidualPlot[xdata, ydata] gives a residual plot for the best fitting linear function to the data whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata. LinearResidualPlot[data] will also produce this output, where data is a list of x-y pairs of the form {{x1,y1},{x2,y2},...}. LinearResidualPlot can accept any of the options accepted by ListPlot.

ExponentialFit[xdata, ydata] gives the equation of the best fitting exponential function to the data whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata. This function is obtained by performing linear regression on Log[10,ydata] vs. xdata. Also reported are the value of r-squared, and a scatterplot of the data with the exponential function superimposed. ExponentialFit[data] will also produce this output, where data is a list of x-y pairs of the form {{x1,y1},{x2,y2},...}. ExponentialFit can accept any options that ListPlot accepts.

ExponentialResidualPlot[xdata, ydata] gives a residual plot for the best fitting exponential function to the data whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata. ExponentialResidualPlot[data] will also produce this output, where data is a list of x-y pairs of the form {{x1,y1},{x2,y2},...}. ExponentialResidualPlot can accept any of the options accepted by ListPlot.

PowerFit[xdata, ydata] gives the equation of the best fitting power function to the data whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata. This function is obtained by performing linear regression on Log[10,ydata] vs. Log[10,xdata]. Also reported are the value of r-squared, and a scatterplot of the data with the power function superimposed. PowerFit[data] will also produce this output, where data is a list of x-y pairs of the form {{x1,y1},{x2,y2},...}. PowerFit can accept any options that ListPlot accepts.

PowerResidualPlot[xdata, ydata] gives a residual plot for the best fitting power function to the data whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata. PowerResidualPlot[data] will also produce this output, where data is a list of x-y pairs of the form {{x1,y1},{x2,y2},...}. PowerResidualPlot can accept any of the options accepted by ListPlot.

ResidualTable[xdata,ydata] gives a table of values for the data whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata. Also reported are the predicted responses according to the least-squares regression line, the residuals, and the squares of the residuals. ResidualTable[data] will also produce this output, where data is a list of x-y pairs of the form {{x1,y1},{x2,y2},...}. ResidualTable[xdata,ydata,intercept,slope] or ResidualTable[data,intercept,slope] gives a similar table, but bases the predicted responses on the line with the given y-intercept and slope. The sum of squares of residuals is reported in either case, as is a plot of the data with the appropriate line superimposed, and a residual plot. ResidualTable can accept any of the options accepted by ListPlot.

SquaredResidualPlot[xdata,ydata, y-intercept,slope] produces a scatterplot of the points whose x coordinates are stored in the list xdata and whose y coordinates are stored in the list ydata, together with a graph of the line whose y-intercept and slope are specified. The scatterplot will superimpose a square (one for each data point) whose area represents the square of that data point's residual. Thus the picture provides a geometrical interpretation of the sum of the squares of residuals. If the y-intercept and slope are omitted, the least-squares regression line will be used. Also, the first two arguments xdata and ydata may be replaced with a list of 2-tuples of the form {{x1,y1},{x2,y2},...}. SquaredResidualPlot will accept any option that ListPlot does.