1) Since the Slope values are dependent of the numbers in the time series, then how can we compare two different time series lin reg slopes?
2) Is this possible to even find how steep or not is the slope? is it called a Angel or Degree?
1) Once you have modeled your data with two linear regressions, you can compare directly the slope of both models. Remember that the slope is defined as the ratio of the vertical to the horizontal change between two points. Thus, the slope of a line is always the same. I attach you an example in matlab:
x=[ 1 2.2 3.1 4 5 6.2 7 8.2 9.1 9.9 11 12 13 14 15]; % signal1
x2 = [2 4 6 8 10 12 14 16 18 20 22 24 26 28 30]; % signal2
t = 1:15; %time
plot(t,x,'.'); hold on; set(gcf,'color','w');
plot(t,x2,'.r');
p = polyfit(t,x,1); % linear model 1
slope_1 = p(1); % slope lm1
p = polyfit(t,x2,1); % linear model 2
slope_2 = p(1); % slope lm2
slope_2/slope_1 % relation between linear models
> 2
In the example, the slope of x2 is double than the slope of x, which can be confirmed by relating both measures with a simple division. Thus, 2) the slope of a time series (how steep it is at any point) can be determined across all its points. Think also in the concept of derivative.
Interesting answer. But, can we obtain a statistic number for that? I mean, .....can we say the slopes are statistically different?
Might we compare the beta coefficients? With the use of their confidence intervals, probably? Some analysis of covariance?
Cheers
Ibai
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