## Line of Best Fit

### The line of best fit, also known as the regression line, is a straight line that represents the relationship between two variables in a scatter plot

The line of best fit, also known as the regression line, is a straight line that represents the relationship between two variables in a scatter plot. It is used to find the general trend or pattern in the data points and make predictions about future values.

To find the line of best fit, we use a method called linear regression. There are different ways to do this, but one common method is called the least squares method. This method aims to minimize the sum of the squared distances between the actual data points and the predicted values on the line.

Here are the steps to find the line of best fit:

Step 1: Plot the scatter plot of the given data points on a graph.

Step 2: Determine which variable will be the independent variable (usually denoted as x) and which will be the dependent variable (usually denoted as y). The independent variable is the one you think influences or determines the other variable.

Step 3: Calculate the mean (average) of both the x and y values in the data set.

Step 4: Calculate the deviations of each data point from their respective means. Subtract the mean from each x value and each y value.

Step 5: Multiply the deviations of x and y for each data point. Sum up these products.

Step 6: Square each of the deviations of x and sum them up. This gives us the sum of the squared deviations of x.

Step 7: Calculate the slope of the line of best fit (m) using the following formula:

m = (sum of the products of deviations)/(sum of squared deviations of x)

Step 8: Calculate the y-intercept (b) of the line of best fit using the following formula:

b = mean(y) – m * mean(x)

Step 9: Use the slope and y-intercept to find the equation of the line of best fit in the form y = mx + b.

Step 10: Plot the line of best fit on the scatter plot.

The line of best fit essentially summarizes the general trend of the data points. It may not pass exactly through all the data points but it should minimize the total distance between the points and the line. This allows us to make predictions about y-values for given x-values that are within the range of the data set.

It is important to note that the line of best fit may not be appropriate for all data sets. Sometimes the relationship between the variables is not linear and another type of regression, such as polynomial or exponential regression, might be more suitable.

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