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What characteristic makes regression line of best fit?
The equation of the regression line is calculated so as to minimise the sum of the squares of the vertical distances between the observations and the line. The regression line represents the relationship between the variables if (and only if) that relationship is linear. The equation of this line ensures that the overall discrepancy between the actual observations and the predictions from the regression are minimised and, in that respect, the line is the best that can be fitted to the data set. Other criteria for measuring the overall discrepancy will result in different lines of best fit.
Why is it important to know the regression line?
Yes, that is what allows you to predict data values based on the information you have. It also tells you other things about the data set such as the correlation.
What does the term residual mean?
Let's say that you fit a simple regression line y = mx + b to a set of (x,y) data points. In a typical research situation the regression line will not touch all of the points; it might not touch any of them. The vertical difference between the y-co-ordinate of one of the data points and the y value of the regression line for the x-co-ordinate of that data point is called a residual.There will be one residual for each data point.To see some labelled diagrams of residuals search images.google.com for residuals.
How do you calculate a straight line in statistics?
The method used to calculated the best straight line through a set of data is called linear regression. It is also called the least squares method. I've included two links. I know the wikipedia link is a bit complicated. The slope and intercept are calculated based on "minimum least squares." If I draw a line through the set if points, for every x value in the data set I will have a y value and a predicted y value (y-hat) based on the straight line. The error (E) is this case is the predicted y minus the actual y. Linear regression finds the slope and intercept of the equation that minimizes the sum of the square of the errors. Mathematically this is stated as: Min z = sum (yi - y-hat)^2 To hand calculate a linear regression line wold take some time. The second link that I've included shows how to calculated this using excel.
What is one formula statisticians use?
Some formulas statisticians may use are population mean, sample mean, variance, and standard deviation. They may also use linear regression line and standard error equations. Another can be the mean value of a data set, where one adds all data points given in a set and divides this number by the number of data points in the set.
