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I am having a problem with interpreting the summary output I need to FIT a Linear Regression Model to explain the "Actual Sales Price" (V104) in terms of the of the other variables excluding the variable "Actual Construction Costs" (V105).

But the lm() gives so many coeffeients, I am confused which to select and which not to.

Total Predictors = 103 (all quantitative)
Response Variable = Actual Cost Price (V104) 

My code:

 library(ISLR)
 library(MASS)
 library(readxl)
 library(tidyverse)
 library(caret)
 library(leaps)
 mydata = read_excel("Residential-Data-Set.xlsx", skip = 1)

 Model1 = lm(V104 ~ ., data=mydata)
summary(Model1)

Call:
lm(formula = V104 ~ ., data = mydata)

Residuals:
Min      1Q  Median      3Q     Max 
-940.48  -43.26   -3.03   43.58  651.13 

Coefficients: (29 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.087e+04  1.428e+04  -0.761 0.447352    
 V1          -5.067e+00  2.246e+00  -2.256 0.024823 *  
 V2           6.358e-02  2.217e-02   2.868 0.004425 ** 
 V3          -2.224e-01  6.509e-02  -3.417 0.000722 ***
 V4           1.012e-02  3.606e-02   0.281 0.779061    
 V5          -6.638e-01  3.378e-01  -1.965 0.050302 .  
 V6           9.169e-02  6.389e-02   1.435 0.152294    
 V7           3.851e+01  4.264e+00   9.031  < 2e-16 ***
 V8           1.199e+00  1.692e-02  70.863  < 2e-16 ***
 V9           4.548e-01  5.809e-01   0.783 0.434330    
V10         -2.459e+01  1.795e+02  -0.137 0.891137    
V11         -6.278e+01  1.191e+02  -0.527 0.598579    
V12         -9.492e+01  1.373e+02  -0.691 0.489892    
V13          1.266e-02  3.081e-02   0.411 0.681479    
V14          1.283e-01  3.066e-01   0.418 0.676001    
V15          8.906e+00  6.603e+01   0.135 0.892805    
V16          4.075e-01  2.887e+00   0.141 0.887844    
V17         -2.051e-02  9.346e-02  -0.219 0.826446    
V18          3.574e+02  4.549e+02   0.786 0.432725    
V19         -1.295e+00  1.929e+00  -0.671 0.502687    
V20         -3.948e-01  9.179e-01  -0.430 0.667447    
V21          1.086e-01  1.255e-01   0.865 0.387715    
V22          1.422e-01  4.311e-01   0.330 0.741651    
V23         -1.495e+02  2.440e+02  -0.613 0.540618    
V24         -2.304e+01  1.267e+02  -0.182 0.855839    
V25         -1.269e-01  2.063e-01  -0.615 0.539107    
V26          5.320e-02  7.094e-02   0.750 0.453872    
V27         -2.200e-03  4.069e-03  -0.541 0.589181    
V28         -7.146e-02  1.666e-01  -0.429 0.668369    
V29          8.585e+01  2.568e+02   0.334 0.738395   
V29          8.585e+01  2.568e+02   0.334 0.738395    
V30         -9.308e+01  1.767e+02  -0.527 0.598835    
V31          3.006e+02  5.082e+02   0.591 0.554664    
V32         -3.437e-02  5.320e-02  -0.646 0.518675    
V33         -3.673e-01  4.615e-01  -0.796 0.426789    
V34          7.885e+01  1.276e+02   0.618 0.536969    
V35          5.092e-01  4.057e+00   0.126 0.900196    
V36          5.501e-02  1.167e-01   0.471 0.637640    
V37         -6.174e+01  2.372e+02  -0.260 0.794784    
V38         -1.688e+00  3.137e+00  -0.538 0.590865    
V39          8.868e-01  2.218e+00   0.400 0.689591    
V40          2.398e-01  3.902e-01   0.615 0.539305    
V41         -1.930e-01  2.511e-01  -0.768 0.442817    
V42          1.611e+01  8.484e+01   0.190 0.849513    
V43         -3.841e+02  5.641e+02  -0.681 0.496427    
V44         -5.614e-02  1.884e-01  -0.298 0.765970    
V45          2.901e-02  4.102e-02   0.707 0.480051    
V46          4.318e-03  6.865e-03   0.629 0.529875    
V47          1.544e-02  2.124e-01   0.073 0.942105    
V48          3.600e+02  5.459e+02   0.659 0.510121    
V49          6.157e+01  8.911e+01   0.691 0.490171    
V50         -2.329e+02  3.977e+02  -0.586 0.558539    
V51         -3.120e-03  2.925e-02  -0.107 0.915148    
V52         -5.434e-01  7.644e-01  -0.711 0.477765    
V53         -2.20e+01  5.311e+01  -0.418 0.676297    
V54          7.525e+00  9.711e+00   0.775 0.439029    
V55         -4.800e-02  7.478e-02  -0.642 0.521483    
V56          1.148e+02  2.755e+02   0.417 0.677215    
V57         -1.268e+00  2.554e+00  -0.496 0.619959    
V58          8.348e-01  2.974e+00   0.281 0.779138    
V59          2.366e-01  3.286e-01   0.720 0.472143    
V60         -1.270e-01  3.762e-01  -0.338 0.735832    
V61         -6.149e+01  1.659e+02  -0.371 0.711220    
V62          5.443e+02  7.057e+02   0.771 0.441115    
V63         -1.100e-01  4.250e-01  -0.259 0.796013    
V64          2.504e-02  4.549e-02   0.550 0.582420    
V65          1.728e-05  3.926e-03   0.004 0.996492    
V66          1.874e-01  4.333e-01   0.433 0.665632    
V67         -1.450e+02  1.818e+02  -0.797 0.425832    
V68         -2.799e+01  8.874e+01  -0.315 0.752693    
V69          3.884e+02  4.310e+02   0.901 0.368246    
V70          1.822e-02  3.518e-02   0.518 0.604996    
V71         -3.242e-01  3.765e-01  -0.861 0.389853    
V72         -6.484e+01  6.286e+01  -1.031 0.303193    
V73          1.032e+01  1.211e+01   0.852 0.395033    
V74         -5.530e-02  1.428e-01  -0.387 0.698941    
V75                 NA         NA      NA       NA    
V76                 NA         NA      NA       NA    
V77                 NA         NA      NA       NA    
V78                 NA         NA      NA       NA    
V79                 NA         NA      NA       NA    
V80                 NA         NA      NA       NA   
V81                 NA         NA      NA       NA    
..                   ....       ..      ..      ..

V100                NA         NA      NA       NA    
V101                NA         NA      NA       NA    
V102                NA         NA      NA       NA    
V103                NA         NA      NA       NA  

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 150.2 on 297 degrees of freedom
Multiple R-squared:  0.9876,    Adjusted R-squared:  0.9845 
F-statistic: 319.2 on 74 and 297 DF,  p-value: < 2.2e-16

Could someone please help me understand what to make of this. and interpreting the output of the summary function please? ** In a subquent task, I have been asked to fit a model for the data using backward selection and stepwise selection. So, when we simply say "Fit a linear model", does it refer to forward regression?

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  • $\begingroup$ It seems an homework. Have you tested the linear model hypotesis before to apply a lm()? If so, are validated? $\endgroup$ – s__ May 29 '18 at 6:39
  • $\begingroup$ @nhi, Yes, I have tested the model hypothesis before applying lm(). And this is a drill question meant to help beginners like myself. $\endgroup$ – Pamela May 29 '18 at 6:50
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The last column gives the p values of each independent variables. If p value is less than 0.05 (It rejects the null hypotheses), it means that particular variable has significant impact to the dependent variables(i.e. sales price).

You can see that * are marked where p value is less than 0.05.

So you can select the variables where p value is less than 0.05 and build the model.

It is neither the backward nor step wise selection (It gives better idea what variables to select). It's just the summary when you include all the variables.

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  • $\begingroup$ So,I simply consider the values with significant p values, and discard the others. Correct? Also, could you please help me understand what the summary function of output is conveying? And the "NA" values mean multi-collinearity? Should that be addressed before trying other regression methods please? $\endgroup$ – Pamela May 29 '18 at 6:58

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