# Using MANOVA to Analyse a Banking Crisis Exercises

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In this set of exercises we will practice multivariate analysis of variance – MANOVA.

We shall try to find if there is a difference in the combination of export and bank reserves, depending on the status of banking sector (is there a crisis or not). The data set is fictitious and servers for education purposes only. It consist of variables `crisis`

, which is factor, meaning that there exists or there does not exist banking crisis and `export`

and `reserves`

, in billions of currency units. You can download it here.

In this set of exercises we use two packages: `MVN`

and `heplots`

. If you haven’t already installed them, do it using the following code:

```
install.packages(c("MVN", "heplots"))
```

and load them into the session using the following code:

```
library("MVN")
library("heplots")
```

before proceeding.

Answers to the exercises are available here.

If you have different solution, feel free to post it.

**Exercise 1**

Is the sample size large enough for conducting MANOVA? *(Tip: You should have at least 2 cases for each cell.)*

- Yes
- No

**Exercise 2**

Are there univariate and multivariate outliers?

- There are univariate, but not multivariate outliers
- There doesn’t exist a univariate outlier, but there are multivariate outliers
- There exist both univariate and multivariate outliers

**Exercise 3**

How do you estimate univariate and multivariate normality of dependent variables?

- Both variables are univariate normal, but they are not multivariate normally distributed
- None of the variables is univariate normal, and hence there doesn’t exist multivariate normality
- Both variables are univariate normal and the data is multivariate normally distributed

**Exercise 4**

Using the matrix of scatter plots, check for the linearity between dependent variables `export`

and `reserves`

for each category of independent variable.

**Exercise 5**

Calculate the correlation between dependent variables `export`

and `reserves`

. Is it appropriate to justify conducting MANOVA?

- Yes
- No

**Exercise 6**

Is there equality of covariances of the dependent variables `export`

and `reserves`

across the groups. *(Tip: You should perform Box’s M test of equality of covariance matrices.)*

- Yes
- No

**Exercise 7**

Is there equality of variances of the dependent variables `export`

and `reserves`

across groups? *(Tip: Use Levens’s test of error variances.)*

- Yes
- No

**Exercise 8**

On the level of significance of 0.05, is there effect of banking crisis to export and banking reserves combination?

- Yes
- No

**Exercise 9**

How much of the variance in the dependent variables `export`

and `reserves`

is explained by banking crisis?

**Exercise 10**

Does the export differ when banking sector is in the crisis compared to when banking sector is not in the crisis? What about reserves?

- Only export differ
- Only reserves differ
- Both export and reserves differ
- None of them differ

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