## Introduction

Chapter 1 introduces linear models and statistical control. Among the topics that are relevant to your work includes the addition of “tidy data”. Below, several examples are provided wherein we further discuss each of these topics. Given this is an introductory chapter, we do not go into much depth here.

## Linear Models

1. Linear models are just that: a model that describes linear relationships. Why, in all the complexity of the behavioral and social sciences, could linear models be useful?

2. Consider the following quote: “All models are wrong; some models are useful,” ( George E. P. Box ). How does this apply to our discussion about linear models?

3. What methods have you learned that are actually a linear model?

## Statistical Control

In the following situations, which would need statistical controls? If some are needed, provide an example of a variable that could be a control variable.

1. We are looking at the relationship between weight gain (outcome) and depression (predictor).
2. We randomly assign individuals to treatment or control and assess their outcomes 3 weeks later.
3. We investigate the effect of musical ability on understanding foreign accents.

## Tidy Data

Consider the following situations and decide if each is currently in “tidy” form and why.

1. Data set that has a variable called depr_time1
2. Data set that has a variable called time
3. The following data set:
## # A tibble: 5 x 5
##   id            x_1   y_1    x_2   y_2
##   <chr>       <dbl> <dbl>  <dbl> <dbl>
## 1 Subject 1  3.12   0.831 -1.24  0.131
## 2 Subject 2  0.119  0.140 -0.711 0.797
## 3 Subject 3  0.0986 0.124 -0.324 0.455
## 4 Subject 4 -0.543  0.699 -0.562 0.697
## 5 Subject 5 -0.643  0.237  0.256 0.571
1. The following data set:
## # A tibble: 4 x 3
##   id             x     y
##   <chr>      <dbl> <dbl>
## 1 Subject 1 -0.218 0.585
## 2 Subject 1 -0.322 0.631
## 3 Subject 2  1.43  0.403
## 4 Subject 2 -1.35  0.775