# After the linear regression on the main predictors, how to include the interactions of them?

I'm currently using R to do a multiple linear regression with 7 main predictors. I've already completed the first step of regressing the dependent variable onto those main predictors.

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  -17.218435   4.644294  -3.707  0.00024 ***
cylinders     -0.493376   0.323282  -1.526  0.12780
displacement   0.019896   0.007515   2.647  0.00844 **
horsepower    -0.016951   0.013787  -1.230  0.21963
weight        -0.006474   0.000652  -9.929  < 2e-16 ***
acceleration   0.080576   0.098845   0.815  0.41548
year           0.750773   0.050973  14.729  < 2e-16 ***
origin         1.426141   0.278136   5.127 4.67e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


The result shows that 3 of them have their p-value higher than 0.1, which means that they are not significantly important to dependent variable. However, when came to consider the interaction terms, should I neglect those insignificant ones, or still keep them for regression?

If includes, the result will be as follows:

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)                3.548e+01  5.314e+01   0.668  0.50475
cylinders                  6.989e+00  8.248e+00   0.847  0.39738
displacement              -4.785e-01  1.894e-01  -2.527  0.01192 *
horsepower                 5.034e-01  3.470e-01   1.451  0.14769
weight                     4.133e-03  1.759e-02   0.235  0.81442
acceleration              -5.859e+00  2.174e+00  -2.696  0.00735 **
year                       6.974e-01  6.097e-01   1.144  0.25340
origin                    -2.090e+01  7.097e+00  -2.944  0.00345 **
cylinders:displacement    -3.383e-03  6.455e-03  -0.524  0.60051
cylinders:horsepower       1.161e-02  2.420e-02   0.480  0.63157
cylinders:weight           3.575e-04  8.955e-04   0.399  0.69000
cylinders:acceleration     2.779e-01  1.664e-01   1.670  0.09584 .
cylinders:year            -1.741e-01  9.714e-02  -1.793  0.07389 .
cylinders:origin           4.022e-01  4.926e-01   0.816  0.41482
displacement:horsepower   -8.491e-05  2.885e-04  -0.294  0.76867
displacement:weight        2.472e-05  1.470e-05   1.682  0.09342 .
displacement:acceleration -3.479e-03  3.342e-03  -1.041  0.29853
displacement:year          5.934e-03  2.391e-03   2.482  0.01352 *
displacement:origin        2.398e-02  1.947e-02   1.232  0.21875
horsepower:weight         -1.968e-05  2.924e-05  -0.673  0.50124
horsepower:acceleration   -7.213e-03  3.719e-03  -1.939  0.05325 .
horsepower:year           -5.838e-03  3.938e-03  -1.482  0.13916
horsepower:origin          2.233e-03  2.930e-02   0.076  0.93931
weight:acceleration        2.346e-04  2.289e-04   1.025  0.30596
weight:year               -2.245e-04  2.127e-04  -1.056  0.29182
weight:origin             -5.789e-04  1.591e-03  -0.364  0.71623
acceleration:year          5.562e-02  2.558e-02   2.174  0.03033 *
acceleration:origin        4.583e-01  1.567e-01   2.926  0.00365 **
year:origin                1.393e-01  7.399e-02   1.882  0.06062 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


The term acceleration is previously insignificant but now turns to be significant instead, does it mean that it is influenced by the interaction terms so that it conceals its contribution to the dependent variable?