How to compute trend-line coefficients in excel using formulas

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Computing trend line values using excel formulas and functions
Trendline values in excel charts
Warning: This is for those who wish to explore trend lines in excel.
For others, this presentation may be intimidating . Kindly exercise caution!

2. Trendlines in charts
A trend line is a straight line connecting multiple
points on a chart.
A trend is a movement in a particular direction
The magnitude of the slope of a trend line, or
steepness, indicates the strength of the trend.
Trend lines can be used to forecast future !

3. Six types of trend lines
1. Linear
2. Logarithmic
3. Polynomial
4. Power
5. Exponential
6. Moving Average
How to Create a Trendline? – Have a look at my earlier post in LCDing
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4. Rule of thumb : Use type of Trend line
1. Linear trend line : use it if data values are
increasing or decreasing at a steady rate.
2. Logarithmic trend line : Useful when the rate of
change in the data increases or decreases quickly
and then levels out.
3. Polynomial trend line : Used when there are data
fluctuations like the sales following seasonal trends

5. Rule of thumb : use type of Trend line
4. Power trend line : Use with data that has values that
increase at specific rate at regular intervals.
5. Exponential trend line : Use when data values
increase or decrease rates that are constantly
increasing.
6. Moving average trend line : Use it when uneven
fluctuations are in data values

6. Trend line values using excel formulae
You can use the formulas given in the next few slides.
Alternatively, you can download and use the excel attached
with all formulas.
To download excel file, click here

7. Linear Trendline equation
Equation: y = m * x + b
Where,
m =SLOPE(y,x)
b =INTERCEPT(y,x)
RSQ =RSQ(y,x)

8. Logarithmic Trendline equation
Equation: y = (c * LN(x)) + b
Where,
c =INDEX(LINEST(y,LN(x)),1)
b =INDEX(LINEST(y,LN(x)),1,2)
RSQ =RSQ(y,LN(x))

9. Power Trendline Equation
Equation: y=c*x^b
Where,
c =EXP(INDEX(LINEST(LN(y),LN(x),,),1,2))
b =INDEX(LINEST(LN(y),LN(x),,),1)
RSQ =INDEX(LINEST(LN(y),LN(x),TRUE,TRUE),3,1)

10. Exponential Trendline equation
Equation: y = c *e ^(b * x)
Where,
c =EXP(INDEX(LINEST(LN(y),x),1,2))
b =INDEX(LINEST(LN(y),x),1)
RSQ =RSQ(LN(y),x)

11. Polynomial Trendline(2nd order) Equation
Equation: y = (c2 * x ^2) + (c1 * x^1) + b
Where,
c2 =INDEX(LINEST(y,x^{1,2}),1)
c1: =INDEX(LINEST(y,x^{1,2}),1,2)
b = INDEX(LINEST(y,x^{1,2}),1,3)
RSQ =INDEX(LINEST(y,x^{1,2},TRUE,TRUE),3,1)

12. Polynomial Trendline(3rd order) Equation
Equation:
y=(c3*x^3) + (c2*x^2) + (c1*x^1) +b
Where,
c3 =INDEX(LINEST(y,x^{1,2,3},1)
c2 =INDEX(LINEST(y,x^{1,2}),1)
c1 =INDEX(LINEST(y,x^{1,2}),1,2)
b = INDEX(LINEST(y,x^{1,2}),1,3)
RSQ =INDEX(LINEST(y,x^{1,2,3},TRUE,TRUE),3,1)

13. Polynomial Trendline(4th order) Equation
Equation: y= (c4*x^4)+(c3*x^3) + (c2*x^2) + (c1*x^1) +b
Where,
c4 = INDEX(LINEST(y,x^{1,2,3,4},1)
c3 =INDEX(LINEST(y,x^{1,2,3},1)
c2 =INDEX(LINEST(y,x^{1,2}),1)
c1 =INDEX(LINEST(y,x^{1,2}),1,2)
b = INDEX(LINEST(y,x^{1,2}),1,3)
RSQ =INDEX(LINEST(y,x^{1,2,3,4},TRUE,TRUE),3,1)

14. Polynomial Trendline(5th order) Equation
Equation:
y= (c5*x^5)+(c4*x^4)+(c3*x^3) + (c2*x^2) + (c1*x^1) +b
Where,
c5 = INDEX(LINEST(y,x^{1,2,3,4,5},1)
c4 = INDEX(LINEST(y,x^{1,2,3,4},1)
c3 =INDEX(LINEST(y,x^{1,2,3},1)
c2 =INDEX(LINEST(y,x^{1,2}),1)
c1 =INDEX(LINEST(y,x^{1,2}),1,2)
b = INDEX(LINEST(y,x^{1,2}),1,3)
RSQ =INDEX(LINEST(y,x^{1,2,3,4,5},TRUE,TRUE),3,1)

15. Polynomial Trendline(6th order) Equation
Equation:
y=(c6*x^6)+(c5*x^5)+(c4*x^4)+(c3*x^3) + (c2*x^2) + (c1*x^1)+b
Where,
c6 = INDEX(LINEST(y,x^{1,2,3,4,5,6},1)
c5 = INDEX(LINEST(y,x^{1,2,3,4,5},1)
c4 = INDEX(LINEST(y,x^{1,2,3,4},1)
c3 =INDEX(LINEST(y,x^{1,2,3},1)
c2 =INDEX(LINEST(y,x^{1,2}),1)
c1 =INDEX(LINEST(y,x^{1,2}),1,2)
b = INDEX(LINEST(y,x^{1,2}),1,3)
RSQ =INDEX(LINEST(y,x^{1,2,3,4,5,6},TRUE,TRUE),3,1)

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Basics of Excel functions used

17. Few Basics – Excel functions used - 1
X= Known X's (e.g.: Months on X Axis)
Y= Known Y's (e.g.: Sales on Y Axis)
Details of Excel functions are taken from Excel Help
LN
LN(number)
Returns the natural logarithm of a number. Natural logarithms are based
on the constant e (2.71828182845904).
Liniest
LINEST(known_y's,known_x's,const,stats)
Calculates the statistics for a line by using the "least squares" method to
calculate a straight line that best fits your data, and returns an array that
describes the line. Because this function returns an array of values, it must
be entered as an array formula.
Exp
EXP(number)
Returns e raised to the power of number. The constant e equals
2.71828182845904, the base of the natural logarithm.
Index
INDEX(array,row_num,column_num)
INDEX(reference,row_num,column_num,area_num)
Returns a value or the reference to a value from within a table or range.
There are two forms of the INDEX() function: array and reference. The
array form always returns a value or an array of values; the reference form
always returns a reference.

18. Few Basics – Excel functions used - 2
RSQ
RSQ(known_y's,known_x's)
Returns the square of the Pearson product moment correlation coefficient
through data points in known_y's and known_x's. For more information,
see PEARSON. The r-squared value can be interpreted as the proportion of
the variance in y attributable to the variance in x.
Slope
SLOPE(known_y's,known_x's)
Returns the slope of the linear regression line through data points in
known_y's and known_x's. The slope is the vertical distance divided by
the horizontal distance between any two points on the line, which is the
rate of change along the regression line.
Intercept
INTERCEPT(known_y's,known_x's)
Calculates the point at which a line will intersect the y-axis by using
existing x-values and y-values.
Logest
LOGEST(known_y's,known_x's,const,stats)
In regression analysis, calculates an exponential curve that fits your data
and returns an array of values that describes the curve. Because this
function returns an array of values, it must be entered as an array formula.

19. Incase you need more details…
I have learned these formulas form the following
web sites and authors.
Click the links below
Trendline formulas
Bernard Liengme’s website
Tushar Mehta’s article
Ozgrid Forum
Trends-and-forecast-sales-with-charts
Choosing-the-best-trendline-for-your-data

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