Write an article based on this "Create a five column data table. Enter the data values for your measured data. Calculate a regression line. Calculate predicted values from the regression line."
Any statistical work is generally made easier by having your data in a concise format. A simple table serves this purpose very well. To calculate the standard error of estimate, you will be using five different measurements or calculations. Therefore, creating a five-column table is helpful. Label the five columns as follows: x{\displaystyle x} y{\displaystyle y} y{\displaystyle y^{\prime }} yy{\displaystyle y-y^{\prime }} (yy)2{\displaystyle (y-y^{\prime })^{2}} Note that the table shown in the image above performs the opposite subtractions, yy{\displaystyle y^{\prime }-y}. The more standard order, however, is yy{\displaystyle y-y^{\prime }}. Because the values in the final column are squared, the negative is not problematic and will not change the outcome. Nevertheless, you should recognize that the more standard calculation is yy{\displaystyle y-y^{\prime }}. After collecting your data, you will have pairs of data values. For these statistical calculations, the independent variable is labeled x{\displaystyle x} and the dependent, or resulting, variable is y{\displaystyle y}. Enter these values into the first two columns of your data table. The order of the data and the pairing is important for these calculations. You need to be careful to keep your paired data points together in order. For the sample calculations shown above, the data pairs are as follows: (1,2) (2,4) (3,5) (4,4) (5,5) Using your data results, you will be able to calculate a regression line. This is also called a line of best fit or the least squares line. The calculation is tedious but can be done by hand. Alternatively, you can use a handheld graphing calculator or some online programs that will quickly calculate a best fit line using your data. For this article, it is assumed that you will have the regression line equation available or that it has been predicted by some prior means. For the sample data set in the image above, the regression line is y=0.6x+2.2{\displaystyle y^{\prime }=0.6x+2.2}. Using the equation of that line, you can calculate predicted y-values for each x-value in your study, or for other theoretical x-values that you did not measure. Using the equation of the regression line, calculate or "predict" values of y{\displaystyle y^{\prime }} for each value of x. Insert the x-value into the equation, and find the result for y{\displaystyle y^{\prime }} as follows: y=0.6x+2.2{\displaystyle y^{\prime }=0.6x+2.2} y(1)=0.6(1)+2.2=2.8{\displaystyle y^{\prime }(1)=0.6(1)+2.2=2.8} y(2)=0.6(2)+2.2=3.4{\displaystyle y^{\prime }(2)=0.6(2)+2.2=3.4} y(3)=0.6(3)+2.2=4.0{\displaystyle y^{\prime }(3)=0.6(3)+2.2=4.0} y(4)=0.6(4)+2.2=4.6{\displaystyle y^{\prime }(4)=0.6(4)+2.2=4.6} y(5)=0.6(5)+2.2=5.2{\displaystyle y^{\prime }(5)=0.6(5)+2.2=5.2}