# Interpreting the summary function in Linear regression (Using R)

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(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?

• It seems an homework. Have you tested the linear model hypotesis before to apply a lm()? If so, are validated?
– s__
Commented May 29, 2018 at 6:39
• @nhi, Yes, I have tested the model hypothesis before applying lm(). And this is a drill question meant to help beginners like myself. Commented May 29, 2018 at 6:50