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# 统计代写|回归分析代写Regression Analysis代考|Example with Categorical Independent Variables

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## 统计代写|回归分析代写Regression Analysis代考|Example with Categorical Independent Variables

I think of interaction effects as an “it depends” effect. You’ll see why! Let’s start with an intuitive example to help you understand these effects conceptually.

Imagine that we are conducting a taste test to determine which food condiment produces the highest enjoyment. We’ll perform a regression analysis where our dependent variable is Enjoyment. Our two independent variables are both categorical variables: Food and Condiment.
Our model with the interaction term is:
Satisfaction = Food Condiment FoodCondiment The FoodCondiment is the interaction term in the model. Behind the scenes, your statistical software multiples the two variables to calculate the value for the interaction term.

To keep things simple, we’ll include only two foods (ice cream and hot dogs) and two condiments (chocolate sauce and mustard) in our analysis.

Given the specifics of the example, an interaction effect would not be surprising. If someone asks you, “Do you prefer ketchup or chocolate sauce on your food?” Undoubtedly, you will respond, “It depends on the type of food!” That’s the “it depends” nature of an interaction effect. You cannot answer the question without knowing more information about the other variable in the interaction term-which is the type of food in our example!

## 统计代写|回归分析代写Regression Analysis代考|How to Interpret Interaction Effects

Let’s perform our analysis. Download the CSV data file to try it yourself: Interactions_Categorical.

Enjoyment is the dependent variable while Food and Condiment are the independent variables. The p-values in the output below tell us that the interaction effect (Food*Condiment) is statistically significant. Consequently, we know that the satisfaction you derive from the condiment depends on the type of food. In other words, the relationship between Condiment and Enjoyment changes based on the value of Food.

Statistically, it’s just as valid to state that the relationship between Food and Enjoyment changes based on the value of Condiment. While both ways of describing the two-way interaction between Food and Condiment are correct, sometimes one is more appropriate given the subject area. For our study, it’s more natural to start with the food and then determine which condiment maximizes are enjoyment. We don’t usually start with a condiment in mind and then pick the food!

But, how do we interpret the interaction effect and truly understand what the data are saying? The best way to understand these effects is with a special type of graph-an interaction plot. This type of plot displays the fitted values of the dependent variable on the $y$-axis while the $x$-axis shows the values of the first independent variable. Meanwhile, the various lines represent values of the second independent variable.

On an interaction plot, parallel lines indicate that there is no interaction effect while different slopes suggest that one might be present. Below is the plot for Food*Condiment.

The crossed lines on the graph suggest that there is an interaction effect, which the significant p-value for the Food*Condiment term confirms. The graph shows that enjoyment levels are higher for chocolate sauce when the food is ice cream. Conversely, satisfaction levels are higher for mustard when the food is a hot dog. If you put mustard on ice cream or chocolate sauce on hot dogs, you won’t be happy!

Which condiment is best? It depends on the type of food, and we’ve used statistics to demonstrate this effect.

## MATLAB代写

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