Activity 5: Two-way ANOVAWith two factors, there is an additional question beyond whether each factor separately is significant: Is there an interaction between the two factors? That is, does the effect of one factor depend on the level of the other factor?To illustrate this, let’s consider the effects of ethanolic NaOH concentration and coal typeon total acidity. Each of these factors has three levels. Open the data from the website.1. First, let’s look at an interaction plot. Go to Stat > ANOVA > Interactions Plot…. Enter Acidity as the response and NaOH and Coal Type as the factors (in that order). Copy and paste the interaction plot below. For Morwell coal, what concentration of NaOH gives the highest mean acidity? for Yallourn? for Maddingley? Since the lines (for each concentration of NaOH) are roughly parallel, it appears that the effect of NaOH concentration does not depend on the type of coal. This suggests that there is NO INTERACTION between the factors. Thus, when we perform a two-way ANOVA, the interaction term will probably not be significant. (Check but do not answer:Do you get a different intuition if you produce an interaction plot with the factors in the other order?)2. So let’s look at the results. Go to Stat > ANOVA > Two-way…. Enter Acidity as the response, NaOH as the row factor and Coal Type as the column factor. Copy and paste the ANOVA table (and ONLY the table) below. What are the test statistic and p-value for the interaction term? What can you conclude?If the interaction term is not significant, then we can focus on the main effects…the effects of the individual factors.3. Since the interaction term isn’t significant, let’s not waste those 4 degrees of freedom on the interaction when they could be used to give a more accurate estimate of the mean square error. Refit the model without the interaction term by clicking the “Fit additive model” box in Stat > ANOVA > Two-way…. Paste the new ANOVA table below. Does NaOH concentration have a significant effect on acidity? What about the type of coal?Let’s consider a different example…the effects of brand of pen and writing surface on writing lifetime.4. Obtain an interaction plot (paste it below). Which brand of pen lasted longest on the first surface? the second surface? the third surface?Here, the effect of brand depends on the surface! This suggests that THERE IS AN INTERACTION between the two factors. Notice that the lines cross (intersect) multipletimes. Thus, we will most likely find a significant interaction term.5. Perform a two-way ANOVA. Be sure NOT to fit the additive model so that you can obtain an interaction term. What are the test statistic and p-value for the interaction term?What can you conclude?That’s it. However, a word to the wise: Be sure you know how to use the Stat > ANOVA> General Linear Model… function to obtain a two-way ANOVA table with an interaction term, just in case you need it for the homework in order to obtain Tukey