Getting Started: Clearing the Work space

In the last lab, we learned that the “data environment” (the upper right hand panel of RStudio) is where all of our data sets are stored. If you look at your Environment now, you will probably see the data set from the last lab. If your Environment is blank, don’t worry about it! If it’s not blank, there is a way to clear your Environment, i.e., remove data sets that you no longer need.

To clear all of the data in the upper right hand panel, look at the top of the panel. Beside “Import Dataset” there is an image that looks like a small broom. Pushing that will “clean” your space, meaning that it will remove all the contents within the panel.

It is good practice to do this before you start each lab. This keeps us from having a lot of unnecessary stuff cluttering up this window, making the data sets you need easier to find.

Everything we learned in Lab 1 still applies. Flip back to those more detailed instructions as you need to throughout the course. We recall that we begin every new lab by creating a Markdown file. Go ahead and do that, and remember that you need to delete everything after the first chunk in the template that comes up. You will do this for every Markdown you create in this class.

Now that you have a clean template and a clean Environment, we’re ready to start a new lab.

Loading the Data: Coffee, anyone?

Today, we are going to work with data on nutrition information for Tall (12 ounce) drinks at Starbucks. You can download the data from here., or following copying and pasting the following into your browser: https://drive.google.com/file/d/1KAxD9jTODqeI4zOErDsL6zg0PYqeBEm0/view?usp=sharing

Now that you have downloaded the data, let’s move it into R!

• Step 1 Look at the upper right hand panel of your RStudio screen (the Environment tab).
• Step 2 Find “Import Dataset” or “Import” and click on it. If you don’t see it, look for this symbol instead and click on it. If you have none of these, let Dr. Dalzell know!!

• Step 3 Choose “Text (base)” or “From CSV” (it will depend on your computer).
• Step 4 Navigate to your data (Starbucks.csv) in the list that comes up. Choose it!
• Step 5 Now, look the bottom right hand panel of your screen. You should see a line of code with something like Starbucks <- read.csv(“Starbucks.csv”) or Starbucks <- read.csv(“Starbucks.csv”). Copy that ENTIRE line of code.
• Step 6 In your Markdown file, insert a code chunk.
• Step 7 Paste the line from Step 5 into this gray code chunk, and press the green arrow (the play button).

This means your Markdown should currently look like this (though what is inside the “” will look different for you, as it will point to where the file is on your computer!!)

And you are ready to go!! You now have the data loaded and you can work with it!

Exploratory Data Analysis

Based on the name of this lab and the stated goals, it’s probably safe to assume we will be using a LSLR line for the relationship between our two variables of interest. However, in practice we will not have that information at the beginning of an analysis. What we will have is data, and a question of interest. It is then the job of the statistician to determine what techniques are appropriate to help address the question of interest.

Sugar content and its relationship to the obesity epidemic in the United States is a hot topic of research and debate. Restaurants are being required to post calories and sugar content of items on their menus, and companies like soda manufacturers are posting information cautioning consumers on the health risks associated with sugar. Today, we are going to explore the relationship between sugar content and the number of calories in 230 Starbucks beverages. Specifically, we want to answer the question: Is higher sugar content associated with higher calories in Starbucks beverages? In other words, as sugar content increases, is this associated with higher calories?

With our question of interest defined, we can now begin the process of exploring the data. As a first step, we will conduct exploratory data analysis, or EDA. This process of visualizing and otherwise exploring the data provides information that will help us decide on statistical techniques appropriate for the task we are trying to accomplish. This is the first step in any modeling task. .

The process of conducting EDA is different for different types of data. If we have one numeric variable, for instance, we tend to make a histogram or a box plot. Sometimes we can tell what type of variable we have just by looking at the data. However, we can also use R to help us. To use R to determine whether a variable is numeric, we use the command class. For instance, to check to see what kind of variable calories is, we can use the code:

class(Starbucks$Calories)

Notice that when we run this code, R returns the word "integer", which tells us that calories contains only integers, and is therefore a numeric variable. The result "numeric" is another option that suggests we have a numeric variable.

In this code that we have provided R (1) the name of data set and (2) the name of the column. This means that if you want to get the class of calories, you actually need the code Starbucks$Calories. This tells R “Hey, look at the data set Starbucks and grab a column ($) called Calories”.

Why do we need to bother to check this? Didn’t we learn how to distinguish numeric and categorical variables in intro stat? We did, but just because our intuition tells us that a variable should be numeric does not mean the creators of the data set chose to record the values as a number. For instance, let’s consider the variable VitaminA, which tells us how much Vitamin A is in each Starbucks drink. Our intuition likely tells us that this is a numeric variable. Let’s check.

The moral of the story: It is important to check to see how a variable is actually recorded in a data set. It may not be what you think!

Sugar and Calories

Let’s return to our research question. Is higher sugar content associated with higher calories in Starbucks beverages? This means that we are going to focus our attention on two variables: Calories and Sugars.

ggplot( dataset, aes( x = explanatory variable, y = response variable)) + 
  geom_point( ) + 
  labs( x = "X axis label", y = "Y axis label")

Now that we have used R to create a plot, we need to read it. Reading a plot means interpreting the information the plot is telling us. When we create a plot for two numeric variables, there are typically four pieces of information we try to read:

1. Form (Shape): What is the shape of the relationship? Does it look like the pattern in the plot can be described by a line? A curve?
2. Strength: Does the relationship between these variables seem to be strong, weak, moderate, or is there no apparent relationship?
3. Direction: Is the relationship positive, negative, or flat (no relationship)?
4. Outliers: Are there any points that seem not to follow the trend of the rest of the data?

There is a reason why we are interested in these four specific questions. The first question ( What is the shape of the relationship?) tells us whether or not using a line makes sense for this data set. All models have assumptions. A big one for LSLR lines is that the relationship between the two variables we are modeling should be able to be described using a line. In other words, the relationship should look linear. If it does not, we should not use a LSLR line.

The second question tells us whether or not there seems to be an informative relationship between the variables. If there is really no relationship, building a statistical model is not going to be particularly useful.

We have learned that one way to quantify the strength of a linear relationship is with the correlation. To determine the correlation of two variables firstvariable and secondvariablein R, use the following code:

cor(firstvariable , secondvariable )

To do this with your data, replace firstvariable and secondvariable with your variables of interest. Remember that do to do this, you have to provide R (1) the name of data set and (2) the name of the column. This means that if you want to use Caloriesas your first variable, you actually need to type Starbucks$Calories.

The third question (Is the relationship positive, negative, or neither?) tells us what sort of slope to expect when we fit a LSLR line to the data. Do we expect a positive slope? A negative one? This intuition will allows us to check our model once we fit it. Do the results of the model make sense with what the plot is telling us?

The fourth question (Are there any points that seem not to follow the trend of the rest of the data?) helps with identifying points that can strongly impact the fit of a model. We’ll learn more about these in coming classes.

At this point in the course, this is the end of EDA. One plot, and the correlation. As we move deeper into the material, we will learn that there are more things to look for in this stage of the modeling process. For now, the thing to keep in mind is that the first step to any modeling task is some form of EDA. This helps us to choose the form of the model that might be appropriate for a given data set.

Estimating the slope and intercept

We have seen the formula in class for how to compute the slope and intercept of the LSLR line. However, today we want to focus on how we would typically find these values in the real world by using statistical computing.

To obtain the slope and intercept for our LSLR line in R, create a chunk, copy in the following code, and press play:

lm(Calories ~ Sugars, data = Starbucks)

This code is a little different from those we have worked with. The command lm tells R that we want to build an LSLR line. Our next step is to tell R what to use to actually build the line. What is the response variable? What is the explanatory variable?

To tell R what variable to use to create the line, we use a formula that takes the form y ~ x. See how our code says lm(Calories~Sugars, data = Starbucks)? This can be read as telling R we want to make a LSLR line (lm) with Calories as our response variable and Sugars as our explanatory variable. We notice that we don’t use the $ notation here. Why? Because there is a part of the command that specifies that R should look in the Starbucks data frame to find the Calories and Sugars variables.

The output of lm shows us the values of \(\hat{\beta}_0\) and \(\hat{\beta}_1\) that we need to make our LSLR line.

Now that we have the line, we can start to describe the relationship between sugar and calories in a little more detail than we did with our scatter plot. Instead of just saying that we have a positive relationship, we can say something more specific.

Visualizing the LSLR line

Now that we have created our line, we can also draw this line on top of our scatter plot. To do so, copy and paste the following code into a chunk and press play:

ggplot(Starbucks, aes(x=Sugars, y = Calories)) +
     geom_point() + 
     stat_smooth(formula = y ~ x, method = "lm", se = FALSE) + 
     labs(x = "Sugars (in grams)", y = "Calories" , title = "Figure 2")

The first two lines of the code above are familiar - we did these earlier today! The third line is new. This part of the code (stat_smooth(...)) tells R to draw the LSLR line onto the scatter plot.

We notice that even though the relationship between sugars and calories is linear, the line will not go through every single dot on the graph. Some dots are below the line, and some dots are above the line. This should not surprise us. A LSLR line is a way to approximate the relationship between the response variable Y and explanatory variable X. If it went through every point, we would not have a line!

It turns out that choosing a line has some distinct advantages. The first is that lines are not difficult to use.