代做ECON10151: Computing for Social Scientists Lecture 7: Advanced Data Analysis in Excel using ToolPa

2024-12-18

Lecture 7: Advanced Data Analysis in Excel using ToolPak

ECON10151: Computing for Social Scientists

November 10, 2024

In previous lectures, we covered essential Excel tools for organising and summarising data. We manually calculated mea- sures like the mean, variance, and standard deviation, and used Pivot Tables for flexible data summaries. Today, we’ll take this further by introducing a more efficient method — the Excel Analysis ToolPak.

The ToolPak is an add-in that performs statistical calculations quickly and accurately, allowing you to run analyses with just a few clicks. This is especially valuable for larger datasets, saving time and reducing errors. The ToolPak provides tools for advanced data analysis, including statistical tests, visualisations, and regression, all within Excel.

We’ll start by using the ToolPak to analyse student performance data from a sample dataset with scores of 72 students across different subjects. The dataset includes:

• Student ID

• Gender

• Math score

• Writing score

1 Installation Guide: Setting Up the Data Analysis ToolPak

To get started, let’s make sure the ToolPak is enabled in Excel. Follow the steps below for your specific operating system.

1.1 Mac

To enable the Analysis ToolPak on a Mac:

1. Open the Tools menu.

2. Select Excel Add-Ins.

3. Tick the Analysis ToolPak checkbox and click OK.

4. If the Analysis ToolPak is not listed, click Browse to find it, or select Yes if prompted to install it.

5. Once installed, the Data Analysis button will appear on the Data tab.

1.2 Windows

To enable the Analysis ToolPak on Windows:

1. Navigate to File > Options > Add-Ins.

2. In the Manage dropdown box, choose Excel Add-ins and click Go.

3. Tick the Analysis ToolPak checkbox and click OK.

4. If the Analysis ToolPak is not available, click Browse to locate it, or select Yes if prompted to install it.

5. Once installed, the Data Analysis option will appear in the Analysis group on the Data tab.

1.3 ToolPak Overview

Clicking on Data Analysis opens a dialog box with a variety of tools for performing data analysis using built-in mathematical formulas.

Here are the key tools we will be using today:

• Descriptive Statistics

• Rank and Percentile

• Correlation

• Regression

These tools are crucial for identifying data patterns, summarising information, and supporting informed decision-making. If some of these terms are new, don’t worry — we will cover each tool in detail with practical examples.

2 Descriptive Statistics

The Descriptive Statistics tool is one of the simplest yet most powerful options for summarising data. This tool provides a quick overview by producing essential summary measures, such as the mean, median, and variance. Let’s use this tool to analyse the math score variable in our dataset.

Once the Analysis ToolPak is enabled, follow these steps to generate descriptive statistics in Excel: Step 1: Open the Data Analysis Dialog Box:

• Mac: Go to Data > Data Analysis.

• Windows: On the Data tab, in the Analysis group, click Data Analysis. Step 2: Select Descriptive Statistics from the list and click OK.

Step 3: In the Descriptive Statistics dialog box, set the following options:

(a) Input Range: Select the range of data to analyse. For our example, choose the math scores in C1:C73.

(b) Grouped By: Select whether your data is organised by columns (default) or rows. For this dataset, keep "Columns" selected.

• Choose "Rows" only if your data is arranged horizontally.

(d) Output Range: Specify where to display the results. You can:

• Place the output in a new worksheet to keep things organised, or

• Select a specific cell, such as H1, in the current worksheet, ensuring there is enough space for the output. Note: The output requires at least 2 columns per variable, so make sure there is adequate space.

(e) Tick Summary Statistics to generate key measures. (f) Click OK to produce the table.

The report will include important statistics such as:

• Central Tendency: Measures that summarise the centre of a dataset, including the mean (average value), median (mid- dle value in sorted data),and mode (most common value).

• Variability: Statistics that show how spread out the data is, including:

– Standard Deviation and Variance: Indicate the dispersion of data points around the mean.

– Minimum and Maximum: The smallest and largest values in the dataset.

– Range: The difference between the maximum and minimum, indicating the total spread.

• Sum and Count: The total of all values and the number of data points.

Note: Kurtosis and Skewness are also shown to indicate the shape of the data distribution; the Standard Error shows how much the average value (mean) might vary if we took different samples. It helps indicate how precise the mean is. These details are not crucial to know for this course.

2.1 Analysis Limitations: Text Data

Attempting to generate a descriptive statistics table for the Gender variable will result in an error message: “Descriptive Statistics - Input range contains non-numeric data.”

Text data can be difficult to analyse quantitatively, so it often needs to be recoded into a numerical format:

• Binary Text Data (e.g., yes/no, true/false) can be converted to 0s and 1s for easier analysis.

• Ordered Categories can sometimes be mapped to integers. Examples include:

– Freshman, Sophomore, Junior, Senior

– Strongly Agree, Agree, Disagree, Strongly Disagree

• Some text data may not translate meaningfully into numbers. For instance, country names cannot be easily ranked or quantified.

In our dataset, the Gender column is binary (female/male), so we can recode it as 1s and 0s using the IF function. Recall that this function performs a conditional test, returning one value if the condition is TRUE and another if it is FALSE:

= IF(logical_test,value if true,value if false)

To create a binary numerical variable for Gender, enter the following formula in a new column (e.g., cell E2): = IF(B2 = “female” , 1, 0)

This assigns a value of 1 if the student is female (as indicated in B2) and 0 otherwise. Label Column E as Gender Dummy.

Once recoded, we can generate descriptive statistics for all three variables in the dataset by setting the Input Range in Step

3 above to C1:E73.

3 Rank and Percentile

The Rank and Percentile tool in the Analysis ToolPak helps quickly identify the rank of values in a list and the corresponding percentile for each value. The percentile indicates the percentage of data points that fall below a given number, showing the relative position of each data point within the dataset.

To illustrate, let’s calculate the Rank and Percentile for the writing score data: Step 1: Open the Data Analysis Dialog Box:

• Mac: Go to Data > Data Analysis.

• Windows: On the Data tab, in the Analysis group, click Data Analysis.

Step 2: Select Rank and Percentile from the list and click OK.

Step 3: In the Rank and Percentile dialog box, set the following options:

(a) Input Range: Select the range for the writing scores (e.g., D1:D73). (b) Grouped By: Ensure it is set to Columns.

(d) Output Range: Choose where to display the results (e.g., O1), ensuring there is enough space for the output. (e) Click OK to generate the table.

The output table includes four columns:

• Point: The position of each value in the original list, allowing you to match values to their original order.

• Writing Score: The original data values (e.g., writing scores), retaining the original label.

• Rank: The rank of each writing score, sorted in descending order, shows how each score compares within the dataset.

For example, the highest score will have a rank of 1, the next highest will be 2, and so on. This helps you quickly identify where each value stands in relation to others.

Note: Scores with the same value will share the same rank.

• Percent: The percentile rank indicates the percentage of data points that fall below each writing score. This helps show the relative standing of each score within the dataset.

For instance:

– If a writing score is in the 100th percentile, 100% of the scores in the dataset are lower than this value — this score will have the highest rank.

– If a writing score is in the 50th percentile, 50% of the scores in the dataset are lower — this represents the median.

4 Correlation

Loosely speaking, correlation measures how strongly two variables are related, indicating whether they move together in a similar way:

• A positive correlation means that as one variable increases, the other tends to increase as well (or if one decreases, the other also decreases). For example, as study time goes up, test scores might also go up.

• A negative correlation means that as one variable increases, the other tends to decrease. For instance, as the number of hours spent watching Netflix increases, time spent studying might decrease.

• Correlation takes values between -1 and 1:

– A correlation value close to ±1 indicates a strong linear relationship between the variables, meaning they move closely in sync, either in the same direction (positive correlation) or in opposite directions (negative correlation).

– Values near 0 suggest little to no linear relationship between the variables.

(You will learn about correlation more formally in the Semester 2 Advanced Statistics course.)

To explore the relationship between variables, follow these steps: Step 1: Open the Data Analysis Dialog Box:

• Mac: Go to Data > Data Analysis.

• Windows: On the Data tab, in the Analysis group, click Data Analysis. Step 2: Select Correlation from the list and click OK.

Step 3: In the Correlation dialog box, set the following options:

(a) Input Range: Select the range for the data you want to analyse (e.g., C1:E73 for the scores and gender dummy). (b) Grouped By: Ensure it is set to Columns.

(d) Output Range: Choose where the results should be displayed (e.g., H22), ensuring there is enough space for the output.

(e) Click OK. Excel will generate a table showing the correlation coefficients between the variables.

5 Regression

Regression analysis helps us identify trends and understand relationships between variables. Today, we’ll use Excel to perform simple regression analysis on a dataset from Starbucks. The dataset includes annual advertising costs from 2000 to 2018 in column B (input variable, X) and sales revenues in column C (output variable, Y). Although many factors affect sales, we will focus on these two variables for simplicity.

Previously, we used scatter plots to visualise the relationship between variables by plotting data points.

Today, we’ll take this further by applying simple linear regression, which fits a line to the data to quantify the rela- tionship and make predictions. Specifically, we’ll model the relationship between advertising costs (X) and sales revenue (Y).

Our objective is to learn how to use simple linear regression to predict sales revenue from advertising costs. In short, we want to answer: If we know the advertising cost, can we predict sales revenue, and how?

The linear regression model is expressed as:

Y = a+bX + e,

where:

• X: The input variable (advertising cost).

• Y: The output variable (sales revenue).

• a: The Y-intercept, or the estimated Y value when X is 0.

• b: The slope, which tells us how much Y is predicted to change for a one-unit change in X.

• a+bX: The equation used to predict Y based on X.

• e: The error term, or prediction error — the difference between actual and predicted Y values, also known as the residual.

The e term indicates that our predictions may not be perfect due to factors not included in the model. Usually, e is not zero because other variables, such as customer preferences or store locations, can influence sales revenue.

5.1 Creating a Scatter Plot with a Trendline in Excel

Let’s revisit how to create a scatter plot and add a trendline to visualise a simple linear regression. Follow these steps:

Step 1: Select the Data: Highlight the data range for the input (X) and output (Y) variables. For example, select the range

B1:C20 to include both advertising costs and sales revenues.

Step 2: Insert the Scatter Plot:

• Go to the Insert tab at the top of the Excel window.

• In the Charts group, click on the Scatter icon and select Scatter with only Markers.

Step 3: Add Labels and Titles:

• Click on the chart to activate the Chart Design Tools.

• Click the Add Chart Element icon (the + sign) and add Axis Titles and a Chart Title.

• Label the x-axis as “Advertising Costs (X)” and the y-axis as “Sales Revenue (Y)” .

• Edit the chart title to a descriptive name, such as “Relationship Between Advertising Costs and Sales Revenue” .

Step 4: Add a Trendline:

• Right-click on any data point in the scatter plot and select Add Trendline.

Alternatively, you can click the Add Chart Element icon (the + sign) and choose Trendline from the dropdown menu.

• Choose Linear as the trendline type.

• Tick the Display Equation on chart box to show the regression equation.

• To make the trendline more visible, change the line colour to red and adjust the line style if desired.

Explanation: The trendline represents the best-fit straight line through the data points (in the sense of minimising prediction errors), illustrating the linear relationship between advertising costs and sales revenue. The displayed equation (e.g., y = 1.1343x − 8.0544) is your regression line, where a = −8.0544 is the intercept and b = 1. 1343 is the slope.

5.2 The Regression Tool in ToolPak

We can take this regression analysis further with the Regression Tool in the Analysis ToolPak. This tool allows us to gain more detailed insights into the relationship between variables by providing key statistical outputs.

To perform. regression analysis in Excel:

Step 1: Open the Data Analysis Dialog Box:

• Mac: Go to Data > Data Analysis.

• Windows: On the Data tab, in the Analysis group, click Data Analysis.

Step 2: Select Regression from the list and click OK.

Step 3: In the Regression dialog box, set the following options:

(a) Input Y Range: Select the output variable, e.g., Sales Revenues (C1:C20).

(b) Input X Range: Select the input variable, e.g., Advertising Costs ( B1:B20). (If there are multiple X variables, they should be in adjacent columns.)

(d) Choose where to display the output, either in a new worksheet or in a specific cell (e.g., E1) in the current worksheet, ensuring there is enough space for the results.

(e) Optional settings:

• Check Residuals to see the differences between predicted and actual values.

• Check Line Fit Plots to visualise actual versus predicted values.

• Check Residual Plots to visualise the residuals.

(f) Click OK to generate the regression analysis output.

Key Insights from Regression Outputs:

• The coefficients show the values of a (intercept) and b (slope), which define the regression line equation.

• The residual output includes the predicted Y values, calculated as a+bX for each X , and the residuals, e = Y −(a+bX), which are the differences between actual and predicted Y values.

• The line fit plot shows the actual data alongside the predicted Y values, similar to a scatter plot with a trendline.

To customise the marker format, click any marker in the plot to open the Format Data Series pane. Then, click the Marker button, expand the Marker Options dropdown, and change the setting from Automatic to Built-in to modify the marker style.

• The residual plot visualises the residuals, indicating where the predicted line deviates from actual data points. Positive and negative residuals show over- and under-predictions, respectively.

Note: The output may include standardised residuals and a normal probability plot, which standardise the residuals by their mean and standard deviation to check if they are normally distributed. For this course, you do not need to know these two in detail.

Take-Home Exercise:

Use the Regression Tool to find the line that best predicts the Math score based on the Writing score and Gender from the student performance dataset.

Hint: In Step 3 above, for the Input Y Range, select the Math score (C1:C73), and for the Input X Range, select both the Writing score and Gender Dummy (D1:E73). (You do not need to generate the line fit plot or the residual plot for this exercise.)