How do I do a regress like this?

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Leon 2023-9-16

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评论： Leon 2023-9-26

I have a series of numbers that decrease by about the same percetentage rate with time. How do I do the regression to find the exact percentage rate it is changing?

For example, it can be something like the below:

1 100

2 95

3 91

4 86

5 80

Many thanks.

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Walter Roberson 2023-9-16

think about logarithm

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Answer 1

Image Analyst 2023-9-16

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Not sure why you need a regression. How about this to just find out the percentage decrease at each time point. Then compute the average percentage decrease over all time points if you want.

y = [100, 95, 91, 86, 80];
deltaY = diff(y)
deltaY = 1×4
    -5    -4    -5    -6
percentageDecreases = 100 * deltaY ./ y(1:end-1)
percentageDecreases = 1×4
   -5.0000   -4.2105   -5.4945   -6.9767
averagePercentageDecrease = mean(percentageDecreases)
averagePercentageDecrease = -5.4204

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Image Analyst 2023-9-19

fitnlm just needs a starting point for some reason. So what I usually do is to just put anything there. It will do it's best and then I use the returned, estimated coordinates for the guess next time and do it again. After a few times of this, the values should converge. You could put it in a loop and do it like 5 or 10 times and see how the values settle on the final, good values.

Leon 2023-9-26

Thank you so much!

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Answer 2

Sam Chak 2023-9-16

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Hi @Leon

I'm not exactly sure what you want. If you're looking to find the exact percentage drop, as @Image Analyst has shown you, that's one approach. If you want to use MATLAB to create a linear regression model fit, you can do so using the 'fitlm()' function.

y = [100, 95, 91, 86, 80]; % data

x = 1:numel(y);

mdl = fitlm(x, y) % linear regression model

mdl =

Linear regression model: y ~ 1 + x1 Estimated Coefficients: Estimate SE tStat pValue ________ _______ _______ __________ (Intercept) 105.1 0.63509 165.49 4.8652e-07 x1 -4.9 0.19149 -25.589 0.00013089 Number of observations: 5, Error degrees of freedom: 3 Root Mean Squared Error: 0.606 R-squared: 0.995, Adjusted R-Squared: 0.994 F-statistic vs. constant model: 655, p-value = 0.000131

plot(mdl)

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Leon 2023-9-16

Thanks for the reply.

The change should be exponential (e.g., 5% decrease during each time period), instead of linear (a fixed decrease rate of 5). In this case, how should I do the regression?