# 1
seedl<-read.delim2("clipboard")
summary(seedl)

lm.0<-lm(seedlings~+1, data=seedl)
summary(lm.0)

add1(lm.0, .~.+(treatment+productivity+temperature)^2, test="F")
# Single term additions
# 
# Model:
# seedlings ~ +1
#              Df Sum of Sq    RSS     AIC F value    Pr(>F)    
# <none>                    819.37 101.220                      
# treatment     2    400.47 418.90  85.093 12.9059 0.0001166 ***
# productivity  1    100.72 718.65  99.285  3.9241 0.0574976 .  
# temperature   1     39.55 779.81 101.736  1.4203 0.2433658    
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

lm.1<-update(lm.0, .~.+treatment)
summary(lm.1)
add1(lm.1, .~.+(treatment+productivity+temperature)^2, test="F")
# Single term additions
# 
# Model:
# seedlings ~ treatment
#              Df Sum of Sq    RSS    AIC F value  Pr(>F)  
# <none>                    418.90 85.093                  
# productivity  1    48.958 369.94 83.364  3.4408 0.07498 .
# temperature   1    45.090 373.81 83.677  3.1362 0.08830 .
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

lm.2<-update(lm.1, .~.+productivity)
summary(lm.2)
add1(lm.2, .~.+(treatment+productivity+temperature)^2, test="F")
lm.3<-update(lm.2, .~.+treatment:productivity)
add1(lm.3, .~.+(treatment+productivity+temperature)^2, test="F")
Single term additions

# Model:
# seedlings ~ treatment + productivity + treatment:productivity
#             Df Sum of Sq    RSS    AIC F value Pr(>F)
# <none>                   290.73 80.135               
# temperature  1    26.427 264.30 79.276  2.2998  0.143

plot(lm.3)

anova(lm.0, lm.1, lm.3, test="F")

summary(lm.3)
# Call:
# lm(formula = seedlings ~ treatment + productivity + treatment:productivity, 
#     data = seedl)
# 
# Residuals:
#     Min      1Q  Median      3Q     Max 
# -6.5919 -2.1628 -0.1457  1.9462  5.5582 
# 
# Coefficients:
#                              Estimate Std. Error t value Pr(>|t|)   
# (Intercept)                 12.881195   4.483482   2.873  0.00837 **
# treatmentmown1               4.868860   6.052372   0.804  0.42903   
# treatmentmown2               5.794768   5.659757   1.024  0.31611   
# productivity                 0.012357   0.009391   1.316  0.20068   
# treatmentmown1:productivity -0.025282   0.011947  -2.116  0.04490 * 
# treatmentmown2:productivity -0.028249   0.011482  -2.460  0.02147 * 
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# 
# Residual standard error: 3.48 on 24 degrees of freedom
# Multiple R-squared:  0.6452,	Adjusted R-squared:  0.5713 
# F-statistic: 8.728 on 5 and 24 DF,  p-value: 7.967e-05

# Task 2
transpi<-read.delim2("clipboard")
summary(transpi)

lm.0<-lm(transpiration~+1, data=transpi)
add1(lm.0, .~.+wind+temperature+humidity+sunshine, test="F")
# Single term additions
# 
# Model:
# transpiration ~ +1
#             Df Sum of Sq     RSS    AIC F value   Pr(>F)   
# <none>                   158.000 35.930                    
# wind         1    75.369  82.631 28.855 10.9454 0.006243 **
# temperature  1    93.763  64.237 25.329 17.5157 0.001265 **
# humidity     1     0.038 157.962 37.926  0.0029 0.958179   
# sunshine     1     4.667 153.333 37.510  0.3652 0.556876   
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

lm.1<-update(lm.0, .~.+temperature)
summary(lm.1)
add1(lm.1, .~.+wind+temperature+humidity+sunshine, test="F")
lm.2<-update(lm.1, .~.+wind)
add1(lm.2, .~.+wind+temperature+humidity+sunshine, test="F")
summary(lm.2)
# Call:
# lm(formula = transpiration ~ temperature + wind, data = transpi)
# 
# Residuals:
#     Min      1Q  Median      3Q     Max 
# -2.8698 -0.7002 -0.2190  0.8018  2.2732 
# 
# Coefficients:
#             Estimate Std. Error t value Pr(>|t|)    
# (Intercept)  5.45464    1.14007   4.784 0.000567 ***
# temperature  0.38619    0.08048   4.798 0.000555 ***
# wind         0.67796    0.17247   3.931 0.002349 ** 
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# 
# Residual standard error: 1.558 on 11 degrees of freedom
# Multiple R-squared:  0.8309,	Adjusted R-squared:  0.8002 
# F-statistic: 27.03 on 2 and 11 DF,  p-value: 5.681e-05

plot(lm.2)

#Task 3
plants<-read.delim2("clipboard")
summary(plants)

lm.1<-lm(biomass~watering*fertil, data=plants)
summary(lm.1)
plot(lm.1)

lm.1<-lm(log(biomass)~watering*fertil, data=plants)
plot(lm.1)
summary(lm.1)
# Call:
# lm(formula = log(biomass) ~ watering * fertil, data = plants)
# 
# Residuals:
#       Min        1Q    Median        3Q       Max 
# -0.215320 -0.065523  0.009066  0.081658  0.213493 
# 
# Coefficients:
#                                  Estimate Std. Error t value Pr(>|t|)    
# (Intercept)                       4.36385    0.05277  82.695  < 2e-16 ***
# wateringWatered                   0.07558    0.07463   1.013  0.32328    
# fertilFertilized                  0.24639    0.07463   3.301  0.00356 ** 
# wateringWatered:fertilFertilized  0.37369    0.10554   3.541  0.00205 ** 
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# 
# Residual standard error: 0.1293 on 20 degrees of freedom
# Multiple R-squared:  0.8396,	Adjusted R-squared:  0.8155 
# F-statistic: 34.89 on 3 and 20 DF,  p-value: 3.862e-08

library(sciplot)
lineplot.CI(plants$watering, log(plants$biomass), group=plants$fertil)

#Task 4
people<-read.delim("clipboard")
summary(people)

lm.0<-lm(mass~+1, data=people)
lm.sel<-step(lm.0, .~+sex+height+colour+vegetarian+hours, direction="forward")
summary(lm.sel)
plot(lm.sel)