For common data, let's motivate the problem with mtcars
, a built-in data set that we can make structurally similar to your situation.
Using the transformation shown in the help page and adding cohort
, which like your Cohort
,categorizes records, this time month of manufacture, we can do a stepwise selection, successively leaving out variables that do not improve the p-value of the F Statistic
from the fully saturated model. In this example, cohort
is eliminated on that basis. That shouldn't be surprising, given that it is randomly assigned. Your Cohort
, the month of whichever year the customer first joined may not be. But I'd still recommend going through the process, rather than assuming that Cohort
is necessarily useful. An alternative is to run separate models on each Cohort
group.
mtcars2 <- within(mtcars, {
vs <- factor(vs, labels = c("V", "S"))
am <- factor(am, labels = c("automatic", "manual"))
cyl <- ordered(cyl)
gear <- ordered(gear)
carb <- ordered(carb)
})
set.seed(137)
month_mfg <- factor(c("JAN", "FEB", "MAR", "APR", "MAY", "JUN", "JUL", "AUG", "SEP", "OCT", "NOV", "DEC"))
cohort <- sample(month_mfg, 32, replace = TRUE)
mtcars2 <- cbind(mtcars2, cohort)
saturated_fit <- lm(mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear + carb + cohort, data = mtcars2)
summary(saturated_fit)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + drat + wt + qsec + vs +
#> am + gear + carb + cohort, data = mtcars2)
#>
#> Residuals:
#> Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
#> -1.203e-02 8.630e-17 1.874e-16 -1.202e+00
#> Hornet Sportabout Valiant Duster 360 Merc 240D
#> -5.161e-01 -3.447e-01 -7.302e-01 -1.532e+00
#> Merc 230 Merc 280 Merc 280C Merc 450SE
#> -2.658e-02 4.868e-16 1.559e+00 -3.487e-01
#> Merc 450SL Merc 450SLC Cadillac Fleetwood Lincoln Continental
#> 1.087e+00 -7.382e-01 -5.918e-01 -7.411e-01
#> Chrysler Imperial Fiat 128 Honda Civic Toyota Corolla
#> 1.547e+00 2.520e+00 -5.918e-01 1.116e+00
#> Toyota Corona Dodge Challenger AMC Javelin Camaro Z28
#> -8.266e-16 -3.839e-01 -1.559e+00 5.161e-01
#> Pontiac Firebird Fiat X1-9 Porsche 914-2 Lotus Europa
#> 4.006e+00 -2.090e+00 1.203e-02 1.535e+00
#> Ford Pantera L Ferrari Dino Maserati Bora Volvo 142E
#> -1.547e+00 -6.061e-16 1.435e-16 -9.431e-01
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 92.05920 48.59510 1.894 0.131
#> cyl.L -9.53505 12.39861 -0.769 0.485
#> cyl.Q 3.08191 3.44601 0.894 0.422
#> disp 0.06208 0.06064 1.024 0.364
#> hp -0.08646 0.06715 -1.288 0.267
#> drat -3.36513 6.27561 -0.536 0.620
#> wt -6.95625 4.65615 -1.494 0.209
#> qsec -1.56006 2.17737 -0.716 0.513
#> vsS 1.13629 5.53658 0.205 0.847
#> ammanual -3.73157 9.96853 -0.374 0.727
#> gear.L 0.02536 5.85367 0.004 0.997
#> gear.Q -3.39014 5.35238 -0.633 0.561
#> carb.L 12.74030 11.03873 1.154 0.313
#> carb.Q 6.97853 8.00820 0.871 0.433
#> carb.C 2.71334 5.14883 0.527 0.626
#> carb^4 2.41526 5.16384 0.468 0.664
#> carb^5 -4.44901 5.18699 -0.858 0.439
#> cohortAUG -13.88802 7.33987 -1.892 0.131
#> cohortDEC -4.15082 4.92709 -0.842 0.447
#> cohortFEB -4.10415 7.77175 -0.528 0.625
#> cohortJAN -6.14826 7.23151 -0.850 0.443
#> cohortJUL -5.40789 6.40341 -0.845 0.446
#> cohortJUN -6.04268 5.66448 -1.067 0.346
#> cohortMAR -9.28431 6.57149 -1.413 0.231
#> cohortMAY -7.10596 6.33567 -1.122 0.325
#> cohortNOV -6.73959 6.19751 -1.087 0.338
#> cohortOCT -4.12539 8.46815 -0.487 0.652
#> cohortSEP -12.46692 9.61299 -1.297 0.264
#>
#> Residual standard error: 3.504 on 4 degrees of freedom
#> Multiple R-squared: 0.9564, Adjusted R-squared: 0.6619
#> F-statistic: 3.248 on 27 and 4 DF, p-value: 0.1299
saturated_ex_cohort <- lm(mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear + carb, data = mtcars2)
summary(saturated_ex_cohort)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + drat + wt + qsec + vs +
#> am + gear + carb, data = mtcars2)
#>
#> 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) 26.57171 19.56616 1.358 0.1945
#> cyl.L -0.23770 5.06256 -0.047 0.9632
#> cyl.Q 2.02541 2.14952 0.942 0.3610
#> 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
#> vsS 1.93085 2.87126 0.672 0.5115
#> ammanual 1.21212 3.21355 0.377 0.7113
#> gear.L 1.78785 2.64200 0.677 0.5089
#> gear.Q 0.12235 2.40896 0.051 0.9602
#> carb.L 6.06156 6.72822 0.901 0.3819
#> carb.Q 1.78825 2.80043 0.639 0.5327
#> carb.C 0.42384 2.57389 0.165 0.8714
#> carb^4 0.93317 2.45041 0.381 0.7087
#> carb^5 -2.46410 2.90450 -0.848 0.4096
#> ---
#> 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
saturated_ex_carb <- lm(mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear, data = mtcars2)
summary(saturated_ex_carb)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + drat + wt + qsec + vs +
#> am + gear, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.4785 -1.3834 -0.0234 1.2211 4.2132
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 17.310552 16.249080 1.065 0.299
#> cyl.L 1.762848 3.339081 0.528 0.603
#> cyl.Q 1.632148 1.192410 1.369 0.186
#> disp 0.005862 0.015225 0.385 0.704
#> hp -0.039460 0.021394 -1.844 0.080 .
#> drat 0.824468 1.960118 0.421 0.679
#> wt -2.853681 1.660172 -1.719 0.101
#> qsec 0.643871 0.726451 0.886 0.386
#> vsS 1.698405 2.292846 0.741 0.467
#> ammanual 2.936464 2.201030 1.334 0.197
#> gear.L 1.384525 1.951508 0.709 0.486
#> gear.Q 0.717851 1.649410 0.435 0.668
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.588 on 20 degrees of freedom
#> Multiple R-squared: 0.881, Adjusted R-squared: 0.8155
#> F-statistic: 13.46 on 11 and 20 DF, p-value: 6.004e-07
saturated_ex_gear <- lm(mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am, data = mtcars2)
summary(saturated_ex_gear)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + drat + wt + qsec + vs +
#> am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.9978 -1.3551 -0.3108 1.1992 4.1102
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 19.540985 14.146419 1.381 0.1810
#> cyl.L 0.342558 2.764833 0.124 0.9025
#> cyl.Q 1.388429 1.112097 1.248 0.2250
#> disp 0.006688 0.013512 0.495 0.6255
#> hp -0.029141 0.017182 -1.696 0.1040
#> drat 0.588059 1.503111 0.391 0.6994
#> wt -3.155246 1.420235 -2.222 0.0369 *
#> qsec 0.523235 0.690130 0.758 0.4564
#> vsS 1.237800 2.106056 0.588 0.5627
#> ammanual 3.000910 1.853400 1.619 0.1197
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.514 on 22 degrees of freedom
#> Multiple R-squared: 0.8765, Adjusted R-squared: 0.826
#> F-statistic: 17.35 on 9 and 22 DF, p-value: 4.814e-08
saturated_ex_am <- lm(mpg ~ cyl + disp + hp + drat + wt + qsec + vs, data = mtcars2)
summary(saturated_ex_am)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + drat + wt + qsec + vs, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -4.0403 -1.3502 -0.3096 1.1330 5.0843
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 26.176702 14.008939 1.869 0.0745 .
#> cyl.L -1.530866 2.598096 -0.589 0.5615
#> cyl.Q 1.227223 1.146013 1.071 0.2953
#> disp 0.005948 0.013972 0.426 0.6743
#> hp -0.023866 0.017455 -1.367 0.1848
#> drat 1.144625 1.513984 0.756 0.4573
#> wt -3.545791 1.448101 -2.449 0.0224 *
#> qsec 0.171817 0.677814 0.253 0.8021
#> vsS 0.447950 2.119775 0.211 0.8345
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.601 on 23 degrees of freedom
#> Multiple R-squared: 0.8618, Adjusted R-squared: 0.8138
#> F-statistic: 17.93 on 8 and 23 DF, p-value: 3.535e-08
with_am_ex_vs <- lm(mpg ~ cyl + disp + hp + drat + wt + qsec + am, data = mtcars2)
summary(with_am_ex_vs)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + drat + wt + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.7362 -1.3973 -0.3513 1.4311 4.2267
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 16.735984 13.126182 1.275 0.2150
#> cyl.L -0.369506 2.449630 -0.151 0.8814
#> cyl.Q 1.172300 1.034497 1.133 0.2688
#> disp 0.007572 0.013236 0.572 0.5728
#> hp -0.025353 0.015699 -1.615 0.1200
#> drat 0.633293 1.479625 0.428 0.6726
#> wt -3.426768 1.323748 -2.589 0.0164 *
#> qsec 0.718097 0.596598 1.204 0.2410
#> ammanual 2.748596 1.777155 1.547 0.1356
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.478 on 23 degrees of freedom
#> Multiple R-squared: 0.8746, Adjusted R-squared: 0.831
#> F-statistic: 20.05 on 8 and 23 DF, p-value: 1.206e-08
with_am_ex_qsec <- lm(mpg ~ cyl + disp + hp + drat + wt + am, data = mtcars2)
summary(with_am_ex_qsec)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + drat + wt + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.8267 -1.4366 -0.4153 1.1649 5.0671
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 30.755744 6.108432 5.035 3.8e-05 ***
#> cyl.L -1.797442 2.163142 -0.831 0.4142
#> cyl.Q 1.433586 1.020878 1.404 0.1730
#> disp 0.004395 0.013090 0.336 0.7400
#> hp -0.033038 0.014476 -2.282 0.0316 *
#> drat 0.326616 1.471086 0.222 0.8262
#> wt -2.726729 1.200207 -2.272 0.0323 *
#> ammanual 1.681130 1.554386 1.082 0.2902
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.501 on 24 degrees of freedom
#> Multiple R-squared: 0.8667, Adjusted R-squared: 0.8278
#> F-statistic: 22.29 on 7 and 24 DF, p-value: 4.768e-09
with_qsec_ex_wt <- lm(mpg ~ cyl + disp + hp + drat + qsec + am, data = mtcars2)
summary(with_qsec_ex_wt)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + drat + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -4.8814 -1.5577 -0.3294 1.2071 5.0712
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 25.09113 14.15396 1.773 0.0890 .
#> cyl.L -0.44501 2.72491 -0.163 0.8716
#> cyl.Q 2.18396 1.06555 2.050 0.0515 .
#> disp -0.01453 0.01125 -1.292 0.2087
#> hp -0.03901 0.01645 -2.371 0.0261 *
#> drat 0.49570 1.64495 0.301 0.7657
#> qsec 0.03955 0.59620 0.066 0.9477
#> ammanual 3.22115 1.96655 1.638 0.1145
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.756 on 24 degrees of freedom
#> Multiple R-squared: 0.8381, Adjusted R-squared: 0.7908
#> F-statistic: 17.74 on 7 and 24 DF, p-value: 4.565e-08
with_wt_ex_drat <- lm(mpg ~ cyl + disp + hp + wt + qsec + am, data = mtcars2)
summary(with_wt_ex_drat)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + wt + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.9501 -1.4335 -0.1542 1.3632 4.1917
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 19.77177 10.85529 1.821 0.0810 .
#> cyl.L -0.69084 2.29172 -0.301 0.7657
#> cyl.Q 1.22117 1.01053 1.208 0.2386
#> disp 0.00680 0.01289 0.528 0.6026
#> hp -0.02477 0.01537 -1.612 0.1201
#> wt -3.40642 1.30019 -2.620 0.0150 *
#> qsec 0.67413 0.57760 1.167 0.2546
#> ammanual 2.91836 1.70260 1.714 0.0994 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.435 on 24 degrees of freedom
#> Multiple R-squared: 0.8736, Adjusted R-squared: 0.8367
#> F-statistic: 23.7 on 7 and 24 DF, p-value: 2.566e-09
with_wt_ex_hp <- lm(mpg ~ cyl + disp + wt + qsec + am, data = mtcars2)
summary(with_wt_ex_hp)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + wt + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.8692 -1.3132 -0.3668 1.4187 4.5144
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 11.55295 9.88420 1.169 0.25350
#> cyl.L -1.54479 2.29975 -0.672 0.50792
#> cyl.Q 0.76403 1.00041 0.764 0.45218
#> disp 0.00688 0.01329 0.518 0.60927
#> wt -4.11995 1.26093 -3.267 0.00315 **
#> qsec 1.07389 0.53803 1.996 0.05694 .
#> ammanual 2.54221 1.73957 1.461 0.15636
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.512 on 25 degrees of freedom
#> Multiple R-squared: 0.8599, Adjusted R-squared: 0.8263
#> F-statistic: 25.58 on 6 and 25 DF, p-value: 1.584e-09
with_hp_ex_disp <- lm(mpg ~ cyl + disp + hp + wt + qsec + am, data = mtcars2)
summary(with_hp_ex_disp)
#>
#> Call:
#> lm(formula = mpg ~ cyl + disp + hp + wt + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.9501 -1.4335 -0.1542 1.3632 4.1917
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 19.77177 10.85529 1.821 0.0810 .
#> cyl.L -0.69084 2.29172 -0.301 0.7657
#> cyl.Q 1.22117 1.01053 1.208 0.2386
#> disp 0.00680 0.01289 0.528 0.6026
#> hp -0.02477 0.01537 -1.612 0.1201
#> wt -3.40642 1.30019 -2.620 0.0150 *
#> qsec 0.67413 0.57760 1.167 0.2546
#> ammanual 2.91836 1.70260 1.714 0.0994 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.435 on 24 degrees of freedom
#> Multiple R-squared: 0.8736, Adjusted R-squared: 0.8367
#> F-statistic: 23.7 on 7 and 24 DF, p-value: 2.566e-09
with_hp_ex_cyl <- lm(mpg ~ disp + hp + wt + qsec + am, data = mtcars2)
summary(with_hp_ex_cyl)
#>
#> Call:
#> lm(formula = mpg ~ disp + hp + wt + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.5399 -1.7398 -0.3196 1.1676 4.5534
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 14.36190 9.74079 1.474 0.15238
#> disp 0.01124 0.01060 1.060 0.29897
#> hp -0.02117 0.01450 -1.460 0.15639
#> wt -4.08433 1.19410 -3.420 0.00208 **
#> qsec 1.00690 0.47543 2.118 0.04391 *
#> ammanual 3.47045 1.48578 2.336 0.02749 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.429 on 26 degrees of freedom
#> Multiple R-squared: 0.8637, Adjusted R-squared: 0.8375
#> F-statistic: 32.96 on 5 and 26 DF, p-value: 1.844e-10
ex_cyl_ex_hp <- lm(mpg ~ disp + wt + qsec + am, data = mtcars2)
summary(ex_cyl_ex_hp)
#>
#> Call:
#> lm(formula = mpg ~ disp + wt + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.5078 -1.4121 -0.6645 1.3611 4.7150
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 6.44238 8.25723 0.780 0.442054
#> disp 0.00769 0.01053 0.730 0.471709
#> wt -4.58828 1.16677 -3.932 0.000529 ***
#> qsec 1.41696 0.39149 3.619 0.001200 **
#> ammanual 3.31015 1.51241 2.189 0.037448 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.48 on 27 degrees of freedom
#> Multiple R-squared: 0.8526, Adjusted R-squared: 0.8307
#> F-statistic: 39.04 on 4 and 27 DF, p-value: 7.465e-11
ex_cyl_ex_hp_ex_disp <- lm(mpg ~ wt + qsec + am, data = mtcars2)
summary(ex_cyl_ex_hp_ex_disp)
#>
#> Call:
#> lm(formula = mpg ~ wt + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.4811 -1.5555 -0.7257 1.4110 4.6610
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.6178 6.9596 1.382 0.177915
#> wt -3.9165 0.7112 -5.507 6.95e-06 ***
#> qsec 1.2259 0.2887 4.247 0.000216 ***
#> ammanual 2.9358 1.4109 2.081 0.046716 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.459 on 28 degrees of freedom
#> Multiple R-squared: 0.8497, Adjusted R-squared: 0.8336
#> F-statistic: 52.75 on 3 and 28 DF, p-value: 1.21e-11
fitted <- ex_cyl_ex_hp_ex_disp
summary(fitted)
#>
#> Call:
#> lm(formula = mpg ~ wt + qsec + am, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.4811 -1.5555 -0.7257 1.4110 4.6610
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.6178 6.9596 1.382 0.177915
#> wt -3.9165 0.7112 -5.507 6.95e-06 ***
#> qsec 1.2259 0.2887 4.247 0.000216 ***
#> ammanual 2.9358 1.4109 2.081 0.046716 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.459 on 28 degrees of freedom
#> Multiple R-squared: 0.8497, Adjusted R-squared: 0.8336
#> F-statistic: 52.75 on 3 and 28 DF, p-value: 1.21e-11
fitted_w_cohort <- lm(mpg ~ wt + qsec + am + cohort, data = mtcars2)
summary(fitted_w_cohort)
#>
#> Call:
#> lm(formula = mpg ~ wt + qsec + am + cohort, data = mtcars2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.8324 -1.0646 0.0000 0.6143 3.7044
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 16.1874 10.0917 1.604 0.127124
#> wt -4.7057 0.9895 -4.756 0.000183 ***
#> qsec 1.1512 0.3938 2.924 0.009477 **
#> ammanual 1.4463 2.0472 0.706 0.489450
#> cohortAUG -5.3411 3.4340 -1.555 0.138272
#> cohortDEC -1.0956 2.5620 -0.428 0.674281
#> cohortFEB -2.6990 3.2768 -0.824 0.421525
#> cohortJAN -4.3491 2.9897 -1.455 0.163969
#> cohortJUL -2.0652 2.6523 -0.779 0.446892
#> cohortJUN -1.0003 2.5467 -0.393 0.699373
#> cohortMAR -1.4996 2.4070 -0.623 0.541535
#> cohortMAY -1.9723 2.5074 -0.787 0.442340
#> cohortNOV -3.3148 2.5280 -1.311 0.207215
#> cohortOCT -1.8676 3.5052 -0.533 0.601061
#> cohortSEP -6.1242 3.9160 -1.564 0.136260
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.594 on 17 degrees of freedom
#> Multiple R-squared: 0.8984, Adjusted R-squared: 0.8148
#> F-statistic: 10.74 on 14 and 17 DF, p-value: 7.968e-06
Created on 2019-11-28 by the reprex package (v0.3.0)