reading in data

data <- read.csv("wpa_lena_pos.csv")

loading libraries

library(psych)
library(report)

descriptive statistics on all variables

describe(data$sit_time)
##    vars   n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 850 0.51 0.3   0.48    0.51 0.33   0   1     1 0.11    -1.01 0.01
describe(data$held_time)
##    vars   n mean   sd median trimmed  mad min  max range skew kurtosis se
## X1    1 850 0.07 0.14   0.01    0.04 0.02   0 0.98  0.98 3.21    12.41  0
describe(data$prone_time)
##    vars   n mean  sd median trimmed  mad min max range skew kurtosis   se
## X1    1 850 0.14 0.2   0.08     0.1 0.12   0   1     1 2.54     7.28 0.01
describe(data$supine_time)
##    vars   n mean   sd median trimmed  mad min max range skew kurtosis   se
## X1    1 850 0.12 0.21   0.03    0.07 0.04   0   1     1 2.59     6.86 0.01
describe(data$upright_time)
##    vars   n mean   sd median trimmed  mad min  max range skew kurtosis   se
## X1    1 850 0.16 0.19   0.09    0.12 0.13   0 0.98  0.98 1.49     2.16 0.01
describe(data$adult_word_cnt)
##    vars   n   mean     sd median trimmed    mad min     max   range skew
## X1    1 850 241.66 206.78 189.55  214.21 174.35   0 1370.62 1370.62 1.45
##    kurtosis   se
## X1     2.85 7.09

correlation between time spent sitting and adult word count

correlation_sitting <- corr.test(data$sit_time, data$adult_word_cnt)
print(correlation_sitting, short = F)
## Call:corr.test(x = data$sit_time, y = data$adult_word_cnt)
## Correlation matrix 
## [1] 0.18
## Sample Size 
## [1] 850
## These are the unadjusted probability values.
##   The probability values  adjusted for multiple tests are in the p.adj object. 
## [1] 0
## 
##  Confidence intervals based upon normal theory.  To get bootstrapped values, try cor.ci
##       raw.lower raw.r raw.upper raw.p lower.adj upper.adj
## NA-NA      0.12  0.18      0.25     0      0.12      0.25
plot(data$sit_time, data$adult_word_cnt)

correlation between time spent held and adult word count

correlation_held <- corr.test(data$held_time, data$adult_word_cnt)
print(correlation_held, short = F)
## Call:corr.test(x = data$held_time, y = data$adult_word_cnt)
## Correlation matrix 
## [1] 0.19
## Sample Size 
## [1] 850
## These are the unadjusted probability values.
##   The probability values  adjusted for multiple tests are in the p.adj object. 
## [1] 0
## 
##  Confidence intervals based upon normal theory.  To get bootstrapped values, try cor.ci
##       raw.lower raw.r raw.upper raw.p lower.adj upper.adj
## NA-NA      0.13  0.19      0.26     0      0.13      0.26
plot(data$held_time, data$adult_word_cnt)

correlation between time spent prone and adult word count

correlation_prone <- corr.test(data$prone_time, data$adult_word_cnt)
print(correlation_prone, short = F)
## Call:corr.test(x = data$prone_time, y = data$adult_word_cnt)
## Correlation matrix 
## [1] -0.18
## Sample Size 
## [1] 850
## These are the unadjusted probability values.
##   The probability values  adjusted for multiple tests are in the p.adj object. 
## [1] 0
## 
##  Confidence intervals based upon normal theory.  To get bootstrapped values, try cor.ci
##       raw.lower raw.r raw.upper raw.p lower.adj upper.adj
## NA-NA     -0.24 -0.18     -0.11     0     -0.24     -0.11
plot(data$prone_time, data$adult_word_cnt)

correlation between time spent supine and adult word count

correlation_supine <- corr.test(data$supine_time, data$adult_word_cnt)
print(correlation_supine, short = F)
## Call:corr.test(x = data$supine_time, y = data$adult_word_cnt)
## Correlation matrix 
## [1] -0.15
## Sample Size 
## [1] 850
## These are the unadjusted probability values.
##   The probability values  adjusted for multiple tests are in the p.adj object. 
## [1] 0
## 
##  Confidence intervals based upon normal theory.  To get bootstrapped values, try cor.ci
##       raw.lower raw.r raw.upper raw.p lower.adj upper.adj
## NA-NA     -0.22 -0.15     -0.08     0     -0.22     -0.08
plot(data$supine_time, data$adult_word_cnt)

correlation between time spent upright and adult word count

correlation_upright <- corr.test(data$upright_time, data$adult_word_cnt)
print(correlation_upright, short = F)
## Call:corr.test(x = data$upright_time, y = data$adult_word_cnt)
## Correlation matrix 
## [1] -0.08
## Sample Size 
## [1] 850
## These are the unadjusted probability values.
##   The probability values  adjusted for multiple tests are in the p.adj object. 
## [1] 0.02
## 
##  Confidence intervals based upon normal theory.  To get bootstrapped values, try cor.ci
##       raw.lower raw.r raw.upper raw.p lower.adj upper.adj
## NA-NA     -0.14 -0.08     -0.01  0.02     -0.14     -0.01
plot(data$upright_time, data$adult_word_cnt)

regression: time spent sitting as a predictor of adult word count

regression_sitting <- lm(adult_word_cnt~sit_time, data=data)
summary(regression_sitting)
## 
## Call:
## lm(formula = adult_word_cnt ~ sit_time, data = data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -300.2 -151.9  -57.3   95.7 1074.5 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   177.75      13.78  12.896  < 2e-16 ***
## sit_time      125.03      23.26   5.376 9.84e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 203.5 on 848 degrees of freedom
## Multiple R-squared:  0.03296,    Adjusted R-squared:  0.03182 
## F-statistic:  28.9 on 1 and 848 DF,  p-value: 9.84e-08
report(regression_sitting)
## We fitted a linear model (estimated using OLS) to predict adult_word_cnt with
## sit_time (formula: adult_word_cnt ~ sit_time). The model explains a
## statistically significant and weak proportion of variance (R2 = 0.03, F(1, 848)
## = 28.90, p < .001, adj. R2 = 0.03). The model's intercept, corresponding to
## sit_time = 0, is at 177.75 (95% CI [150.70, 204.81], t(848) = 12.90, p < .001).
## Within this model:
## 
##   - The effect of sit time is statistically significant and positive (beta =
## 125.03, 95% CI [79.39, 170.68], t(848) = 5.38, p < .001; Std. beta = 0.18, 95%
## CI [0.12, 0.25])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.

regression: time spent held as a predictor of adult word count

regression_held <- lm(adult_word_cnt~held_time, data=data)
summary(regression_held)
## 
## Call:
## lm(formula = adult_word_cnt ~ held_time, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -376.96 -145.17  -53.13   91.11 1149.86 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  220.759      7.873  28.038  < 2e-16 ***
## held_time    286.700     50.374   5.691 1.73e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 203.1 on 848 degrees of freedom
## Multiple R-squared:  0.03679,    Adjusted R-squared:  0.03566 
## F-statistic: 32.39 on 1 and 848 DF,  p-value: 1.735e-08
report(regression_held)
## We fitted a linear model (estimated using OLS) to predict adult_word_cnt with
## held_time (formula: adult_word_cnt ~ held_time). The model explains a
## statistically significant and weak proportion of variance (R2 = 0.04, F(1, 848)
## = 32.39, p < .001, adj. R2 = 0.04). The model's intercept, corresponding to
## held_time = 0, is at 220.76 (95% CI [205.31, 236.21], t(848) = 28.04, p <
## .001). Within this model:
## 
##   - The effect of held time is statistically significant and positive (beta =
## 286.70, 95% CI [187.83, 385.57], t(848) = 5.69, p < .001; Std. beta = 0.19, 95%
## CI [0.13, 0.26])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.

regression: time spent prone as a predictor of adult word count

regression_prone <- lm(adult_word_cnt~prone_time, data=data)
summary(regression_prone)
## 
## Call:
## lm(formula = adult_word_cnt ~ prone_time, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -267.41 -146.73  -51.77   90.70 1103.21 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  267.411      8.563  31.229  < 2e-16 ***
## prone_time  -181.502     34.894  -5.201 2.48e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 203.7 on 848 degrees of freedom
## Multiple R-squared:  0.03092,    Adjusted R-squared:  0.02978 
## F-statistic: 27.06 on 1 and 848 DF,  p-value: 2.48e-07
report(regression_prone)
## We fitted a linear model (estimated using OLS) to predict adult_word_cnt with
## prone_time (formula: adult_word_cnt ~ prone_time). The model explains a
## statistically significant and weak proportion of variance (R2 = 0.03, F(1, 848)
## = 27.06, p < .001, adj. R2 = 0.03). The model's intercept, corresponding to
## prone_time = 0, is at 267.41 (95% CI [250.60, 284.22], t(848) = 31.23, p <
## .001). Within this model:
## 
##   - The effect of prone time is statistically significant and negative (beta =
## -181.50, 95% CI [-249.99, -113.01], t(848) = -5.20, p < .001; Std. beta =
## -0.18, 95% CI [-0.24, -0.11])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.

regression: time spent supine as a predictor of adult word count

regression_supine <- lm(adult_word_cnt~supine_time, data=data)
summary(regression_supine)
## 
## Call:
## lm(formula = adult_word_cnt ~ supine_time, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -259.42 -143.52  -52.28   93.10 1119.24 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  259.418      8.082  32.100  < 2e-16 ***
## supine_time -150.313     33.944  -4.428 1.07e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 204.5 on 848 degrees of freedom
## Multiple R-squared:  0.0226, Adjusted R-squared:  0.02145 
## F-statistic: 19.61 on 1 and 848 DF,  p-value: 1.074e-05
report(regression_supine)
## We fitted a linear model (estimated using OLS) to predict adult_word_cnt with
## supine_time (formula: adult_word_cnt ~ supine_time). The model explains a
## statistically significant and weak proportion of variance (R2 = 0.02, F(1, 848)
## = 19.61, p < .001, adj. R2 = 0.02). The model's intercept, corresponding to
## supine_time = 0, is at 259.42 (95% CI [243.56, 275.28], t(848) = 32.10, p <
## .001). Within this model:
## 
##   - The effect of supine time is statistically significant and negative (beta =
## -150.31, 95% CI [-216.94, -83.69], t(848) = -4.43, p < .001; Std. beta = -0.15,
## 95% CI [-0.22, -0.08])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.

regression: time spent upright as a predictor of adult word count

regression_upright <- lm(adult_word_cnt~upright_time, data=data)
summary(regression_upright)
## 
## Call:
## lm(formula = adult_word_cnt ~ upright_time, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -254.94 -151.59  -51.85   95.10 1115.67 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   254.945      9.174  27.791   <2e-16 ***
## upright_time  -85.200     37.440  -2.276   0.0231 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 206.3 on 848 degrees of freedom
## Multiple R-squared:  0.006069,   Adjusted R-squared:  0.004897 
## F-statistic: 5.178 on 1 and 848 DF,  p-value: 0.02312
report(regression_upright)
## We fitted a linear model (estimated using OLS) to predict adult_word_cnt with
## upright_time (formula: adult_word_cnt ~ upright_time). The model explains a
## statistically significant and very weak proportion of variance (R2 = 6.07e-03,
## F(1, 848) = 5.18, p = 0.023, adj. R2 = 4.90e-03). The model's intercept,
## corresponding to upright_time = 0, is at 254.94 (95% CI [236.94, 272.95],
## t(848) = 27.79, p < .001). Within this model:
## 
##   - The effect of upright time is statistically significant and negative (beta =
## -85.20, 95% CI [-158.69, -11.71], t(848) = -2.28, p = 0.023; Std. beta = -0.08,
## 95% CI [-0.15, -0.01])
## 
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.