DO NOT USE CHATGPT $($ you can use your own values or simulate $).$do it manually and on R$/$python$.$

Imagine you are conducting a factorial experiment to study the effects of diet, exercise, and

supplementation on health outcomes. The factors and their levels are as follows:

Factor A: Diet $(3$ levels: Low, Medium, High$)-$ Fixed Effect

Factor B: Exercise $(2$ levels: None, Daily$)-$ Fixed Effect

Factor C: Supplement $(2$ levels: With, Without$)-$ Fixed Effect

$1.$ Calculate the total number of possible treatment combinations for the given levels of each

factor.

$2.$ Create a full factorial design matrix that lists all possible combinations of the levels of

Factors A$,$ B$,$ and C$.$ Each row should represent a unique treatment combination.

$3.$ Assume you have collected data on a response variable $($e$.$g$.,$ a health outcome$)$ for each

treatment combination. Perform a factorial ANOVA to assess the main effects and

interaction effects of Factors A$,$ B$,$ and C on the response variable.

$4.$ Provide the ANOVA table summarizing the results, including the sum of squares, degrees of

freedom, mean squares, F$-$values, and p$-$values for each main effect and interaction.

$5.$ Interpret the p$-$values to determine which factors and interactions have statistically

significant effects on the response variable. Discuss the implications of these findings.

DO NOT USE CHATGPT