INTC (Intel Corporation) revenues for past few years (source: https://stockrow.com/INTC )

2011,  2012,  2013,  2014,  2015,  2016,  2017,  2018,  2019,  2020,  2021,  2022,  2023	
53999, 53341, 52708, 55870, 55355, 59387, 62761, 70848, 71965, 77867, 73753, 73273, 75907

--------------------------------------------------------------------
OCTAVE

octave:1> format long
octave:2> X = [ 1 2011;  1 2012; 1 2013; 1 2014; 1 2015; 1 2016; 1 2017; 1 2018; 1 2019; 1 2020; 1 2021; 1 2022];
octave:3> Y = [ 53999;  53341; 52708; 55870; 55355; 59387; 62761; 70848; 71965; 77867; 73753; 73273];
octave:4> w = inv(X'*X)*X'*Y
w =

  -4887312.92333068978
      2455.11538474036

octave:5> [1 2030]*w
ans =  96571.3076922437

***this is an alternate way of solving it; when X's cols > rows.
octave:6> w = X'*inv( X*X' + 0.0000001*eye(12,12))*Y
w =

  -4875445.77506429516
      2449.63078665733



--------------------------------------------------------------------
JAVA

$ javac hw4hint.java 
$ java hw4hint
w = -4887312.923077829, 2455.115384615279
2030 prediction = 96571.30769118667

code: 

public class hw4hint {
    
    public static double[] t(double[] x,int rows, int cols){        
        double[] o = new double[x.length];
        for(int i=0;i<rows;i++)
            for(int j=0;j<cols;j++)
                o[j*rows+i] = x[i*cols+j];
        return o;
    }

    public static double[] mult(double[] a, int rows, int cols, double[] b, int bcols){
        double[] o = new double[rows*bcols];
        for(int i=0;i<rows;i++){
            for(int j=0;j<bcols;j++){
                double sum = 0;
                for(int k=0;k<cols;k++)
                    sum += a[i*cols+k] * b[k*bcols+j];
                o[i * bcols + j] = sum;
            }
        }
        return o;
    }

    public static double[] inv2x2(double[] a){
        double d = a[0]*a[3]-a[1]*a[2];
        double[] o = {
            a[3]/d, -a[1]/d, 
            -a[2]/d, a[0]/d
        };
        return o;
    }

    public static void main(String[] args) throws Throwable {
        double[] X = { 
            1, 2011,  1, 2012,  1, 2013, 1, 2014,  1, 2015, 1, 2016,
            1, 2017,  1, 2018,  1, 2019, 1, 2020,  1, 2021, 1, 2022
            //,1 2023 
        };	
        double[] Y = { 
            53999, 53341, 52708, 55870, 55355, 59387, 
            62761, 70848, 71965, 77867, 73753, 73273
            //, 75907
        };
        // w = inv(X'*X)*X'*Y
        var Xt = t(X,12,2);
        var XtX = mult(Xt,2,12, X, 2);
        var invXtX = inv2x2(XtX);
        var invXtXXt = mult(invXtX,2,2, Xt, 12);
        var w = mult( invXtXXt, 2,12, Y, 1);
        
        System.out.println("w = "+w[0]+", "+w[1]);
        
        var p = mult(new double[]{ 1, 2030 }, 1,2, w, 1);

        System.out.println("2030 prediction = "+p[0]);
    }
}

--------------------------------------------------------------------
JAVA2, with https://math.nist.gov/javanumerics/jama/

$ javac hw4hint2.java 
$ java hw4hint2
w = -4887312.923076374, 2455.1153846151137
2030 prediction = 96571.30769230612

import Jama.*;

public class hw4hint2 {
    
    public static void main(String[] args) throws Throwable {
        double[][] X = { 
            {1, 2011},  {1, 2012},  {1, 2013}, {1, 2014},  {1, 2015}, {1, 2016},
            {1, 2017},  {1, 2018},  {1, 2019}, {1, 2020},  {1, 2021}, {1, 2022}
            //,1 2023 
        };
        double[] Y = { 
            53999, 53341, 52708, 55870, 55355, 59387, 
            62761, 70848, 71965, 77867, 73753, 73273
            //, 75907
        };

        var x = new Matrix(X);
        var y = new Matrix(Y,Y.length);
        var w = x.solve(y);      // solve xw=y
        
        System.out.println("w = "+w.get(0,0)+", "+w.get(1,0));

        var p = new Matrix( new double[][]{ {1, 2030} }).times(w);
        System.out.println("2030 prediction = "+p.get(0,0));   
    } 
}

--------------------------------------------------------------------
OCTAVE; 

build a linear [y = a+bx ];

octave:1> format long
octave:2> X = [ 1 2011;  1 2012; 1 2013; 1 2014; 1 2015; 1 2016; 1 2017; 1 2018; 1 2019; 1 2020; 1 2021];
octave:3> Y = [ 53999;  53341; 52708; 55870; 55355; 59387; 62761; 70848; 71965; 77867; 73753];
octave:4> x = [1 2022];
octave:5> X1 = [X(:,1), X(:,2)-min(X(:,2))+1];
octave:6> w = inv(X1'*X1)*X1'*Y;
octave:7> x1 = [x(:,1), x(:,2)-min(X(:,2))+1];
octave:8> x1*w
ans =  78459.8363636363
octave:9> a = w(1);
octave:10> b = w(2);
octave:11> y = a + b * 12
y =  78459.8363636363


logarithmic [y = a+b*log(x) ]

octave:1> format long
octave:2> X = [ 1 2011;  1 2012; 1 2013; 1 2014; 1 2015; 1 2016; 1 2017; 1 2018; 1 2019; 1 2020; 1 2021];
octave:3> Y = [ 53999;  53341; 52708; 55870; 55355; 59387; 62761; 70848; 71965; 77867; 73753];
octave:4> x = [1 2022];
octave:5> X1 = [X(:,1), log( X(:,2)-min(X(:,2))+1) ];
octave:6> w = inv(X1'*X1)*X1'*Y;
octave:7> x1 = [x(:,1), log(x(:,2)-min(X(:,2))+1) ];
octave:8> x1*w
ans =  71723.5329618965
octave:9> a = w(1);
octave:10> b = w(2);
octave:11> y = a + b * log(12)
y =  71723.5329618965


exponential [ y=b*exp(a*x) ]; log of both sides: log(y) = log(b) + a*x

octave:1> format long
octave:2> X = [ 1 2011;  1 2012; 1 2013; 1 2014; 1 2015; 1 2016; 1 2017; 1 2018; 1 2019; 1 2020; 1 2021];
octave:3> Y = [ 53999;  53341; 52708; 55870; 55355; 59387; 62761; 70848; 71965; 77867; 73753];
octave:4> x = [1 2022];
octave:5> X1 = [X(:,1), X(:,2)-min(X(:,2))+1 ];
octave:6> Y1 = log(Y);
octave:7> w = inv(X1'*X1)*X1'*Y1;
octave:8> x1 = [x(:,1), x(:,2)-min(X(:,2))+1 ];
octave:9> exp(x1*w)
ans =  79600.0172959047
octave:10> b = exp( w(1) );
octave:11> a = w(2);
octave:12> y = b * exp(a * 12)
y =  79600.0172959046


power curve [ y=b*x^a ]; log of both sides: log(y) = log(b) + a * log(x)

octave:1> format long
octave:2> X = [ 1 2011;  1 2012; 1 2013; 1 2014; 1 2015; 1 2016; 1 2017; 1 2018; 1 2019; 1 2020; 1 2021];
octave:3> Y = [ 53999;  53341; 52708; 55870; 55355; 59387; 62761; 70848; 71965; 77867; 73753];
octave:4> x = [1 2022];
octave:5> X1 = [X(:,1), log( X(:,2)-min(X(:,2))+1) ];
octave:6> Y1 = log(Y);
octave:7> w = inv(X1'*X1)*X1'*Y1;
octave:8> x1 = [x(:,1), log( x(:,2)-min(X(:,2))+1) ];
octave:9> exp(x1*w)
ans =  71652.4328410171
octave:10> b = exp( w(1) );
octave:11> a = w(2);
octave:12> y = b * 12^a
y =  71652.4328410171