Fitting data polynomial fitlm

I am trying to fit data, first to a polynomial of degree 1 and then to a polynomial of degree 1 but log(y) instead of y. How make a predicting to what the data would look like the year 2020 and plot it? (The first x-value is 1972 and it increases with 1 until 2011)

clear all
clf
load moore.mat %xtime and y are 40x1 double 
%data for mooores law

%polynomial of degree 1
figure(13)
mdl1 = fitlm(xtime,y)
subplot(2,1,1)
plot(mdl1,'Color','m')
hold on
ttime = 1972:1:2020;
T = [];
for j=1972:1:2020
t = ((j.*4.4366.^20) -8.8006^10);
    T = [T t];
end
plot(ttime,T)

%polynomial of degree 1 mwith log y instead of y
mdl3 = fitlm((xtime),log(y));

%maybe I should use predict
%R^2 för modellerna -> this I get with fitlm
%transforming the logarithmically fitted version back to normal
%using data from fitlm

Y = [];
for i=1972:1:2020
y_ny = (i.*0.52342-1030.3);
    Y = [Y y_ny];
end
xtime_ny = 1972:1:2020;
%Får ut med fitlm i cmd window
subplot(2,1,2)
plot(xtime_ny,Y,'c-*')
legend('label1')

%are the residuals normally distributed, investigate with qqplot
%making a new plot with a prediction in year 2020 (the x data is in years)
%this plot is supposed to be with the polynomial of the first degree... 
%...and the polynomial that used the logaritm

%look at graphs for the year 2020

Answer 1

[Mathieu NOE]

hello Karolina

here my suggestion; if you need further help , let me know

yes, it's a first polynomial fit once the y data are in log scale

clear all
clf
load moore.mat %xtime and y are 40x1 double 
%data for mooores law

% so log(y) is linear with time (linear)
figure(1);semilogy(xtime,y);

y_log10 = log10(y);

% do some smoothing ? 
N = 10;
y_log10_smoothed = myslidingavg(y_log10, N);
figure(2);plot(xtime,y_log10,'b',xtime,y_log10_smoothed,'*-r');

% polynomial fit 
% Fit a polynomial p of degree 1 to the (x,y) data:
% + remove first and last points of smoothed data
ind = 2:length(xtime)-1;
xs = xtime(ind);
yls = y_log10_smoothed(ind);

p = polyfit(xs,yls,1);

% Evaluate the fitted polynomial p and plot:
% yls_fit = polyval(p,xtime);
%   Y = POLYVAL(P,X) returns the value of a polynomial P evaluated at X. P
%   is a vector of length N+1 whose elements are the coefficients of the
%   polynomial in descending powers:
%
%       Y = P(1)*X^N + P(2)*X^(N-1) + ... + P(N)*X + P(N+1)

yls_fit = p(1)*xtime + p(2);

figure(3);plot(xtime,y_log10,'o', xs,yls,'--',xtime,yls_fit,'-')
legend('data','data smoothed','linear fit')

% going back from log to linear scale for y 
y_lin = 10.^(yls_fit);


% now use the fit model to predict future value
new_x_data = [2015 2020 2025]; % can be scalar or vector
new_y_data = 10.^(p(1)*new_x_data + p(2)); % can be scalar or vector

figure(4);semilogy(xtime,y,'o',xtime,y_lin,'-',new_x_data,new_y_data,'*');
legend('data','model fit','extrapolation')