How can I find the line of best fit from a table:
3 4
8 10
15 21
27 31
35 33
47 45
To find the line of best fit from a table, you would typically use a method called linear regression. Linear regression aims to find the straight line that best represents the relationship between two variables.
Here's how you can find the line of best fit using linear regression:
Step 1: Plot the points on a graph. Label the x-axis with the independent variable and the y-axis with the dependent variable.
Step 2: Examine the scatterplot to see if there appears to be a linear relationship between the variables. If the points roughly form a straight line, then linear regression is appropriate. If the points do not seem to follow a linear pattern, linear regression might not be the best approach.
Step 3: Calculate the slope (m) and y-intercept (b) of the line. You can use the following formulas:
m = (n ∑xy - ∑x ∑y) / (n ∑x^2 - (∑x)^2)
b = (∑y - m ∑x) / n
where n is the number of points, ∑ represents summation, ∑xy is the sum of the product of x and y values, ∑x is the sum of the x-values, and ∑y is the sum of the y-values.
Step 4: Use the calculated slope (m) and y-intercept (b) to form the equation of the line of best fit in the form of y = mx + b.
Using your table of points, let's calculate the slope and y-intercept:
n = 6 (number of points),
∑x = 135,
∑y = 144,
∑xy = 915,
∑x^2 = 5355
Now, applying these values into the formulas:
m = (n ∑xy - ∑x ∑y) / (n ∑x^2 - (∑x)^2)
= (6 * 915 - 135 * 144) / (6 * 5355 - (135)^2)
= 4980 / 1365
≈ 3.647
b = (∑y - m ∑x) / n
= (144 - 3.647 * 135) / 6
= (144 - 492.945) / 6
≈ -58.824
Hence, the equation of the line of best fit is approximately y = 3.647x - 58.824.