**Make sure you run this chunk before attempting any of the problems:**

```{r setup, message=FALSE, warning=FALSE}

library(tidyverse)

library(sjPlot)

```

# The demand for cocaine

This data on cocaine sales contain 56 observations on variables related to sales of cocaine powder in northeastern California over the period 1984-1991. The data come from a a study by Caulkins, J. P. and R. Padman (1993), Quantity Discounts and Quality Premia for Illicit Drugs, Journal of the American Statistical Association, 88, 748-757.

```{r cocaine data, message=FALSE, warning=FALSE}

cocaine = read_csv("https://query.data.world/s/k2dlmaj4mtn3swiqbjziqoyrux653g")

```

The variables are:

| **Variable name** | **Description** |

|-------------------|-------------------------------------------------------|

| `price` | price per gram in dollars for a cocaine sale |

| `quant` | number of grams of cocaine in a given sale |

| `qual` | quality of the cocaine expressed as percentage purity |

| `trend` | a time variable with 1984=1 up to 1991=8 |

**[Q1.1] [CODE] Plot a histogram of prices..**

```{r q1.1 code}

# hist(read_csv)

```

**[Q1.2] [CODE] Plot price as a function of quantity and comment on what you see (i.e. linear or nonlinear relationship). Include a regression line.**

```{r q1.2 code}

# your code here

```

**[Q1.2] [WRITE] If you were to estimate the following model, what signs (postive or negative) would you expect for $\beta_1$, $\beta_2$, and $\beta_3$, and why?:**

$$

price = \beta_0 + \beta_1quant + \beta_2 qual + \beta_3trend + \epsilon

$$

**[Q1.4] [CODE] Estimate the model and assign the output to the object `cocaine_model`. Then use `summary()` to view the results.**

```{r q1.4 code}

# your code here

```

**[Q1.5] [WRITE] It is claimed that the greater the number of sales, the higher the risk of getting caught. Thus, sellers are willing to accept a lower price if they can make sales in larger quantities. Based on the regression results, do sellers offer quantity discounts?**

**[Q1.6] [WRITE] Do consumers pay a premium for higher _quality_ cocaine? Why or why not?**

**[Q1.7] [WRITE] According to your model, do prices change over time? Why or why not?**

**[Q1.8] [WRITE] Explain two limitations with the data.**

**[Q1.9] [WRITE] Explain two limitations with the model**

**[Q1.10] [CODE] Use `sjPlot` to plot the predicted prices for different quantities.**

```{r q1.10 code}

# your code here

```