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Least Squares Regression In this livescript, you will learn how To apply least squares regression Given a set of data points, we may approximate the relationship by assuming a functional relationship y_{i}=f(x_{i};\textbf{a}) , where \textbf{a} the parameters defining the problem. For a linear relationship y=a_{0}+a_{1}x a_{0} and a_{1} are the parameters. Define the error as e_{i}=|y_{i}-f(x_{i})| Then to determine f , we want to choose out a_{i} ‘s such that it minimises the total error. The total square error is therefore S=\sum^{N}_{i=1}{e_{i}^{2} Equation 1. Our goal is to find the a_{i} ‘s that minimise S . Thus, we compute the derivatives with respect to a_{i} and set it to zero. Thus, we obtain the set of equations \pmatrix{\frac{\partial S}{\partial a_{1}}\cr\frac{\partial S}{\partial a_{2}}\cr\vdots}
=
\pmatrix{\sum^{N}_{i=1}{2e_{i}\frac{\partial e_{i}}{\partial a_{1}}} \cr \sum^{N}_{i=1}{2e_{i}\frac{\partial e_{i}}{\partial a_{2}}} \cr \vdots}
=
\pmatrix{0 \cr 0 \cr \vdots} Equation 2. Eq. (2) defines the least squares problem. As an example, we consider the set of data x = [1.2712 1.6767 3.0656 3.7720 4.9970 6.0655 6.7446 7.7158 9.1419 9.8807];
y = [0.9835 1.5948 3.0609 4.0504 5.3752 5.7974 7.1778 7.8748 8.6854 9.7225]; A good idea before we conduct a regression analysis is to plot a scatter plot, so that we get an idea of what the functional relationship is figure(1)
plot(x,y,’.’,’MarkerSize’,15) The data is quite linear, so let’s assume a model of the form y=a_{0}+a_{1}x Part 1: (a) Show that the leasts squares problem is given by \pmatrix{\sum^{10}_{i=1}{x_{i}^{2}} & \sum^{10}_{i=1}{x_{i}} \cr \sum^{10}_{i=1}{x_{i}^{2}} & 10}
\pmatrix{a_{1} \cr a_{0}}
=
\pmatrix{\sum^{10}_{i=1}{x_{i}y_{i}} \cr \sum^{10}_{i=1}{y_{i}}} Equation 3. If we have a vector \texttt{x} , that contains all the x_{i} s, MATLAB has this great function \texttt{sum} , which as you may have guessed, determines the sum of all the elements of \texttt{x} . The following code uses \texttt{sum} to assemble the right and left-hand-side of Eq. (3). A = [sum(x.^2) sum(x);
sum(x) 10];
c = [sum(x.*y);
sum(y)]; Solving for the coefficients \{a\} and plotting a = A\c
xplot = linspace(1,10,100);
f = a(2) + a(1)*xplot;
figure(2)
plot(x,y,’.’,’MarkerSize’,15)
hold on
plot(xplot,f)
hold off (b) Run this code and see if it provides a good fit. (c) Use \texttt{fitlm} or the ‘Basic Fitting’ toolbox to check the answer. fitlm(x,y) You may have noticed that \texttt{fitlm} gives you quite a few outputs, including R^{2} , rms error, etc. To obtain a estimate of how good the regression is, a common measure is the R^{2} value. Define \bar{y}=\frac{1}{N}\sum^{N}_{i=1}{y_{i}} as the mean value of the measurements, which can be used as a crude estimate of the model. In MATLAB, we can find this using the \texttt{mean} command, whose input is a vector of the values. ybar = mean(y) Then the R^{2} value is defined as R^{2}=1-\frac{\sum^{N}_{i=1}{(y_{i}-f_{i}})^{2}}{\sum^{N}_{i=1}{(y_{i}-\bar{y}})^{2}} Equation 4. NOTES: The numerator may be interpreted as the residual sum of squares (i.e. how well f models the data) The denominator on the other hand is the total sum of squares (i.e. how well the mean models the data) R^{2} varies between -1\leq R^{2} \leq 1 . Applying this in MATLAB yi = y;
fi = a(2) + a(1)*x;
R2 = 1-(sum((yi-fi).^2))/(sum((yi-ybar).^2)) which does match the results we got from \texttt{fitlm} . There is a direct way of finding the R^{2} value in MATLAB. And it is based on the relation between R^{2} and a statistical measure called the Pearson correlation coefficient defined as r^{2}_{y,f}=\frac{(\text{Cov}(y,f))^{2}}{\text{Var}(y)\text{Var}(f)} Under some general assumptions, the R^{2} -value will be given by R^{2}=r^{2}_{y,f} Thus, we have cov(yi,fi).^2/(var(yi)*var(fi)) Alternatively, this can be determined using the function \texttt{corrcoef} , which takes the data \texttt{y} and \texttt{f} as inputs, and outputs a matrix of the cross correlations between \texttt{y} and \texttt{f} . corrcoef(yi,fi).^2
manual code ready 0.4 figure 504bf812-a320-4b3a-aaac-caeb4ca6cdda 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 560 420 2 3 2 3 4 matrix a 2×1 2 1 double 0.9908
0.0493
double double [[{“value”:”{\”value\”:\”0.9908\”}”},{“value”:”{\”value\”:\”0.0493\”}”}]] 9 figure 7586bf60-a6f3-4911-a8e3-ab3bf9988257 data:image/png;base64,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×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 560 420 9 10 11 12 13 9 14 15 16 17 18 variableString ans Linear regression model:
y ~ 1 + x1
Estimated Coefficients:
Estimate SE tStat pValue
________ ________ _______ __________
(Intercept) 0.049323 0.21852 0.22571 0.82708
x1 0.99077 0.035635 27.803 3.0226e-09
Number of observations: 10, Error degrees of freedom: 8
Root Mean Squared Error: 0.32
R-squared: 0.99, Adjusted R-Squared: 0.988
F-statistic vs. constant model: 773, p-value = 3.02e-09 false false 1 1 19 variable R2 0.9898 1 1 24 matrix ans 2×2 2 2 double 1.0103 0.9898
0.9898 0.9898
double double [[{“value”:”{\”value\”:\”1.0103\”}”},{“value”:”{\”value\”:\”0.9898\”}”}]] 25 matrix ans 2×2 2 2 double 1.0000 0.9898
0.9898 1.0000
double double [[{“value”:”{\”value\”:\”1.0000\”}”},{“value”:”{\”value\”:\”0.9898\”}”}]] 26 true false x = [1.2712 1.6767 3.0656 3.7720 4.9970 6.0655 6.7446 7.7158 9.1419 9.8807]; 0 26 26 false true y = [0.9835 1.5948 3.0609 4.0504 5.3752 5.7974 7.1778 7.8748 8.6854 9.7225]; 1 27 27 true false figure(1) 2 30 30 0 false true plot(x,y,’.’,’MarkerSize’,15) 3 31 31 0 true false A = [sum(x.^2) sum(x);
sum(x) 10]; 4 43 44 false true c = [sum(x.*y);
sum(y)]; 5 45 46 true false a = A\c 6 49 49 1 false false xx = linspace(1,10,100); 7 51 51 false false f = a(2) + a(1)*xx; 8 52 52 false false figure(2) 9 54 54 2 false false plot(x,y,’.’,’MarkerSize’,15) 10 55 55 2 false false hold on 11 56 56 2 false false plot(xx,f) 12 57 57 2 false true hold off 13 58 58 2 true true fitlm(x,y) 14 63 63 3 true false yi = y; 15 80 80 false false fi = a(2) + a(1)*x; 16 81 81 false true R2 = 1-(sum((yi-fi).^2))/(sum((yi-ybar).^2)) 17 83 83 4 true false cov(yi,fi).^2/(var(yi)*var(fi)) 18 91 91 5 false true corrcoef(yi,fi).^2 19 93 93 6
2020-03-26T14:29:54Z 2020-04-09T07:04:51Z
application/vnd.mathworks.matlab.code MATLAB Code R2019b
9.7.0.1183724 b052da3d-afe4-4d54-8efa-c8680abb3de2
9.7.0.1296695
R2019b
Update 4
Jan 20 2020
3546228467