Help with Linear Regression
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I'm trying to conduct a simple linear regression fitting using fitlm, but the results that is provided when I plot the curve with the original data and the linear equation line found through fitlm is really off. I'm just using the first 20 data points from the list
mdl = fitlm(time(1:20),price(1:20))
mdl =
Linear regression model:
y ~ 1 + x1
Estimated Coefficients:
Estimate SE tStat pValue
__________ _______ _______ _________
(Intercept) 2.4736e+05 42743 5.7871 1.748e-05
x1 -5.7654 0.99663 -5.7849 1.756e-05
Number of observations: 20, Error degrees of freedom: 18
Root Mean Squared Error: 0.0178
R-squared: 0.65, Adjusted R-Squared 0.631
F-statistic vs. constant model: 33.5, p-value = 1.76e-05
Then I prepped for plot using.
x=time(1:20)
y1=2.4736e+05+(x*-5.7654)
plot(time(1:20),price(1:20),x,y1)
I would get this plot attached. I've also attached the data. Please help with a better fit or explanation as to why it is so far off. I'm not sure what I'm doing incorrectly.
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Star Strider
2017-6-14
This works:
d = load('liu James Linear .mat');
Price = d.Price;
time = d.time;
mdl = fitlm(time, Price, 'linear')
ypred = predict(mdl, [min(time) max(time)]');
figure(1)
plot(time, Price, '+')
hold on
plot([min(time) max(time)]', ypred, '-r')
hold off
grid
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Star Strider
2017-6-15
That appears to be correct for the first 20 values. (I get the same result, not surprisingly.)
I would use the predict function rather than writing your own function to calculate the fit (that you then use to plot the line). The predict function uses full internal precision of the slope and intercept, while your equation uses only the precision that fitlm reports in its results. That is likely the reason your results seem to be in error. For example, for ‘time(1)’ and ‘time(20)’, predict gives [94.5918, 94.5157], and your equation gives [97.0681, 96.9920]. The difference will be noticeable on the plot.
So your equation is mathematically correct, but computationally incorrect, in that it does not use the full precision that fitlm calculates.
You have to ask for the full precision parameter estimates with:
coefs = mdl.Coefficients.Estimate;
Your equation rewritten as:
y1 = coefs(1) + coefs(2)*x;
then gives results identical to those predict produces.
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