# An experiment was conducted to determine whether firing temperature and/or furnace position…

An experiment was conducted to determine whether firing temperature and/or furnace position affect the baked density of a carbon anode. The file Anode_Density.xlsx contains density measurements of sixty carbon anodes subjected to various furnace positions and temperature levels. The columns are:column 1: furnace position (1 or 2),column 2: temperature (low=1, medium=2. High=3),column 3: density.Analyze this data set using the ANOVA method. Perform a complete analysis and prepare a thorough report as you would do for a client. This report should include all the steps used in the analysis, their justifications and your conclusions. Also comment on the possible improvements that can be made on your analysis if you detect unequal variance, outliers etc. Please paste the relevant portions from your computer printouts along with codes that you have used.ANOVA Model Analysis on Anode Density Data1. IntroductionThe Anode Density Data contains density measurements of sixty carbon anodes subjected to various furnace positions and temperature levels. For the furnace positions, there are two levels 1 and 2. For the temperature variable, there are 3 levels: 1 is for low temperature, 2 is for medium temperature and 3 is for high temperature. From this dataset, we want to know whether firing temperature and furnace position have effects the baked density of a carbon anode. Since the two variables are categorical, ANOVA model will be applied to conduct data analysis.2. Data AnalysisSince in the data, we only two categorical variables, thus there are three potential variables we need to evaluate: main temperature variable, main position variable and interaction variable between temperature and position.2.1 Variable Main effectsLook at the box-plot for each factor:From the boxplot above, we can see there is an obvious difference in anode density for different temperatures. However, the left boxplot shows that the difference is less pronounced between 2 different positions. The variance appears to be equal and not related to the mean response.2.2 Variable Interaction EffectThen we can draw interaction plots to determine whether an interaction term should be included in our ANOVA model.The interaction plots above show parallel patterns indicating there is no interaction effect between position and temperature.2.3 Model FittingIn order to further confirm whether we should fit a two-way ANOVA with an interaction term, we fit the following model:From the result above, we can see that there is no evidence of a significant interaction effect (F = 0.71, p = 0.4962). Therefore, we cannot conclude that there is an interaction effect between position and temperature. However, the two main effectsposition effect and temperature effect are both very significant. For the position main effect: F value is 165.80 and pr