The dataset shows the variables Salt, Ultrasound time, Oil amount, and the difference in oil removed. Each row represents one observation from the experiment.
Dot Plots
Dot Plot: Oil Amount
ggplot(OilDeapsorbtion, aes(x = Oil, y = Diff)) +geom_dotplot(binaxis ="y", stackdir ="center", binwidth =0.25) +labs(title ="Dot Plot of Difference by Amount of Oil",x ="Amount of Oil",y ="Difference in Oil Removed" )
The dot plot shows that when the oil amount is 10 ml, the difference in oil removed is generally higher compared to 5 ml. This suggests that higher oil amount may increase oil removal.
Dot Plot: Ultrasound Time
ggplot(OilDeapsorbtion, aes(x = Ultra, y = Diff)) +geom_dotplot(binaxis ="y", stackdir ="center", binwidth =0.25) +labs(title ="Dot Plot of Difference by Ultrasound Time",x ="Ultrasound Time",y ="Difference in Oil Removed" )
The dot plot shows that ultrasound time of 10 minutes generally has slightly higher and more consistent oil removal compared to 5 minutes. This suggests that longer ultrasound time may improve oil removal.
Interaction Plot
interaction.plot(x.factor = OilDeapsorbtion$Oil,trace.factor = OilDeapsorbtion$Ultra,response = OilDeapsorbtion$Diff,xlab ="Amount of Oil",ylab ="Mean Difference in Oil Removed",trace.label ="Ultrasound Time",main ="Interaction Plot")
The lines in the interaction plot are not parallel and cross each other, which suggests there may be an interaction between oil amount and ultrasound time. This means the effect of ultrasound time may depend on the amount of oil. However, the ANOVA results show that this interaction is not statistically significant.
Check Model Conditions
model <-lm(Diff ~ Oil * Ultra, data = OilDeapsorbtion)par(mfrow =c(1,1)) # reset layoutplot(model, which =1) # Residuals vs Fitted
plot(model, which =2) # Normal Q-Q
plot(model, which =3) # Scale-Location
plot(model, which =5) # Residuals vs Leverage
Residuals vs Fitted
The points are scattered randomly around zero with no clear pattern. This suggests that the model fits the data reasonably well and the linearity assumption is satisfied.
Q-Q Plot
The points are mostly close to the straight line, with a few slight deviations at the ends. This suggests that the residuals are approximately normally distributed.
Scale-Location Plot
The spread of the points is fairly consistent across the fitted values. This suggests that the variance is approximately constant, although there may be slight variation.
Residuals vs Leverage
Most points lie within the boundary lines, with no strong influential points. This suggests that there are no highly influential observations affecting the model.”
Call:
lm(formula = Diff ~ Oil * Ultra, data = OilDeapsorbtion)
Residuals:
Min 1Q Median 3Q Max
-2.55 -0.15 0.00 0.45 1.45
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.5000 0.2281 2.192 0.03490 *
Oil10 1.0500 0.3225 3.255 0.00247 **
Ultra10 0.3000 0.3225 0.930 0.35850
Oil10:Ultra10 -0.7500 0.4561 -1.644 0.10883
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.7212 on 36 degrees of freedom
Multiple R-squared: 0.2432, Adjusted R-squared: 0.1802
F-statistic: 3.857 on 3 and 36 DF, p-value: 0.01719
The results show that the amount of oil has a significant effect on oil removal because its p-value is less than 0.05. However, ultrasound time does not have a significant effect since its p-value is high. The interaction between oil amount and ultrasound time is also not significant. Overall, only the amount of oil affects the difference in oil removed.
The confidence intervals show the average difference in oil removed for each combination of oil amount and ultrasound time. For all groups, the intervals are above 0, which means ultrasound helps remove more oil than the control. The highest oil removal is seen when oil = 10 and ultrasound time = 5. Overall, higher oil amount generally gives higher oil removal.
Most of the group differences are not important because their p-values are greater than 0.05. Only one comparison is important, which is between oil = 5 and oil = 10 at ultrasound time = 5. This means increasing oil amount at 5 minutes increases oil removal. Overall, most group differences are not significant.
Conclusion
This study shows that the amount of oil has a significant effect on oil removal, while ultrasound time does not have a strong effect. There is also no strong interaction between oil amount and ultrasound time. The results suggest that increasing the amount of oil leads to better oil removal. Overall, oil amount is the main factor affecting the difference in oil removed.
