Gradient of a line

WillyNelson · 20 Jun 2014 at 11:39

I'm struggling to convert the equation of a linear trend line to a % gradient.

I've plotted two series of activity which both show an increasing trend. The trendline for series 1 equates to y=119.45x+51062 and series 2 is y=396.05x+50052.

Can anyone explain simply how I can convert these equations into a % gradient, essentially a % increase trend over the period?

Thanks

Sunbed · 20 Jun 2014 at 11:50

The gradients are 119.45 and 396.05 respectively. So I think as a % then your answers would be 11945% and 39605%.

cheesyboy · 20 Jun 2014 at 11:51

WillyNelson said:
I'm struggling to convert the equation of a linear trend line to a % gradient.

I've plotted two series of activity which both show an increasing trend. The trendline for series 1 equates to y=119.45x+51062 and series 2 is y=396.05x+50052.

Can anyone explain simply how I can convert these equations into a % gradient, essentially a % increase trend over the period?

Thanks

Gradient is 11945% and 39605%, being the multiplier of X

toasteh · 20 Jun 2014 at 11:59

Sunbed is correct. For each increase of 1 on the x-axis, the y-axis increases by a factor of 119.45 or 396.05.

dirtychinchilla · 20 Jun 2014 at 12:00

Differentiate. This removes the constants, x and y.

WillyNelson · 20 Jun 2014 at 12:02

Except the values are not increasing by 11,945% from the beginning of the series to the end. 100% is a 45deg upward slope so that would be an insane increase.

cheesyboy · 20 Jun 2014 at 12:04

WillyNelson said:
Except the values are not increasing by 11,945% from the beginning of the series to the end. 100% is a 45deg upward slope so that would be an insane increase.

Well, that depends on the scale you're using for X and Y respectively.

WillyNelson · 20 Jun 2014 at 12:06

x are months Oct 2012 through to May 2014
y values are between 40,000 and 65,000

Sunbed · 20 Jun 2014 at 12:07

Remember the y = mx + c formula.

For a 100% gradient (45 degree) y = (1)x + 0, i.e. for every 1 across, you go 1 up. Are you sure your gradients are 119.45 and 396.05 to begin with?

Sunbed · 20 Jun 2014 at 12:12

(65000-40000)/40000*100 is a 62.5% increase. You sure you've not accidentally multiplied your gradients by 100?

cheesyboy · 20 Jun 2014 at 12:13

WillyNelson said:
x are months Oct 2012 through to May 2014
y values are between 40,000 and 65,000

I see, so you don't want the Y increase as a % of X.

Well, just substitute X in to each of your equations for each month

Month one, replace X with "1"
Month two, replace X with "2"
and so on.

This gives you Y values for each month.

Then, calculate the increase for each month (subtract later month from previous month), and calculate the % increase

It will be a curve, if you plot it.

Hagar · 20 Jun 2014 at 12:13

http://www.1728.org/gradient.htm

3.9605e+4 % Grade

WillyNelson · 20 Jun 2014 at 12:14

Sunbed said:
Are you sure your gradients are 119.45 and 396.05 to begin with?

It's plotted in Excel with a linear trendline. The formula for the line is from excel as per my OP.

D D Danneh · 20 Jun 2014 at 12:15

You can't just use gradient as a measure of % increase. Your percent increase is relative to which two months you are comparing. Just take your Y value at the end of the period, subtract the Y value at the start of the period, and then divide by the starting Y value, then multiply by 100. For example, at X = 0, you have Y = 51602, and at X = 3 you have 51960.35, so you percent increase is

(358.35*100) / 51602 = 0.694% increase.

Note that from X = 0 to X = k this is just the same as doing 11945*k / 51602, but this will change if you don't start at 0.

cheesyboy · 20 Jun 2014 at 12:17

cheesyboy said:
I see, so you don't want the Y increase as a % of X.

Well, just substitute X in to each of your equations for each month

Month one, replace X with "1"
Month two, replace X with "2"
and so on.

This gives you Y values for each month.

Then, calculate the increase for each month (subtract later month from previous month), and calculate the % increase

It will be a curve, if you plot it.

Something like this;

Code:

Month	X	Y = 119X + 51062		Y-increase	% increase
Oct-12	1	51181		0	
Nov-12	2	51300		119	0.2325%
Dec-12	3	51419		119	0.2320%
Jan-13	4	51538		119	0.2314%
Feb-13	5	51657		119	0.2309%
Mar-13	6	51776		119	0.2304%
Apr-13	7	51895		119	0.2298%
May-13	8	52014		119	0.2293%
Jun-13	9	52133		119	0.2288%
Jul-13	10	52252		119	0.2283%
Aug-13	11	52371		119	0.2277%
Sep-13	12	52490		119	0.2272%

pfff... formatting :mad:

WillyNelson · 20 Jun 2014 at 12:24

That's ok if you've got a constant increase from month to month, but I've got ups & downs. It's the long term trend that I want to get growth for.

Here's my data & the chart

Tuppy_Glossop · 20 Jun 2014 at 12:35

(m/c)*100

cheesyboy · 20 Jun 2014 at 12:35

WillyNelson said:
That's ok if you've got a constant increase from month to month, but I've got ups & downs. It's the long term trend that I want to get growth for.

that's why you use the formulas (formulae?) from your first post - you've already got a formula for the trend.

There's a straightforward way of getting an actual formula for the % increase curve, but my stats skills are too rusty to remember how without spending time working it out. If you just want to plot it, then do what I've done above.

D D Danneh · 20 Jun 2014 at 12:43

% increase is just the difference between months divided by the value of the first.

Theophany · 20 Jun 2014 at 12:46

Each time you cut it in half, you essentially double the amount of sandwiches you have.