Multiple Regression and Intercept

% Load the data from the Excel file
data = readtable('데이터(최종).xlsx', 'Sheet', 'Sheet5');

% Define the dependent variable
y = data.Arrive;

% Define the independent variables
X = [data.Price_m, data.Volme, data.Relative_y, data.Relative_m, ...
     data.mine, data.debt, data.Quin, data.Cpi, data.Rate, data.Depo, ...
     data.Bull, data.Sale, data.Move, data.Sub];

% Add a column of ones to the independent variables matrix for the intercept
X = [ones(size(X, 1), 1), X];

% Perform the multiple linear regression
[b, ~, ~, ~, stats] = regress(y, X);

% Display the results
disp('Regression Coefficients:');
disp(b);

disp('R-squared:');
disp(stats(1));

disp('F-statistic:');
disp(stats(2));

disp('p-value:');
disp(stats(3));

disp('Error Variance:');
disp(stats(4));

I'm going to proceed with a multilinear regression analysis with the data string called Arrive as the dependent variable, and the result is as follows. Is it ok...?

disp(stats(4));

Regression Coefficients:

1.0e+06 *

4.1453

-0.0190

0.0040

-0.0960

-0.6115

-0.0022

-0.0140

0.0259

0.0070

-0.0602

-0.0196

-0.0003

-0.0000

0.0000

0.0000

R-squared:

0.3997

F-statistic:

4.5189

p-value:

3.5809e-06

Error Variance:

3.8687e+09

Answer 1

[Star Strider]

I see nothing wrong with the code, and it conforms to the example in the regress documentation.

The only suggestion I have is to use table indexing to replace the initial ‘X’ so —

data = readtable('데이터(최종).xlsx', 'Sheet', 'Sheet5')

data = 110x16 table
       Date          Arrive      Price_m    Volme     Relative_y    Relative_m     mine      debt     Quin      Cpi       Rate    Depo    Bull    Sale     Move        Sub    
    ___________    __________    _______    ______    __________    __________    ______    ______    ____    ________    ____    ____    ____    _____    _____    __________

    01-Jan-2015    6.1513e+05    84.854     99.224     0.90087        1.0464      57.982      72.6    8.8      0.67762       2    25.7      57    12546    22145    9.4723e+06
    01-Feb-2015    6.6337e+05     85.05     99.845     0.89997        1.0553      57.783    73.078    8.8     -0.05917       2    25.7    68.7    10484    24046    1.5481e+07
    01-Mar-2015    7.7112e+05    85.322     102.01     0.89923        1.0714      57.604    73.543    8.8     0.009515    1.75    25.7    86.2    27303    10931    1.5779e+07
    01-Apr-2015    6.4945e+05    85.656     102.89     0.90282        1.0768      57.445    73.994    8.8     0.030657    1.75    25.7    81.8    34230    20550     1.605e+07
    01-May-2015    6.0572e+05    85.965     102.38     0.90459         1.083      57.304    74.428    8.8      0.28005    1.75    25.7    78.2    38583    15743    1.6232e+07
    01-Jun-2015     6.504e+05    86.288     102.58     0.90773        1.0863      57.182    74.844    8.9     0.020023     1.5    25.7      79    33416    30593    1.6469e+07
    01-Jul-2015     6.271e+05    86.579     101.88      0.9152        1.0744      57.078    75.241    9.6      0.18017     1.5    25.7    83.5    28688    25411    1.6677e+07
    01-Aug-2015    6.1878e+05    86.829     101.88     0.91788        1.0769      56.991    75.616    9.7      0.13988     1.5    25.7    79.2    27539    22182    1.6866e+07
    01-Sep-2015    5.5042e+05    87.085     102.37     0.91793        1.0752      56.921    75.967    9.7     -0.25942     1.5    25.7    79.1    16934    23636    1.7093e+07
    01-Oct-2015    6.5344e+05    87.299     103.25     0.92311        1.0807      56.867    76.293    9.7            0     1.5    25.6    83.5    67650    39265    1.7348e+07
    01-Nov-2015     6.502e+05    87.516     103.41     0.92408        1.0846       56.83    76.592    9.7     -0.18954     1.5    25.6    65.5    54509    22046    1.7536e+07
    01-Dec-2015    7.0015e+05    87.657     100.56     0.91532         1.065      56.807    76.861    9.7      0.29962     1.5    25.5    54.5    21638    25647    1.7673e+07
    01-Jan-2016    5.9513e+05     87.73      99.79     0.91401        1.0541        56.8      77.1    9.7       0.1704     1.5    25.4    47.8     9552    19836    1.7761e+07
    01-Feb-2016    7.0941e+05    87.758     98.834     0.91328        1.0468      56.807    77.312    9.7      0.42843     1.5    25.4    47.2    10983    29027    1.7954e+07
    01-Mar-2016    6.8613e+05    87.778     97.904     0.91169         1.036      56.828    77.505    9.7     -0.25826     1.5    25.4      46    22978    11587    1.8112e+07
    01-Apr-2016    5.6423e+05    87.787     97.601      0.9105        1.0316      56.863    77.681    9.7      0.18869     1.5    25.4    49.3    30154    24567     1.822e+07

% Define the dependent variable
y = data.Arrive;

% Add a column of ones to the independent variables matrix for the intercept, Add a column of ones to the independent variables matrix for the intercept
X = [ones(size(data{:,1})) data{:,3:end}];


% Perform the multiple linear regression
[b, ~, ~, ~, stats] = regress(y, X);

% Display the results
disp('Regression Coefficients:');

Regression Coefficients:

disp(b);

   1.0e+06 *

    4.1453
   -0.0190
    0.0040
   -0.0960
   -0.6115
   -0.0022
   -0.0140
    0.0259
    0.0070
   -0.0602
   -0.0196
   -0.0003
   -0.0000
    0.0000
    0.0000

disp('R-squared:');

R-squared:

disp(stats(1));

    0.3997

disp('F-statistic:');

F-statistic:

disp(stats(2));

    4.5189

disp('p-value:');

p-value:

disp(stats(3));

   3.5809e-06

disp('Error Variance:');

Error Variance:

disp(stats(4));

   3.8687e+09

This is slightly more efficient code, and the result is the same.

.

[형현]

Is there no problem with statistical significance? When you look at R^2 or regression coefficients...

[Star Strider]

There is a problem with statistical significance, because only four variables (including the Intercept term) are statistically significant, in the usual sense of having . I used fitlm to get those statistics —

data = readtable('데이터(최종).xlsx', 'Sheet', 'Sheet5')

data = 110x16 table
       Date          Arrive      Price_m    Volme     Relative_y    Relative_m     mine      debt     Quin      Cpi       Rate    Depo    Bull    Sale     Move        Sub    
    ___________    __________    _______    ______    __________    __________    ______    ______    ____    ________    ____    ____    ____    _____    _____    __________

    01-Jan-2015    6.1513e+05    84.854     99.224     0.90087        1.0464      57.982      72.6    8.8      0.67762       2    25.7      57    12546    22145    9.4723e+06
    01-Feb-2015    6.6337e+05     85.05     99.845     0.89997        1.0553      57.783    73.078    8.8     -0.05917       2    25.7    68.7    10484    24046    1.5481e+07
    01-Mar-2015    7.7112e+05    85.322     102.01     0.89923        1.0714      57.604    73.543    8.8     0.009515    1.75    25.7    86.2    27303    10931    1.5779e+07
    01-Apr-2015    6.4945e+05    85.656     102.89     0.90282        1.0768      57.445    73.994    8.8     0.030657    1.75    25.7    81.8    34230    20550     1.605e+07
    01-May-2015    6.0572e+05    85.965     102.38     0.90459         1.083      57.304    74.428    8.8      0.28005    1.75    25.7    78.2    38583    15743    1.6232e+07
    01-Jun-2015     6.504e+05    86.288     102.58     0.90773        1.0863      57.182    74.844    8.9     0.020023     1.5    25.7      79    33416    30593    1.6469e+07
    01-Jul-2015     6.271e+05    86.579     101.88      0.9152        1.0744      57.078    75.241    9.6      0.18017     1.5    25.7    83.5    28688    25411    1.6677e+07
    01-Aug-2015    6.1878e+05    86.829     101.88     0.91788        1.0769      56.991    75.616    9.7      0.13988     1.5    25.7    79.2    27539    22182    1.6866e+07
    01-Sep-2015    5.5042e+05    87.085     102.37     0.91793        1.0752      56.921    75.967    9.7     -0.25942     1.5    25.7    79.1    16934    23636    1.7093e+07
    01-Oct-2015    6.5344e+05    87.299     103.25     0.92311        1.0807      56.867    76.293    9.7            0     1.5    25.6    83.5    67650    39265    1.7348e+07
    01-Nov-2015     6.502e+05    87.516     103.41     0.92408        1.0846       56.83    76.592    9.7     -0.18954     1.5    25.6    65.5    54509    22046    1.7536e+07
    01-Dec-2015    7.0015e+05    87.657     100.56     0.91532         1.065      56.807    76.861    9.7      0.29962     1.5    25.5    54.5    21638    25647    1.7673e+07
    01-Jan-2016    5.9513e+05     87.73      99.79     0.91401        1.0541        56.8      77.1    9.7       0.1704     1.5    25.4    47.8     9552    19836    1.7761e+07
    01-Feb-2016    7.0941e+05    87.758     98.834     0.91328        1.0468      56.807    77.312    9.7      0.42843     1.5    25.4    47.2    10983    29027    1.7954e+07
    01-Mar-2016    6.8613e+05    87.778     97.904     0.91169         1.036      56.828    77.505    9.7     -0.25826     1.5    25.4      46    22978    11587    1.8112e+07
    01-Apr-2016    5.6423e+05    87.787     97.601      0.9105        1.0316      56.863    77.681    9.7      0.18869     1.5    25.4    49.3    30154    24567     1.822e+07

% Define the dependent variable
y = data.Arrive;

% Add a column of ones to the independent variables matrix for the intercept, Add a column of ones to the independent variables matrix for the intercept
X = [ones(size(data{:,1})) data{:,3:end}];


% Perform the multiple linear regression
[b, ~, ~, ~, stats] = regress(y, X);

% Display the results
disp('Regression Coefficients:');

Regression Coefficients:

disp(b);

   1.0e+06 *

    4.1453
   -0.0190
    0.0040
   -0.0960
   -0.6115
   -0.0022
   -0.0140
    0.0259
    0.0070
   -0.0602
   -0.0196
   -0.0003
   -0.0000
    0.0000
    0.0000

disp('R-squared:');

R-squared:

disp(stats(1));

    0.3997

disp('F-statistic:');

F-statistic:

disp(stats(2));

    4.5189

disp('p-value:');

p-value:

disp(stats(3));

   3.5809e-06

disp('Error Variance:');

Error Variance:

disp(stats(4));

   3.8687e+09

VN = data.Properties.VariableNames;
mdl = fitlm(data{:,3:end}, data.Arrive, 'VarNames',{VN{3:end},VN{2}})

mdl = 
Linear regression model:
    Arrive ~ 1 + Price_m + Volme + Relative_y + Relative_m + mine + debt + Quin + Cpi + Rate + Depo + Bull + Sale + Move + Sub

Estimated Coefficients:
                    Estimate          SE         tStat       pValue  
                   ___________    __________    ________    _________

    (Intercept)     4.1453e+06    1.3912e+06      2.9797    0.0036636
    Price_m             -19030        8333.1     -2.2837     0.024619
    Volme               3965.4        2458.5       1.613      0.11007
    Relative_y          -95964    4.8213e+05    -0.19904      0.84265
    Relative_m     -6.1154e+05    3.8759e+05     -1.5778      0.11794
    mine                 -2239        2986.8    -0.74964      0.45532
    debt                -14013         10099     -1.3876      0.16852
    Quin                 25869         25464      1.0159      0.31227
    Cpi                 6957.2         20007     0.34773      0.72881
    Rate                -60201         30164     -1.9958     0.048817
    Depo                -19627        8482.7     -2.3137     0.022838
    Bull               -265.79        754.17    -0.35243       0.7253
    Sale              -0.44722       0.71444    -0.62597      0.53284
    Move               0.81287       0.96829     0.83949       0.4033
    Sub              0.0019539     0.0098312     0.19874      0.84289


Number of observations: 110, Error degrees of freedom: 95
Root Mean Squared Error: 6.22e+04
R-squared: 0.4,  Adjusted R-Squared: 0.311
F-statistic vs. constant model: 4.52, p-value = 3.58e-06

Significant_Independent_Variables = mdl.CoefficientNames(mdl.Coefficients.pValue <= 0.05)

Significant_Independent_Variables = 1x4 cell array
    {'(Intercept)'}    {'Price_m'}    {'Rate'}    {'Depo'}

However considering the F-statistic, the regression itself is highly significant.

These are your data. I defer to you to interprret them and the regression results. (I am not even certain what the variables are.)

.