# Thread: Equation for Line Of Best Fit?

1. ## Equation for Line Of Best Fit?

I have a chart out of which I made a graph, On Microsoft Excel (2011 for mac). I then added a Line of Best Fit.

I need to answer questions about the graph, which include knowing the line of best fit. (Teacher said to use any statistical program to figure it out.....)

How do I get the equation for Line of Best Fit/what is the equation?

2. ## Re: Equation for Line Of Best Fit?

If you are trying to find an equation for y as a function of x in the form y= mx+c given you have a sample size n for observations of x and y with means X and Y

Find the sum of squares for y (SSyy)
$SS_{yy}= \sum_{i=1}^n (y_iy_i)-nY^2$

And the sum of squares for xy
$SS_{xy}= \sum_{i=1}^n (x_iy_i)-nXY$

Then
$m=\frac{SS_{xy}}{SS_{yy}}$

$c= Y-m X$

3. ## Re: Equation for Line Of Best Fit?

This is the "Data" I have been given:

Year/ Lowest 20% Of Earners /Highest 20% Of Earners
1977 12000 122500
1978 11800 126400
1979 13100 121100
1980 13700 123200
1981 14600 123200
1982 14300 122300
1983 12800 127600
1984 13900 126300
1985 14800 130700
1986 15100 134300
1987 15800 137000
1988 15700 142800
1989 16800 147800
1990 15500 143100
1991 14300 139100
1992 13900 137400
1993 14100 136700
1994 14100 136300
1995 14300 139900
1996 13000 141900
1997 13200 146500
1998 13600 153900
1999 13500 162300
2000 14300 169600
2001 14700 169400
2002 14700 167800
2003 14800 166700
2004 14200 170600
2005 14300 168500
2006 14700 168000

4. ## Re: Equation for Line Of Best Fit?

You say you put this into Excel and "added a Line of Best Fit". I interpret that to mean that you used an Excel command to plot that line. Does Excel not have a way of giving the equation? If not you could still find two points on that line and use those to find the equation of the line. Shakarri gives the standard formulas for the coefficients of the line but Excel should already have done that for you.

5. ## Re: Equation for Line Of Best Fit?

if you go to your data points that excel plotted, select one and right click then go to "Add trendline" and at the bottom of the window that pops up is a box that says "Display equation on chart" select it and voila!

6. ## Re: Equation for Line Of Best Fit?

^Thanks! Thought there HAD TO be a function in excel that did it!