MATLAB: Polynomial 2nd degree

coefficientsregression

I tried using the curve fitting tool, however i had an error saying that 'Data sizes are incompatible.'
dataset= xlsread('ML.xlsx','sheet2')
a=dataset(:,1)
S=dataset(:,3:9)
D= repelem(a(1:end, :), 1, 7)
cftool

Best Answer

Higher order polynomials aren't going to help here...the following code generated the figure:
for i=3:9
  subplot(4,2,i-2);
  [~,ix]=sort(SB(:,i));
  plot(SB(ix,i),SB(ix,1))
  xlabel(sprintf('B%d',i-2))
end
There's virtually no correlation with most of the corollary variables; what there is in pieces breaks down in other areas of every variable.
Just taking a stab; ran one that uses all variables; another with the only two that were staistically significant -- those results are
>> fitlm(SB(:,3:end),SB(:,1))
ans = 
Linear regression model:
    y ~ 1 + x1 + x2 + x3 + x4 + x5 + x6 + x7
Estimated Coefficients:
                   Estimate     SE      tStat    pValue
                   ________    _____    _____    ______
    (Intercept)     63.33      13.62     4.65    0.13  
    x1             -29.51      18.92    -1.56    0.36  
    x2              20.66      15.52     1.33    0.41  
    x3               4.74      14.23     0.33    0.80  
    x4              -4.83      15.69    -0.31    0.81  
    x5              20.96      33.11     0.63    0.64  
    x6              -0.02      21.87    -0.00    1.00  
    x7               1.42      16.83     0.08    0.95  
Number of observations: 9, Error degrees of freedom: 1
Root Mean Squared Error: 2.49
R-squared: 0.934,  Adjusted R-Squared 0.474
F-statistic vs. constant model: 2.03, p-value = 0.495
>> figure
>> LMA=ans;
>> plot(LMA)
>> title('Salinity ~ 1 + B1 +B2 + B3 +B4 + B5 +B6 + B7')
>> LM12=fitlm(SB(:,3:4),SB(:,1))
LM12 = 
Linear regression model:
    y ~ 1 + x1 + x2
Estimated Coefficients:
                   Estimate     SE     tStat    pValue
                   ________    ____    _____    ______
    (Intercept)     67.74      2.13    31.82    0.00  
    x1             -20.86      5.90    -3.53    0.01  
    x2              21.88      3.21     6.82    0.00  
Number of observations: 9, Error degrees of freedom: 6
Root Mean Squared Error: 1.33
R-squared: 0.887,  Adjusted R-Squared 0.85
F-statistic vs. constant model: 23.6, p-value = 0.00144
>> figure
>> plot(LM12)
>> title('Salinity ~ 1 + B1 +B2')
>> ylim([40 100])
The last puts the plots on the same scale; notice the intervals are much tighter with only two predictors. Whether this would be worth a hoot for future predictions is pretty much pure luck I'd guess...
Related Question