http://www.saburchill.com/physics/chapters/0073.html
I have to draw a best-fit straight line on a graph. How do I know that its really best fitted - in the right angle?
To determine if a best-fit straight line on a graph is truly best fitted and has the correct angle, you can follow these steps:
1. Obtain data points: First, you need to have a set of data points that you'll be plotting on the graph. These data points should represent the relationship between two variables.
2. Plot the points: Using the data points, plot them on a graph with the dependent variable on the vertical y-axis and the independent variable on the horizontal x-axis. Each data point will be represented by a single dot on the graph.
3. Visual inspection: Look at the data points and try to identify the general trend or pattern that they form. This will provide you with an initial visual assessment of how the data might be best fitted with a straight line.
4. Straight line placement: Based on your initial visual assessment, place a straight line on the graph in a way that seems to best match the overall trend of the data points. The line should pass through or be as close as possible to a majority of the data points.
5. Minimizing residuals: After placing the straight line, you need to determine how well it fits the data. To do this, compute the residuals, which are the vertical distances between each data point and the line. Subtract the y-coordinate of each data point from the corresponding y-coordinate on the line.
6. Calculate the sum of squared residuals: Square each residual value (to make them positive) and sum them all up. This will give you the sum of squared residuals.
7. Repeat with alternative lines: To verify if your chosen straight line is the best fit, you need to repeat steps 4-6 with different alternative lines. Ideally, the best-fit line will have the smallest sum of squared residuals compared to the alternative lines.
8. Compare the sum of squared residuals: After performing step 7, compare the sum of squared residuals for each line. The line with the smallest sum of squared residuals will be the best-fit line.
9. Check the angle of the line: Once you have determined the best-fit line, check its angle. The angle is determined by the slope of the line. A best-fit straight line will have a slope that represents the relationship between the variables accurately.
It's important to note that the process described above is a basic manual method for fitting a straight line and may not be appropriate for more complex data sets. In such cases, statistical methods like linear regression can be used to find the best-fit line.