Multivariable Linear Regression — reg

Fits an OLS model via lm(), optionally performing stepwise selection using Akaike's information criterion.

Usage

reg_lm(
  formula,
  data,
  step = FALSE,
  direction = c("both", "forward", "backward"),
  ...
)

Arguments

formula: A formula, e.g. y ~ x1 + x2.
data: A data frame containing the variables in formula.
step: Logical. Whether to perform stepwise selection (TRUE/FALSE). Default is FALSE.
direction: Character: "both" (default), "forward", or "backward".
...: Additional arguments passed to lm() and step().

Value

A named list:

model: Fitted lm object.
coefficient: Tibble of coefficients, standard errors, t-values, p-values, 95% CIs.
model_info: Tibble of fit statistics (r.squared, adj.r.squared, AIC, BIC).
residuals: Tibble of observed, fitted, residuals.
diagnostics: Tibble of key fit metrics (Breusch-Pagan, Durbin-Watson).
formula: Original formula.
input: The original data frame.

Details

When step = TRUE, the function first fits a null model (response only), then uses step() to search for the best combination of terms by AIC.

Examples

set.seed(42)
x1 = rnorm(100); x2 = rnorm(100)
y = 1 + 2*x1 - 3*x2 + rnorm(100, sd = 2)
reg_lm(y ~ x1 + x2, data = data.frame(y, x1, x2))
#> $model
#> 
#> Call:
#> lm(formula = formula, data = data)
#> 
#> Coefficients:
#> (Intercept)           x1           x2  
#>       1.004        1.713       -2.829  
#> 
#> 
#> $coefficient
#> # A tibble: 3 × 7
#>   term        estimate std.error statistic  p.value conf.low conf.high
#>   <chr>          <dbl>     <dbl>     <dbl>    <dbl>    <dbl>     <dbl>
#> 1 (Intercept)     1.00     0.204      4.92 3.48e- 6    0.599      1.41
#> 2 x1              1.71     0.196      8.75 6.72e-14    1.32       2.10
#> 3 x2             -2.83     0.225    -12.5  4.91e-22   -3.28      -2.38
#> 
#> $model_info
#> # A tibble: 1 × 4
#>   r.squared adj.r.squared   aic   bic
#>       <dbl>         <dbl> <dbl> <dbl>
#> 1     0.701         0.695  430.  440.
#> 
#> $residuals
#> # A tibble: 100 × 3
#>    .observed .fitted .residual
#>        <dbl>   <dbl>     <dbl>
#>  1    -3.86  -0.0466    -3.82 
#>  2    -2.60  -2.92       0.323
#>  3     7.08   4.46       2.61 
#>  4     0.839 -3.14       3.98 
#>  5     1.06   3.58      -2.53 
#>  6    -1.83   0.523     -2.35 
#>  7     3.88   4.79      -0.909
#>  8    -0.930  1.19      -2.12 
#>  9     3.18   3.93      -0.747
#> 10     0.146  0.559     -0.413
#> # ℹ 90 more rows
#> 
#> $diagnostics
#> # A tibble: 2 × 2
#>   metric          value
#>   <chr>           <dbl>
#> 1 BP_test_pvalue 0.0139
#> 2 DW_test_pvalue 0.563 
#> 
#> $formula
#> y ~ x1 + x2
#> <environment: 0x00000224a501a698>
#> 
#> $input
#>               y          x1            x2
#> 1   -3.86283771  1.37095845  1.200965e+00
#> 2   -2.59609521 -0.56469817  1.044751e+00
#> 3    7.07853302  0.36312841 -1.003209e+00
#> 4    0.83935799  0.63286260  1.848482e+00
#> 5    1.05513368  0.40426832 -6.667734e-01
#> 6   -1.83050160 -0.10612452  1.055138e-01
#> 7    3.87816885  1.51152200 -4.222559e-01
#> 8   -0.93037913 -0.09465904 -1.223502e-01
#> 9    3.18078088  2.01842371  1.881930e-01
#> 10   0.14633299 -0.06271410  1.191610e-01
#> 11   1.28257286  1.30486965 -2.509255e-02
#> 12   9.32301694  2.28664539  1.080727e-01
#> 13  -0.10586620 -1.38886070 -4.854352e-01
#> 14   1.78685766 -0.27878877 -5.042171e-01
#> 15   6.70789385 -0.13332134 -1.661099e+00
#> 16   3.49373235  0.63595040 -3.823337e-01
#> 17   1.70526886 -0.28425292 -5.126503e-01
#> 18  -9.46500900 -2.65645542  2.701891e+00
#> 19  -0.22864558 -2.44046693 -1.362116e+00
#> 20   0.66125363  1.32011335  1.372562e-01
#> 21   5.63893379 -0.30663859 -1.493625e+00
#> 22   1.14566461 -1.78130843 -1.470436e+00
#> 23  -0.76153406 -0.17191736  1.247024e-01
#> 24   4.28300440  1.21467470 -9.966391e-01
#> 25   5.65258657  1.89519346 -1.822614e-03
#> 26   1.07580191 -0.43046913 -4.282589e-01
#> 27   3.35781151 -0.25726938 -6.136716e-01
#> 28   3.07897681 -1.76316309 -2.024678e+00
#> 29   4.27743171  0.46009735 -1.224748e+00
#> 30   1.68193413 -0.63999488  1.795164e-01
#> 31  -0.33548897  0.45545012  5.676206e-01
#> 32   5.78421073  0.70483734 -4.928774e-01
#> 33   0.66685353  1.03510352  6.288407e-05
#> 34  -4.51875387 -0.60892638  1.122890e+00
#> 35  -2.84835977  0.50495512  1.439856e+00
#> 36   0.07539313 -1.71700868 -1.097114e+00
#> 37   2.48045469 -0.78445901 -1.173196e-01
#> 38  -4.35183979 -0.85090759  1.201498e+00
#> 39  -1.93077486 -2.41420765 -4.697296e-01
#> 40  -0.65508975  0.03612261 -5.246948e-02
#> 41   0.21188454  0.20599860 -8.610730e-02
#> 42   4.93706027 -0.36105730 -8.876790e-01
#> 43   6.36734182  0.75816324 -4.446840e-01
#> 44   2.13265236 -0.72670483 -2.944488e-02
#> 45  -3.25622964 -1.36828104 -4.138688e-01
#> 46   2.62539937  0.43281803  1.113386e+00
#> 47   2.85393783 -0.81139318 -4.809928e-01
#> 48   5.13427469  1.44410126 -4.331690e-01
#> 49  -0.54626458 -0.43144620  6.968626e-01
#> 50   3.53763055  0.65564788 -1.056368e+00
#> 51  -0.42636653  0.32192527 -4.069848e-02
#> 52   4.18505749 -0.78383894 -1.551545e+00
#> 53  -1.74704532  1.57572752  1.167170e+00
#> 54   3.48677371  0.64289931 -2.736457e-01
#> 55   5.17846907  0.08976065 -4.678453e-01
#> 56   3.20011103  0.27655075 -1.238252e+00
#> 57   0.90498223  0.67928882 -7.762034e-03
#> 58   3.67364019  0.08983289 -8.002822e-01
#> 59  -5.42089542 -2.99309008 -5.334923e-01
#> 60  -3.05982775  0.28488295  1.287675e+00
#> 61   2.53761915 -0.36723464 -1.755259e-01
#> 62   6.52489831  0.18523056 -1.071782e+00
#> 63   2.44172014  0.58182373  1.632069e-01
#> 64   1.18457758  1.39973683 -3.627384e-01
#> 65  -2.33261824 -0.72729206  5.900135e-01
#> 66   1.43736591  1.30254263  1.432422e+00
#> 67   6.27616385  0.33584812 -9.926925e-01
#> 68   1.33142836  1.03850610  4.546503e-01
#> 69  -2.81309666  0.92072857  8.489806e-02
#> 70  -0.12300714  0.72087816  8.955656e-01
#> 71   0.75059993 -1.04311894 -2.297781e-01
#> 72  -1.59862282 -0.09018639  8.366191e-01
#> 73   7.79702899  0.62351816 -1.745056e+00
#> 74  -5.11229273 -0.95352336  1.689459e+00
#> 75  -3.47309104 -0.54282881  8.647780e-01
#> 76   5.23427741  0.58099650 -1.507760e-01
#> 77   7.82416567  0.76817874 -1.449007e+00
#> 78  -2.48683146  0.46376759  6.430087e-01
#> 79   0.54201673 -0.88577630  4.831939e-01
#> 80   1.22842296 -1.09978090 -6.355626e-03
#> 81   5.21919427  1.51270701  1.514559e-01
#> 82  -0.05708902  0.25792144 -5.841090e-01
#> 83  -1.06815243  0.08844023  3.688067e-01
#> 84   1.14527154 -0.12089654  2.946543e-01
#> 85  -0.46343566 -1.19432890 -2.792594e-01
#> 86   6.92872837  0.61199690 -1.336237e+00
#> 87   3.38266095 -0.21713985  7.007488e-01
#> 88  -2.66486393 -0.18275671  5.541966e-01
#> 89   1.14921221  0.93334633 -8.363066e-01
#> 90   7.97470125  0.82177311 -1.594588e+00
#> 91   1.79416333  1.39211638  2.049586e-01
#> 92   1.97499819 -0.47617392 -3.450880e-01
#> 93  -0.08190744  0.65034856  2.526117e-01
#> 94  12.08833927  1.39111046 -1.294002e+00
#> 95   1.40852163 -1.11078888 -9.591704e-01
#> 96  -4.93358075 -0.86079259  1.085775e+00
#> 97  -2.80732506 -1.13173868  4.037749e-01
#> 98  -1.95276384 -1.45921400  5.864875e-01
#> 99  -4.09103926  0.07998255  1.815228e+00
#> 100 -1.33128908  0.65320434  1.288214e-01
#>