How do you find the line of best fit slope?

To find the slope of the line of best fit, you will need to perform a series of calculations using your data points. Here's a step-by-step breakdown based on the reference provided:

Calculating the Line of Best Fit Slope

The process involves four key steps:

1. Calculate the Means:

   • Find the average (mean) of all your x values, denoted as x_a.
   • Find the average (mean) of all your y values, denoted as y_a.

2. Calculate Deviations:

   • For each data point, calculate the difference between the x value and the mean of x values (x - x_a).
   • Similarly, for each data point, calculate the difference between the y value and the mean of y values (y - y_a).

3. Calculate Squared and Product Values:

   • For each data point, square the deviation of the x values: (x - x_a)².
   • Also, for each data point, calculate the product of the deviations: (x - x_a)(y - y_a).

4. Calculate the Slope:

   • Sum all the product of deviations (x - x_a)(y - y_a).
   • Sum all the squared deviations of the x values (x - x_a)².
   • Divide the sum of the product of deviations by the sum of the squared deviations: (x - x_a)(y - y_a) / (x - x_a)². This result is the slope of the line of best fit.

Example

Let’s say you have the following data points:

x	y
1	2
2	4
3	5
4	4
5	6

Following the steps:

Step	x	y	x - x_a	y - y_a	(x - x_a)²	(x - x_a)(y - y_a)
1	1	2	-2	-2	4	4
2	2	4	-1	0	1	0
3	3	5	0	1	0	0
4	4	4	1	0	1	0
5	5	6	2	2	4	4
Totals	15	21	0	0	10	8

• Step 1:
  • x_a = 15/5 = 3
  • y_a = 21/5 = 4.2
• Step 2 & 3: Calculated above.
• Step 4:
  • Slope = Sum of (x - x_a)(y - y_a) / Sum of (x - x_a)² = 8 / 10 = 0.8.

Therefore, the slope of the line of best fit for the given data is 0.8.

This process, often calculated using software or spreadsheets, allows you to determine the line that best represents the relationship between your data points, which is crucial for understanding trends and making predictions.