You are interested in examining the factors that determine the average length of

Question

You are interested in examining the factors that determine the average length of stay in a hospital across provinces. You collect data on the following variables:
Y = province-wide average hospital stay
X2 = median provincial income
X3 = 1 if the province is one of the Atlantic provinces, 0 otherwise
X4 = 1 if the province is in Quebec or Ontario, 0 otherwise
X5 = 1 if the province is in the Prairies, 0 otherwise
X6 = 1 if the province is BC or Alberta, 0 otherwise

You run the following regression Y = 1 + 2X2 + 3X3 + 4X4 + 5X5. How would you test whether the average length of stay differs in a statistically significant manner for hospitals in Ontario or Quebec versus hospitals in BC or Alberta?

Explanation / Answer

Since Ontario or Quebec and hospitals in BC or Alberta are categorical variables, and the dependent variable Y = province-wide average hospital stay is a continuous variable. We can perform Two way ANOVA Test to check if the two groups means are significantly different or not.

Two Way ANOVA because we have two independent variables i.e.Ontario or Quebec and hospitals in BC or Alberta

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