---
title: "Assignment: interactions in linear models"
output: html_document
---

# Exercise 1

Read the following fragments from the "Applied multiple regression" book which you can find on the course webpage. We will be interested in Chapter 7 ("Interactions Among Continuous Variables"). Students who are interested (that is a majority) should read the whole chapter, but if some of you cannot manage 50 pages, read the following sections:

- 7.1 Introduction (p. 255 - 260)
- 7.2 Centering Predictors And The Interpretation Of Regression Coefficients In Equations Containing Interactions (p. 261 - 267)
- 7.3 Simple Regression Equations And Simple Slopes (p. 267 - 272)
- 7.4.1 Standard Error of Simple Slopes, 7.4.3 Test of Significance of Simple Slopes (p. 272-273)
- 7.7 Patterns of First-Order and Interactive Effects (p. 285 - 286, only first subsection)

# Exercise 2

In our analysis of relationships between years of service, years since PhD, and salary we have noticed that $R^2$ of the model with interaction is much larger than $R^2$ of the model without one. Is this difference statistically significant? Check it using the method for nested models.

```{r, echo = F}
# Your code here
```

# Exercise 3

Load the `carData` library which contains `Ginzberg` dataset. This dataset concerns patients treated for depression. In the `depression` column are scores of the Beck Depression Inventory (https://en.wikipedia.org/wiki/Beck_Depression_Inventory). In the `fatalism` column are scores on the fatalism scale (I guess this one: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2924582/).
In the `simplicity` column is a score measuring a subject's need to see the world in black and white. Fit a model with interaction with depression as a dependent variable 

```{r}
# Your code here 
```

Then answer the following questions:

1. What is the pattern of interaction here? Describe it and illustrate it using plots from the `interactions` library (or some other graphical representation).

```{r}
# Your code here 
```

2. Is the model with interaction better fitted to the data compared to the model without it? Compare their $R^2$ statistics.

```{r}
# Your code here
```