What influenced the time of sleep
Szymon OryĆczak and Jahid Hasan
2022-06-14
Introduction
The purpose of this report is to examine what factors influences the time of sleep. Our analysis will be based on a database âsleep75â, which was prepared by Jeff E.Biddle and Daniel S.Hamermesh, and used in their worked titled âSleep and the Allocation of Timeâ from 1989. It is worth noting that the collected data come from the 1970s.
Introducing the data
Presentation of variable names and types
## Rows: 706
## Columns: 34
## $ age <dbl> 32, 31, 44, 30, 64, 41, 35, 47, 32, 30, 43, 23, 24, 48, 33, 2~
## $ black <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0~
## $ case <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18~
## $ clerical <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0~
## $ construc <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0~
## $ educ <dbl> 12, 14, 17, 12, 14, 12, 12, 13, 17, 15, 8, 16, 16, 5, 12, 12,~
## $ earns74 <dbl> 0, 9500, 42500, 42500, 2500, 0, 8250, 0, 18750, 11750, 21250,~
## $ gdhlth <dbl> 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1~
## $ inlf <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ leis1 <dbl> 3529, 2140, 4595, 3211, 4052, 4812, 4787, 3544, 4359, 4211, 2~
## $ leis2 <dbl> 3479, 2140, 4505, 3211, 4007, 4797, 4157, 3469, 4359, 4061, 1~
## $ leis3 <dbl> 3479, 2140, 4227, 3211, 4007, 4797, 4157, 3439, 4121, 4061, 1~
## $ smsa <dbl> 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1~
## $ lhrwage <chr> "1.9558610000000001", "0.35767399999999999", "3.021887", "2.2~
## $ lothinc <dbl> 10.075380, 0.000000, 0.000000, 0.000000, 9.328213, 10.657280,~
## $ male <dbl> 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ marr <dbl> 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0~
## $ prot <dbl> 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0~
## $ rlxall <dbl> 3163, 2920, 3038, 3083, 3493, 4078, 3810, 3033, 3606, 3168, 1~
## $ selfe <dbl> 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1~
## $ sleep <dbl> 3113, 2920, 2670, 3083, 3448, 4063, 3180, 2928, 3368, 3018, 1~
## $ slpnaps <dbl> 3163, 2920, 2760, 3083, 3493, 4078, 3810, 3003, 3368, 3168, 1~
## $ south <dbl> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0~
## $ spsepay <dbl> 0, 0, 20000, 5000, 2400, 0, 12000, 0, 0, 6000, 0, 3000, 3000,~
## $ spwrk75 <dbl> 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0~
## $ totwrk <dbl> 3438, 5020, 2815, 3786, 2580, 1205, 2113, 3608, 2353, 2851, 6~
## $ union <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0~
## $ worknrm <dbl> 3438, 5020, 2815, 3786, 2580, 0, 2113, 3608, 2353, 2851, 6415~
## $ workscnd <dbl> 0, 0, 0, 0, 0, 1205, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0~
## $ exper <dbl> 14, 11, 21, 12, 44, 23, 17, 28, 9, 9, 29, 1, 2, 37, 15, 5, 23~
## $ yngkid <dbl> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0~
## $ yrsmarr <dbl> 13, 0, 0, 12, 33, 23, 0, 24, 11, 7, 23, 4, 4, 0, 9, 4, 21, 17~
## $ hrwage <chr> "7.070004", "1.429999", "20.530000000000001", "9.619998000000~
## $ agesq <dbl> 1024, 961, 1936, 900, 4096, 1681, 1225, 2209, 1024, 900, 1849~## age black case clerical
## Min. :23.00 Min. :0.00000 Min. : 1.0 Min. :0.0000
## 1st Qu.:29.00 1st Qu.:0.00000 1st Qu.:177.2 1st Qu.:0.0000
## Median :36.00 Median :0.00000 Median :353.5 Median :0.0000
## Mean :38.82 Mean :0.04958 Mean :353.5 Mean :0.1823
## 3rd Qu.:48.00 3rd Qu.:0.00000 3rd Qu.:529.8 3rd Qu.:0.1823
## Max. :65.00 Max. :1.00000 Max. :706.0 Max. :1.0000
## construc educ earns74 gdhlth
## Min. :0.00000 Min. : 1.00 Min. : 0 Min. :0.0000
## 1st Qu.:0.00000 1st Qu.:12.00 1st Qu.: 2500 1st Qu.:1.0000
## Median :0.00000 Median :12.00 Median : 8250 Median :1.0000
## Mean :0.03008 Mean :12.78 Mean : 9768 Mean :0.8909
## 3rd Qu.:0.03008 3rd Qu.:16.00 3rd Qu.:13750 3rd Qu.:1.0000
## Max. :1.00000 Max. :17.00 Max. :42500 Max. :1.0000
## inlf leis1 leis2 leis3 smsa
## Min. :0.0000 Min. :1745 Min. :1677 Min. :1677 Min. :0.0000
## 1st Qu.:1.0000 1st Qu.:4110 1st Qu.:3986 1st Qu.:3933 1st Qu.:0.0000
## Median :1.0000 Median :4620 Median :4519 Median :4469 Median :0.0000
## Mean :0.7535 Mean :4691 Mean :4574 Mean :4519 Mean :0.3994
## 3rd Qu.:1.0000 3rd Qu.:5204 3rd Qu.:5071 3rd Qu.:5028 3rd Qu.:1.0000
## Max. :1.0000 Max. :7417 Max. :7297 Max. :7282 Max. :1.0000
## lhrwage lothinc male marr
## Length:706 Min. : 0.000 Min. :0.0000 Min. :0.0000
## Class :character 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.:1.0000
## Mode :character Median : 8.613 Median :1.0000 Median :1.0000
## Mean : 6.228 Mean :0.5666 Mean :0.8215
## 3rd Qu.: 9.328 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :10.657 Max. :1.0000 Max. :1.0000
## prot rlxall selfe sleep slpnaps
## Min. :0.0000 Min. :1380 Min. :0.0000 Min. : 755 Min. :1335
## 1st Qu.:0.0000 1st Qu.:3150 1st Qu.:0.0000 1st Qu.:3015 1st Qu.:3106
## Median :1.0000 Median :3428 Median :0.0000 Median :3270 Median :3369
## Mean :0.6629 Mean :3438 Mean :0.1317 Mean :3266 Mean :3383
## 3rd Qu.:1.0000 3rd Qu.:3720 3rd Qu.:0.0000 3rd Qu.:3532 3rd Qu.:3655
## Max. :1.0000 Max. :6110 Max. :1.0000 Max. :4695 Max. :6110
## south spsepay spwrk75 totwrk
## Min. :0.0000 Min. : 0 Min. :0.0000 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000 1st Qu.:1554
## Median :0.0000 Median : 0 Median :0.0000 Median :2288
## Mean :0.1841 Mean : 5144 Mean :0.4802 Mean :2123
## 3rd Qu.:0.0000 3rd Qu.: 8900 3rd Qu.:1.0000 3rd Qu.:2692
## Max. :1.0000 Max. :75000 Max. :1.0000 Max. :6415
## union worknrm workscnd exper
## Min. :0.0000 Min. : 0 Min. : 0.00 Min. : 0.00
## 1st Qu.:0.0000 1st Qu.:1538 1st Qu.: 0.00 1st Qu.:10.00
## Median :0.0000 Median :2275 Median : 0.00 Median :17.00
## Mean :0.2181 Mean :2093 Mean : 29.67 Mean :20.04
## 3rd Qu.:0.0000 3rd Qu.:2636 3rd Qu.: 0.00 3rd Qu.:30.00
## Max. :1.0000 Max. :6415 Max. :1337.00 Max. :55.00
## yngkid yrsmarr hrwage agesq
## Min. :0.0000 Min. : 0.00 Length:706 Min. : 529
## 1st Qu.:0.0000 1st Qu.: 0.00 Class :character 1st Qu.: 841
## Median :0.0000 Median : 9.00 Mode :character Median :1296
## Mean :0.1289 Mean :11.77 Mean :1635
## 3rd Qu.:0.0000 3rd Qu.:20.00 3rd Qu.:2304
## Max. :1.0000 Max. :43.00 Max. :4225Actions taken to facilitate the work on the database
# Making sure that there is no empty values or duplicated
sum(is.na(sleep75))## [1] 0sum(duplicated(sleep75))## [1] 0# Removing identifier
sleep75 <- sleep75 %>%
select(-case)
# Creating useful subsets
sleep75_no_chr <- sleep75 %>%
select(-hrwage, -lhrwage)
sleep75_no_logical <- sleep75_no_chr%>%
select(-black, -clerical, -construc, -gdhlth, -inlf, -smsa, -male, -marr, -selfe, -south, -spwrk75, -union, -yngkid)Letâs take a look at the correlation plot to quickly find correlation
between variables
We can observe over 10 strong correlation, but but in reality they are caused by dependence on other variables. They will be deleted to avoid multicollinearity.
This correlation plot shows correlations without problematic
variables:
Sleep duration study
Correlation plot did not show any strong correlation, so letâs find out what may influence a sleep time.
Here we present a plot that illustrates the strongest correlation.
Letâs see how sleep time is depends on the working time:
cor(totwrk, sleep)## [1] -0.3213835A negative correlation, but itâs not so strong
Because total working time has the biggest influence on the time of sleep, we may examine what effects the time of work.
Work duration study
On the correlation plot we can see what variables have a slight correlation with the total working time. Letâs take a closer look to that relationships.
At this point we should remove a serious outlier - one gentleman has been working for more than 6000 hours. We hope he had a great vacation.
sleep75_removed_man_outlier <- sleep75 %>%
filter(totwrk < 6000)Again, letâs take a look:
And correlation:
cor(sleep75_removed_man_outlier$male, sleep75_removed_man_outlier$totwrk)## [1] 0.3765647This correlation is also not so strong, but we can state, that in the 70s men were more likely to work longer than women.
We may try to create an linear model which describes how sex, time of sleep and spousal wage income (including interatcions between them) are influencing the time of work. Below model anylysis is presented.
summary(totwrk_lm)##
## Call:
## lm(formula = totwrk ~ male * sleep * spsepay)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2610.88 -493.00 61.12 530.51 2806.09
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.453e+03 4.252e+02 8.122 2.08e-15 ***
## male 1.270e+03 5.539e+02 2.293 0.022119 *
## sleep -4.954e-01 1.289e-01 -3.844 0.000132 ***
## spsepay 1.964e-02 3.589e-02 0.547 0.584441
## male:sleep -2.124e-01 1.682e-01 -1.263 0.206958
## male:spsepay 1.956e-02 9.220e-02 0.212 0.832030
## sleep:spsepay -9.966e-06 1.094e-05 -0.911 0.362505
## male:sleep:spsepay -6.750e-07 2.847e-05 -0.024 0.981090
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 825.8 on 698 degrees of freedom
## Multiple R-squared: 0.2479, Adjusted R-squared: 0.2403
## F-statistic: 32.86 on 7 and 698 DF, p-value: < 2.2e-16As we can see: working time model is far from being perfect. Residuals vs Fitted and Normal Q-Q plot does not show any serious problem, but the other two does. Especially Residuals vs Leverage. Adjusted R-squared of 0.24 is also not a great result. Now letâs examine factors affecting earnings as it is somewhat related to working time.
Income study
Take a look at correlation plot:
Letâs dive into the analysis of the potential correlations. Plot below describes othincâs score impact on total earnings in â74
cor(lothinc, earns74)## [1] -0.3209126We can observe a slight negative correlation, that factor should be used while creating linear model of earnings in â74.
Plot below shows relationship between Education score, othinc score, total earnings in â74 and what is more - it is grouped by sex:
No further conclusion can be estimated, relationship is not so strong. But still, we can observe that 5 people with 0 othinc score has had the biggest income - and 4 of them are a man. It is worth noting that a higher education rate means statistically higher earnings. Othinc score seems to not have a much impact on education score.
Here we can see those relations on 2d plots:
Letâs check if spousal income is and important factor:
cor(spsepay, earns74)## [1] 0.2433129Correlation is only 0.24, but it is worth to include this factor into the model. But before that - letâs see if the stereotype is true:
cor(totwrk, earns74)## [1] 0.1158009This correlation is to low to state that if you work more you earn more. Itâs not true based on this data base.
Constructing linear model of earnings - othincs score, sex, education score, smsa variable, spousal wage income, total work and interactions between them are included.
summary(earnings_lm)##
## Call:
## lm(formula = earns74 ~ lothinc * male * educ * smsa * spsepay *
## totwrk)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19159.9 -4117.9 -836.6 3158.2 29125.7
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 8.600e+03 7.506e+03 1.146
## lothinc -6.827e+02 1.488e+03 -0.459
## maleWoman -2.846e+04 1.151e+04 -2.474
## educ -1.740e+01 6.794e+02 -0.026
## smsa -1.765e+04 1.767e+04 -0.999
## spsepay 1.122e+01 9.994e+00 1.123
## totwrk -1.631e+00 2.881e+00 -0.566
## lothinc:maleWoman 3.150e+03 2.011e+03 1.566
## lothinc:educ 3.735e+01 1.284e+02 0.291
## maleWoman:educ 2.411e+03 9.949e+02 2.423
## lothinc:smsa -3.067e+02 3.394e+03 -0.090
## maleWoman:smsa 4.719e+04 2.489e+04 1.896
## educ:smsa 1.979e+03 1.385e+03 1.429
## lothinc:spsepay -1.677e+00 1.177e+00 -1.425
## maleWoman:spsepay -1.305e+01 1.015e+01 -1.286
## educ:spsepay -6.796e-01 7.758e-01 -0.876
## smsa:spsepay -1.571e+01 1.028e+01 -1.528
## lothinc:totwrk -2.848e-01 5.955e-01 -0.478
## maleWoman:totwrk 1.127e+01 5.259e+00 2.143
## educ:totwrk 3.017e-01 2.664e-01 1.132
## smsa:totwrk 6.621e+00 7.372e+00 0.898
## spsepay:totwrk -3.197e-03 3.412e-03 -0.937
## lothinc:maleWoman:educ -3.067e+02 1.699e+02 -1.805
## lothinc:maleWoman:smsa -2.969e+03 4.310e+03 -0.689
## lothinc:educ:smsa -5.712e+01 2.628e+02 -0.217
## maleWoman:educ:smsa -4.928e+03 2.044e+03 -2.411
## lothinc:maleWoman:spsepay 1.839e+00 1.196e+00 1.538
## lothinc:educ:spsepay 1.145e-01 9.124e-02 1.255
## maleWoman:educ:spsepay 8.230e-01 7.834e-01 1.051
## lothinc:smsa:spsepay 2.461e+00 1.284e+00 1.916
## maleWoman:smsa:spsepay 1.963e+01 1.060e+01 1.851
## educ:smsa:spsepay 1.094e+00 8.008e-01 1.366
## lothinc:maleWoman:totwrk -9.335e-01 9.155e-01 -1.020
## lothinc:educ:totwrk 1.265e-03 5.095e-02 0.025
## maleWoman:educ:totwrk -1.188e+00 4.473e-01 -2.655
## lothinc:smsa:totwrk -4.598e-02 1.343e+00 -0.034
## maleWoman:smsa:totwrk -1.760e+01 1.178e+01 -1.494
## educ:smsa:totwrk -7.184e-01 5.731e-01 -1.254
## lothinc:spsepay:totwrk 6.254e-04 4.104e-04 1.524
## maleWoman:spsepay:totwrk 4.954e-03 3.522e-03 1.406
## educ:spsepay:totwrk 2.169e-04 2.718e-04 0.798
## smsa:spsepay:totwrk 6.156e-03 3.639e-03 1.692
## lothinc:maleWoman:educ:smsa 4.141e+02 3.384e+02 1.224
## lothinc:maleWoman:educ:spsepay -1.255e-01 9.223e-02 -1.361
## lothinc:maleWoman:smsa:spsepay -2.964e+00 1.324e+00 -2.239
## lothinc:educ:smsa:spsepay -1.747e-01 9.858e-02 -1.773
## maleWoman:educ:smsa:spsepay -1.345e+00 8.165e-01 -1.647
## lothinc:maleWoman:educ:totwrk 1.257e-01 7.593e-02 1.656
## lothinc:maleWoman:smsa:totwrk 1.184e+00 1.890e+00 0.626
## lothinc:educ:smsa:totwrk 3.010e-02 1.039e-01 0.290
## maleWoman:educ:smsa:totwrk 1.872e+00 9.848e-01 1.901
## lothinc:maleWoman:spsepay:totwrk -8.113e-04 4.235e-04 -1.915
## lothinc:educ:spsepay:totwrk -4.543e-05 3.258e-05 -1.395
## maleWoman:educ:spsepay:totwrk -3.190e-04 2.773e-04 -1.150
## lothinc:smsa:spsepay:totwrk -9.516e-04 4.689e-04 -2.029
## maleWoman:smsa:spsepay:totwrk -9.702e-03 4.183e-03 -2.320
## educ:smsa:spsepay:totwrk -4.157e-04 2.871e-04 -1.448
## lothinc:maleWoman:educ:smsa:spsepay 2.068e-01 1.007e-01 2.054
## lothinc:maleWoman:educ:smsa:totwrk -1.613e-01 1.509e-01 -1.069
## lothinc:maleWoman:educ:spsepay:totwrk 5.588e-05 3.326e-05 1.680
## lothinc:maleWoman:smsa:spsepay:totwrk 1.398e-03 5.246e-04 2.665
## lothinc:educ:smsa:spsepay:totwrk 6.688e-05 3.634e-05 1.841
## maleWoman:educ:smsa:spsepay:totwrk 6.859e-04 3.188e-04 2.152
## lothinc:maleWoman:educ:smsa:spsepay:totwrk -1.003e-04 3.962e-05 -2.531
## Pr(>|t|)
## (Intercept) 0.25235
## lothinc 0.64644
## maleWoman 0.01363 *
## educ 0.97957
## smsa 0.31812
## spsepay 0.26186
## totwrk 0.57147
## lothinc:maleWoman 0.11774
## lothinc:educ 0.77128
## maleWoman:educ 0.01567 *
## lothinc:smsa 0.92803
## maleWoman:smsa 0.05842 .
## educ:smsa 0.15356
## lothinc:spsepay 0.15470
## maleWoman:spsepay 0.19897
## educ:spsepay 0.38141
## smsa:spsepay 0.12709
## lothinc:totwrk 0.63262
## maleWoman:totwrk 0.03251 *
## educ:totwrk 0.25788
## smsa:totwrk 0.36947
## spsepay:totwrk 0.34911
## lothinc:maleWoman:educ 0.07150 .
## lothinc:maleWoman:smsa 0.49120
## lothinc:educ:smsa 0.82799
## maleWoman:educ:smsa 0.01621 *
## lothinc:maleWoman:spsepay 0.12451
## lothinc:educ:spsepay 0.20979
## maleWoman:educ:spsepay 0.29384
## lothinc:smsa:spsepay 0.05580 .
## maleWoman:smsa:spsepay 0.06457 .
## educ:smsa:spsepay 0.17249
## lothinc:maleWoman:totwrk 0.30826
## lothinc:educ:totwrk 0.98020
## maleWoman:educ:totwrk 0.00812 **
## lothinc:smsa:totwrk 0.97271
## maleWoman:smsa:totwrk 0.13567
## educ:smsa:totwrk 0.21048
## lothinc:spsepay:totwrk 0.12805
## maleWoman:spsepay:totwrk 0.16007
## educ:spsepay:totwrk 0.42510
## smsa:spsepay:totwrk 0.09119 .
## lothinc:maleWoman:educ:smsa 0.22153
## lothinc:maleWoman:educ:spsepay 0.17404
## lothinc:maleWoman:smsa:spsepay 0.02552 *
## lothinc:educ:smsa:spsepay 0.07676 .
## maleWoman:educ:smsa:spsepay 0.10010
## lothinc:maleWoman:educ:totwrk 0.09829 .
## lothinc:maleWoman:smsa:totwrk 0.53139
## lothinc:educ:smsa:totwrk 0.77206
## maleWoman:educ:smsa:totwrk 0.05775 .
## lothinc:maleWoman:spsepay:totwrk 0.05588 .
## lothinc:educ:spsepay:totwrk 0.16362
## maleWoman:educ:spsepay:totwrk 0.25037
## lothinc:smsa:spsepay:totwrk 0.04283 *
## maleWoman:smsa:spsepay:totwrk 0.02067 *
## educ:smsa:spsepay:totwrk 0.14814
## lothinc:maleWoman:educ:smsa:spsepay 0.04036 *
## lothinc:maleWoman:educ:smsa:totwrk 0.28535
## lothinc:maleWoman:educ:spsepay:totwrk 0.09346 .
## lothinc:maleWoman:smsa:spsepay:totwrk 0.00790 **
## lothinc:educ:smsa:spsepay:totwrk 0.06614 .
## maleWoman:educ:smsa:spsepay:totwrk 0.03178 *
## lothinc:maleWoman:educ:smsa:spsepay:totwrk 0.01162 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7221 on 642 degrees of freedom
## Multiple R-squared: 0.4537, Adjusted R-squared: 0.4001
## F-statistic: 8.465 on 63 and 642 DF, p-value: < 2.2e-16Adjusted R-squared is satisfactory - but still far from 1.00. Plot analysis shows how hard it is to present a good model of earnings, basically any of them is not great.
Other interesting correlations
Correlation between othinc score an marrige:
cor(lothinc, marr)## [1] 0.3637086More men have higher othinc score:
Sometimes only one person in marriage works:
cor(marr, spwrk75) ## [1] 0.4405547Constructing linear model of sleep time
Take a look at this plot visualizing the most important factors of linear model that is about to be created:
Do older people sleep longer? The answear is yes, they do:
Finally, a linear model:
summary(sleep_lm)##
## Call:
## lm(formula = sleep ~ totwrk * lothinc * spsepay * gdhlth * age)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2397.73 -240.68 7.23 260.09 1347.37
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.767e+03 6.520e+02 5.778 1.16e-08 ***
## totwrk -1.839e-01 3.163e-01 -0.581 0.561
## lothinc -4.899e+01 1.215e+02 -0.403 0.687
## spsepay -9.681e-01 6.553e-01 -1.477 0.140
## gdhlth -5.528e+02 7.153e+02 -0.773 0.440
## age 2.081e+00 1.439e+01 0.145 0.885
## totwrk:lothinc 1.154e-02 5.356e-02 0.215 0.829
## totwrk:spsepay -8.544e-05 4.276e-04 -0.200 0.842
## lothinc:spsepay 9.854e-02 7.321e-02 1.346 0.179
## totwrk:gdhlth 1.672e-01 3.409e-01 0.490 0.624
## lothinc:gdhlth 5.940e+01 1.295e+02 0.459 0.647
## spsepay:gdhlth 9.905e-01 6.561e-01 1.510 0.132
## totwrk:age 4.629e-04 6.884e-03 0.067 0.946
## lothinc:age 5.762e-01 2.443e+00 0.236 0.814
## spsepay:age 3.802e-02 2.691e-02 1.413 0.158
## gdhlth:age 5.805e+00 1.598e+01 0.363 0.717
## totwrk:lothinc:spsepay 1.592e-05 4.763e-05 0.334 0.738
## totwrk:lothinc:gdhlth -1.884e-02 5.690e-02 -0.331 0.741
## totwrk:spsepay:gdhlth 8.027e-05 4.278e-04 0.188 0.851
## lothinc:spsepay:gdhlth -9.785e-02 7.335e-02 -1.334 0.183
## totwrk:lothinc:age -9.366e-05 1.111e-03 -0.084 0.933
## totwrk:spsepay:age -5.135e-06 1.496e-05 -0.343 0.732
## lothinc:spsepay:age -4.123e-03 2.981e-03 -1.383 0.167
## totwrk:gdhlth:age -3.708e-03 7.551e-03 -0.491 0.623
## lothinc:gdhlth:age -5.339e-01 2.661e+00 -0.201 0.841
## spsepay:gdhlth:age -3.863e-02 2.693e-02 -1.434 0.152
## totwrk:lothinc:spsepay:gdhlth -1.612e-05 4.767e-05 -0.338 0.735
## totwrk:lothinc:spsepay:age 4.508e-07 1.633e-06 0.276 0.783
## totwrk:lothinc:gdhlth:age 2.241e-04 1.204e-03 0.186 0.852
## totwrk:spsepay:gdhlth:age 5.309e-06 1.496e-05 0.355 0.723
## lothinc:spsepay:gdhlth:age 4.097e-03 2.984e-03 1.373 0.170
## totwrk:lothinc:spsepay:gdhlth:age -4.479e-07 1.634e-06 -0.274 0.784
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 416.5 on 674 degrees of freedom
## Multiple R-squared: 0.1605, Adjusted R-squared: 0.1219
## F-statistic: 4.156 on 31 and 674 DF, p-value: 1.791e-12R-squared is very low. Residuals vs Fitted looks great, Normal Q-Q is also fine, but troubles begin in the Scale-Location plot. Residuals vs Leverage shows that sleep time is hard to predict, even if that many factors are included.
Conclusion
Due to the low correlation coefficients, it is difficult to tell what influences sleep time. The only real factor affecting sleep time seems to be working time. It is therefore worth taking into account the factors affecting working time and other reports presented throughout the report. Thank you for your attention!