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best fit curve using linear regression

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Pushkar K
Pushkar K 2022 年 2 月 7 日
コメント済み: Star Strider 2022 年 2 月 7 日
Hello,
Iam Pushkar and we are doing research on multiple linear regression wherein we have to train and test a model.
we are trying to predict the compressive strength of cement using 8 variables like air content, water content fly ash etc. so we have 8 x variables and we are predicting y(compressive strength). Since we are new to MATLAB could i please get help on how to go about this. for data please refer to this excel file cement data.
  2 件のコメント
Star Strider
Star Strider 2022 年 2 月 7 日
Ran in:
My impression is the this is a stepwise multiple llinear regression problem. If so, the stepwisefit function is likely appropriate. If that is not the desires approach, the fitlm function (or one of its friends) could be appropriate.
The file format is causing problems —
T1 = readtable('https://docs.google.com/spreadsheets/d/1BgA99g-YV3j5QrI7td0GCjHjuNx-sY5F/edit#gid=1476261111', 'VariableNamingRule','preserve')
Warning: Table variable names were truncated to the length namelengthmax. The original names are saved in the VariableDescriptions property.
T1 = 207×2334 table <!DOCTYPE html><html lang="en-IE"><head><script nonce="jhm3MBwl Var2 Var3 Var4 Var5 Var6 Var7 Var8 Var9 Var10 Var11 Var12 Var13 Var14 Var15 Var16 Var17 Var18 Var19 Var20 Var21 Var22 Var23 Var24 Var25 Var26 Var27 Var28 Var29 Var30 Var31 Var32 Var33 Var34 Var35 Var36 Var37 Var38 Var39 Var40 Var41 Var42 Var43 Var44 Var45 Var46 Var47 Var48 Var49 Var50 Var51 Var52 Var53 Var54 Var55 Var56 Var57 Var58 Var59 Var60 Var61 Var62 Var63 Var64 Var65 Var66 Var67 Var68 Var69 Var70 Var71 Var72 Var73 Var74 Var75 Var76 Var77 Var78 Var79 Var80 Var81 Var82 Var83 Var84 Var85 Var86 Var87 Var88 Var89 Var90 Var91 Var92 Var93 Var94 Var95 Var96 Var97 Var98 Var99 Var100 Var101 Var102 Var103 Var104 Var105 Var106 Var107 Var108 Var109 Var110 Var111 Var112 Var113 Var114 Var115 Var116 Var117 Var118 Var119 Var120 Var121 Var122 Var123 Var124 Var125 Var126 Var127 Var128 Var129 Var130 Var131 Var132 Var133 Var134 Var135 Var136 Var137 Var138 Var139 Var140 Var141 Var142 Var143 Var144 Var145 Var146 Var147 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Var1380 Var1381 Var1382 Var1383 Var1384 Var1385 Var1386 Var1387 Var1388 Var1389 Var1390 Var1391 Var1392 Var1393 Var1394 Var1395 Var1396 Var1397 Var1398 Var1399 Var1400 Var1401 Var1402 Var1403 Var1404 Var1405 Var1406 Var1407 Var1408 Var1409 Var1410 Var1411 Var1412 Var1413 Var1414 Var1415 Var1416 Var1417 Var1418 Var1419...
First10Rows = T1(1:10,1:9)
First10Rows = 10×9 table
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Please post the data as an Excel file or some other format that MATLAB can read, and upload it here rather than to some offiste location.
.
Pushkar K
Pushkar K 2022 年 2 月 7 日
Thank you very much have uploaded the file below

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Star Strider
Star Strider 2022 年 2 月 7 日
Ran in:
Here is the stepwiselm result —
T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/886775/Concrete_Data.xls', 'VariableNamingRule','preserve')
T1 = 1030×9 table
Cement (component 1)(kg in a m^3 mixture) Blast Furnace Slag (component 2)(kg in a m^3 mixture) Fly Ash (component 3)(kg in a m^3 mixture) Water (component 4)(kg in a m^3 mixture) Superplasticizer (component 5)(kg in a m^3 mixture) Coarse Aggregate (component 6)(kg in a m^3 mixture) Fine Aggregate (component 7)(kg in a m^3 mixture) Age (day) Concrete compressive strength(MPa, megapascals) _________________________________________ _____________________________________________________ __________________________________________ _________________________________________ ___________________________________________________ ____________________________________________________ _________________________________________________ _________ _______________________________________________ 540 0 0 162 2.5 1040 676 28 79.986 540 0 0 162 2.5 1055 676 28 61.887 332.5 142.5 0 228 0 932 594 270 40.27 332.5 142.5 0 228 0 932 594 365 41.053 198.6 132.4 0 192 0 978.4 825.5 360 44.296 266 114 0 228 0 932 670 90 47.03 380 95 0 228 0 932 594 365 43.698 380 95 0 228 0 932 594 28 36.448 266 114 0 228 0 932 670 28 45.854 475 0 0 228 0 932 594 28 39.29 198.6 132.4 0 192 0 978.4 825.5 90 38.074 198.6 132.4 0 192 0 978.4 825.5 28 28.022 427.5 47.5 0 228 0 932 594 270 43.013 190 190 0 228 0 932 670 90 42.327 304 76 0 228 0 932 670 28 47.814 380 0 0 228 0 932 670 90 52.908
y = T1{:,9}
y = 1030×1
79.9861 61.8874 40.2695 41.0528 44.2961 47.0298 43.6983 36.4478 45.8543 39.2898
x = T1{:,1:8}
x = 1030×8
1.0e+03 * 0.5400 0 0 0.1620 0.0025 1.0400 0.6760 0.0280 0.5400 0 0 0.1620 0.0025 1.0550 0.6760 0.0280 0.3325 0.1425 0 0.2280 0 0.9320 0.5940 0.2700 0.3325 0.1425 0 0.2280 0 0.9320 0.5940 0.3650 0.1986 0.1324 0 0.1920 0 0.9784 0.8255 0.3600 0.2660 0.1140 0 0.2280 0 0.9320 0.6700 0.0900 0.3800 0.0950 0 0.2280 0 0.9320 0.5940 0.3650 0.3800 0.0950 0 0.2280 0 0.9320 0.5940 0.0280 0.2660 0.1140 0 0.2280 0 0.9320 0.6700 0.0280 0.4750 0 0 0.2280 0 0.9320 0.5940 0.0280
VN = T1.Properties.VariableNames.';
cncrt_mdl = stepwiselm(x,y)
1. Adding x1, FStat = 338.7258, pValue = 1.323458e-65 2. Adding x5, FStat = 163.3824, pValue = 7.963229e-35 3. Adding x8, FStat = 258.4548, pValue = 4.882055e-52 4. Adding x5:x8, FStat = 180.2023, pValue = 5.747721e-38 5. Adding x2, FStat = 203.2321, pValue = 3.374039e-42 6. Adding x3, FStat = 76.0242, pValue = 1.11577e-17 7. Adding x4, FStat = 86.703, pValue = 7.48955e-20 8. Adding x3:x8, FStat = 34.8585, pValue = 4.82205e-09 9. Adding x4:x5, FStat = 31.0144, pValue = 3.27509e-08 10. Adding x2:x8, FStat = 21.0914, pValue = 4.92592e-06 11. Adding x2:x5, FStat = 7.0121, pValue = 0.0082212 12. Adding x4:x8, FStat = 6.1869, pValue = 0.01303 13. Adding x3:x4, FStat = 7.7585, pValue = 0.0054453 14. Adding x3:x5, FStat = 9.9796, pValue = 0.0016297 15. Adding x1:x5, FStat = 7.5392, pValue = 0.0061438 16. Adding x1:x4, FStat = 16.7626, pValue = 4.57345e-05 17. Adding x1:x3, FStat = 10.4966, pValue = 0.00123489 18. Adding x2:x4, FStat = 5.746, pValue = 0.016707 19. Adding x2:x3, FStat = 7.2807, pValue = 0.0070861 20. Adding x1:x2, FStat = 10.6893, pValue = 0.00111396
cncrt_mdl =
Linear regression model: y ~ 1 + x1*x2 + x1*x3 + x1*x4 + x1*x5 + x2*x3 + x2*x4 + x2*x5 + x2*x8 + x3*x4 + x3*x5 + x3*x8 + x4*x5 + x4*x8 + x5*x8 Estimated Coefficients: Estimate SE tStat pValue __________ __________ _______ __________ (Intercept) -113.4 23.132 -4.9023 1.1034e-06 x1 0.39862 0.050343 7.918 6.3387e-15 x2 0.22442 0.062939 3.5657 0.00037987 x3 0.50871 0.085183 5.9719 3.2452e-09 x4 0.53697 0.12077 4.4461 9.7126e-06 x5 1.0107 0.72773 1.3888 0.1652 x8 0.28998 0.057073 5.0809 4.4742e-07 x1:x2 0.00015467 4.7307e-05 3.2695 0.001114 x1:x3 0.00027127 5.8655e-05 4.6248 4.2369e-06 x1:x4 -0.0015362 0.00026385 -5.8222 7.799e-09 x1:x5 -0.0059251 0.0008539 -6.9389 7.0586e-12 x2:x3 0.00035172 8.9039e-05 3.9502 8.3525e-05 x2:x4 -0.0010407 0.00032586 -3.1938 0.0014475 x2:x5 -0.0031075 0.0011175 -2.7809 0.0055222 x2:x8 0.00031091 6.1597e-05 5.0475 5.3084e-07 x3:x4 -0.0028204 0.00044124 -6.392 2.4983e-10 x3:x5 -0.011149 0.0015849 -7.0343 3.6914e-12 x3:x8 0.00095965 0.00015647 6.1333 1.2341e-09 x4:x5 0.0096603 0.0031508 3.066 0.0022273 x4:x8 -0.0010991 0.00028058 -3.9171 9.5641e-05 x5:x8 0.010731 0.0017283 6.209 7.778e-10 Number of observations: 1030, Error degrees of freedom: 1009 Root Mean Squared Error: 8.7 R-squared: 0.734, Adjusted R-Squared: 0.729 F-statistic vs. constant model: 139, p-value = 1.88e-273
[tStatv,sidx] = sort(abs(cncrt_mdl.Coefficients.tStat),'descend');
RankedCoefficients = table(cncrt_mdl.CoefficientNames(sidx)',tStatv)
RankedCoefficients = 21×2 table
Var1 tStatv _______________ ______ {'x1' } 7.918 {'x3:x5' } 7.0343 {'x1:x5' } 6.9389 {'x3:x4' } 6.392 {'x5:x8' } 6.209 {'x3:x8' } 6.1333 {'x3' } 5.9719 {'x1:x4' } 5.8222 {'x8' } 5.0809 {'x2:x8' } 5.0475 {'(Intercept)'} 4.9023 {'x1:x3' } 4.6248 {'x4' } 4.4461 {'x2:x3' } 3.9502 {'x4:x8' } 3.9171 {'x2' } 3.5657
The ‘RankedCoefficients’ table has the coefficient names (as provided to or created by stepwiselm) sorted in order by descending values of the absolute values of the t-statistic (higher values are bettter predictors). See the documentation section on Wilkinson Notation to understand how to interpret these results.
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  2 件のコメント
Pushkar K
Pushkar K 2022 年 2 月 7 日
Thank you very much
Star Strider
Star Strider 2022 年 2 月 7 日
As always, my pleasure!

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