Slope and y-intercept of a Regression Line (Best Fit Line) Calculator 


               




Slope and y-intercept of a Regression Line (Best Fit Line) Calculator



Slope formula of a regression (best fit) line


y intercept formula of a regression (best fit) line




Data Points







This Slope and y-intercept Calculator calculates the best-fitting slope and best-fitting y-intercept for a linear line based on the given data points supplied.

So we begin with a few data points.

We create a regression line to build the best-fitting line for the various data points.

A regression line is a line that tries its best to represent all of the data points as accurately as possible with a straight line. It strives to be the best fit line that represents the various data points.

A regression line can be calculated based off of the sample correlation coefficient, which is a measure of the strength and direction of the linear relationship between 2 quantitative variables. If data points are perfectly linear, the sample correlation will either be 1 (for a line with a positive slope) or -1 (for a line with a negative slope). All values in between are not linear (with the exception of a vertical line which has a correlation coefficient of 0).

So based off of the sample correlation coefficient, we can determine the calculate the slope and y-intercept of the best-fitting line for these data points.

How we determine the slope of the line is complex for a regression line and is not simply rise/run, as the simple formula is. To find the slope of a regression line (or best-fitting line), the formula is, slope, m= ((1/n-1)∑(x-μx) (y-μy)/σxσy)(σyx) Or if we take simplify by putting in r for the sample correlation coefficient, the formula is, slope, m= r(σyx)

So once you have computed the correlation coefficient, then calculating the best fit line is relatively simple.

We first calculate the slope through the formula, m= r(σyx)

Once we have done this, then we can calculate the y-intercept. We do this by multiplying the slope by x. We then subtract this value from y. This is the y-intercept.

With the slope and y-intercept calculated, we then can have our regression line.



Example

Now that you know the steps to do, let's actually do an example.

So as an example, let's say we have a correlation coefficient of 0.98, x of 7, x of 12, σx of 4.58, and σy of 5.

So to find the slope, we use the formula, m= r(σyx)= 0.98(5/4.58)= 1.069

We then need to find the y-intercept. We multiply the slope by x, which is 1.069*7=7.489.

We then subtract this value from y, which is 12-7.489= 4.511

So our final regression line is, y= 1.069x + 4.511

To use this calculator, a user simply enters in the x and y value pairs. A user can enter anywhere from 3 to 10 (x,y) value pairs. After, the user clicks the 'Calculate' and the expected value will be calculated and automatically displayed.


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