# Linear regresson lm or stepwise regression here using R?

It is a basic question but I could not find clear answer on my reading. I am trying to find independent predictors of Infant.Mortality in data frame 'swiss' in R.

> head(swiss)
Fertility Agriculture Examination Education Catholic Infant.Mortality
Courtelary        80.2        17.0          15        12     9.96             22.2
Delemont          83.1        45.1           6         9    84.84             22.2
Franches-Mnt      92.5        39.7           5         5    93.40             20.2
Moutier           85.8        36.5          12         7    33.77             20.3
Neuveville        76.9        43.5          17        15     5.16             20.6
Porrentruy        76.1        35.3           9         7    90.57             26.6


Following are the results using lm and I find only Fertility to be a significant predictor:

> fit = lm(Infant.Mortality~., data=swiss)
> summary(fit)

Call:
lm(formula = Infant.Mortality ~ ., data = swiss)

Residuals:
Min      1Q  Median      3Q     Max
-8.2512 -1.2860  0.1821  1.6914  6.0937

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  8.667e+00  5.435e+00   1.595  0.11850
Fertility    1.510e-01  5.351e-02   2.822  0.00734    #  <<<< NOTE P VALUE HERE
Agriculture -1.175e-02  2.812e-02  -0.418  0.67827
Examination  3.695e-02  9.607e-02   0.385  0.70250
Education    6.099e-02  8.484e-02   0.719  0.47631
Catholic     6.711e-05  1.454e-02   0.005  0.99634

Residual standard error: 2.683 on 41 degrees of freedom
Multiple R-squared:  0.2439,    Adjusted R-squared:  0.1517
F-statistic: 2.645 on 5 and 41 DF,  p-value: 0.03665


Following are the graphs:

plot(fit)


On performing stepwise regression, following are the results:

> step <- stepAIC(fit, direction="both");
Start:  AIC=98.34
Infant.Mortality ~ Fertility + Agriculture + Examination + Education +
Catholic

Df Sum of Sq    RSS     AIC
- Catholic     1     0.000 295.07  96.341
- Examination  1     1.065 296.13  96.511
- Agriculture  1     1.256 296.32  96.541
- Education    1     3.719 298.79  96.930
<none>                     295.07  98.341
- Fertility    1    57.295 352.36 104.682

Step:  AIC=96.34
Infant.Mortality ~ Fertility + Agriculture + Examination + Education

Df Sum of Sq    RSS     AIC
- Examination  1     1.320 296.39  94.551
- Agriculture  1     1.395 296.46  94.563
- Education    1     5.774 300.84  95.252
<none>                     295.07  96.341
+ Catholic     1     0.000 295.07  98.341
- Fertility    1    72.609 367.68 104.681

Step:  AIC=94.55
Infant.Mortality ~ Fertility + Agriculture + Education

Df Sum of Sq    RSS     AIC
- Agriculture  1     4.250 300.64  93.220
- Education    1     6.875 303.26  93.629
<none>                     296.39  94.551
+ Examination  1     1.320 295.07  96.341
+ Catholic     1     0.255 296.13  96.511
- Fertility    1    79.804 376.19 103.758

Step:  AIC=93.22
Infant.Mortality ~ Fertility + Education

Df Sum of Sq    RSS     AIC
<none>                     300.64  93.220
- Education    1    21.902 322.54  94.525
+ Agriculture  1     4.250 296.39  94.551
+ Examination  1     4.175 296.46  94.563
+ Catholic     1     2.318 298.32  94.857
- Fertility    1    85.769 386.41 103.017
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