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I am working with mtcars dataset and using linear regression

data(mtcars)
fit <- lm(mpg ~.,mtcars)    
summary(fit)

When I fit the model with lm it shows the result like this

Call:
lm(formula = mpg ~ ., data = mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.5087 -1.3584 -0.0948  0.7745  4.6251 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept) 23.87913   20.06582   1.190   0.2525  
cyl6        -2.64870    3.04089  -0.871   0.3975  
cyl8        -0.33616    7.15954  -0.047   0.9632  
disp         0.03555    0.03190   1.114   0.2827  
hp          -0.07051    0.03943  -1.788   0.0939 .
drat         1.18283    2.48348   0.476   0.6407  
wt          -4.52978    2.53875  -1.784   0.0946 .
qsec         0.36784    0.93540   0.393   0.6997  
vs1          1.93085    2.87126   0.672   0.5115  
amManual     1.21212    3.21355   0.377   0.7113  
gear4        1.11435    3.79952   0.293   0.7733  
gear5        2.52840    3.73636   0.677   0.5089  
carb2       -0.97935    2.31797  -0.423   0.6787  
carb3        2.99964    4.29355   0.699   0.4955  
carb4        1.09142    4.44962   0.245   0.8096  
carb6        4.47757    6.38406   0.701   0.4938  
carb8        7.25041    8.36057   0.867   0.3995  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.833 on 15 degrees of freedom
Multiple R-squared:  0.8931,    Adjusted R-squared:  0.779 
F-statistic:  7.83 on 16 and 15 DF,  p-value: 0.000124

I found that none of variables are marked as significant at 0.05 significant level.

How to make variables significant at 0.05 significant level?

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  • 2
    $\begingroup$ It can be as hard to force variables to be significant as it is to force students to be smart. But in this case, your problem seems an inevitable result of throwing too many predictors into the model for what is really rather a small dataset. Further, it's often pointed out in discussions of mpg as a response that there's no mechanical or engineering reason to prefer that scale for the a response, at least so long as everything is kept linear. Gallons per mile might be expected to scale with weight, i.e. work with the reciprocal. $\endgroup$ – Nick Cox Nov 12 '15 at 9:13
  • $\begingroup$ In short: use fewer predictors and justify their inclusion; take the possibility of nonlinearity as seriously as it deserves. (In general, it is best not to assume that everyone uses R or is familiar with its provided datasets, as they aren't.) $\endgroup$ – Nick Cox Nov 12 '15 at 9:14

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