Helicopter

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 3.6.3

library(lsmeans)

## Warning: package 'lsmeans' was built under R version 3.6.3

## Loading required package: emmeans

## Welcome to emmeans.
## NOTE -- Important change from versions <= 1.41:
##     Indicator predictors are now treated as 2-level factors by default.
##     To revert to old behavior, use emm_options(cov.keep = character(0))

## The 'lsmeans' package is now basically a front end for 'emmeans'.
## Users are encouraged to switch the rest of the way.
## See help('transition') for more information, including how to
## convert old 'lsmeans' objects and scripts to work with 'emmeans'.

h<-read.csv("C:/Users/User/Desktop/Helicopter - Sheet1.csv",header = T)
h$Wing.Length <- as.factor(h$Wing.Length)

#anova test
atest<-aov(Flight.Time..seconds.~Wing.Length, data = h)
summary(atest)

##             Df Sum Sq Mean Sq F value Pr(>F)    
## Wing.Length  3  6.143  2.0478   138.4 <2e-16 ***
## Residuals   28  0.414  0.0148                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#residual plot - check equal variance and residual normality
#plot(lm(Flight.Time..seconds.~Wing.Length, data = h),1)#Check linearity(not asked in the assignment)
plot(lm(Flight.Time..seconds.~Wing.Length, data = h),2)#Check normality of the residuals

plot(lm(Flight.Time..seconds.~Wing.Length, data = h),3)#Check homogeneity(equal variance)

#plot(lm(Flight.Time..seconds.~Wing.Length, data = h),5)#Check independence of error terms(not asked)

Based on the qq-plot, except for few points, the residuals approximately follow the diagonal line, which indicates that the residual normality holds.
The scale-location plot shows that the residuals seem to be equally spread along the scale of the predictors, thus the equal variance assumption holds.

#Doublecheck-qqplot
#themodel = lm(Flight.Time..seconds.~Wing.Length, data = h) 
#stdres = rstandard(themodel)
#qqnorm(stdres)
#qqline(stdres)

#Check linear trend and quadratic trend 
contrasts(h$Wing.Length) <- contr.poly(4)
summary.aov(atest,split=list(Wing.Length=list("Linear"=1, "Quadratic" = 2)))

##                          Df Sum Sq Mean Sq F value   Pr(>F)    
## Wing.Length               3  6.143  2.0478  138.37  < 2e-16 ***
##   Wing.Length: Linear     1  0.735  0.7350   49.66 1.15e-07 ***
##   Wing.Length: Quadratic  1  0.480  0.4800   32.43 4.17e-06 ***
## Residuals                28  0.414  0.0148                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The above table shows that the p-value for linear and quadratic trend is less than .05, meaning that,under .05 significance level, there is a significant linear and quadratic trend in flight times.