Week 5: Linear Regression - Feedback & Analysis

Oct 21, 2025 by SLV Team 48 views

Hey guys! Let's break down the feedback from Week 5 on Linear Regression. You all did a fantastic job, and I'm stoked to see your progress! This week's exercises were all about getting hands-on with linear regression, from loading and inspecting data to building and interpreting models. Let's dive in and see what we covered, how you all performed, and what we can learn from it. Buckle up, because we're about to explore the world of data and regression, making sure you grasp every detail.

Overall Grade and Performance

First off, huge congrats on the outstanding performance! The overall grade was a solid 10/10, which means you all crushed it. Seriously, well done! The table below provides a detailed breakdown of each exercise, showing the points possible, the grade you achieved, and a brief overview. We'll go through each section individually, but this table gives you a quick snapshot of where you shined and where the focus was.

Exercise	Points Possible	Grade
1.1. Load and inspect DNM data	0.5	0.5
1.2. Create per-proband maternal and paternal DNM counts	0.5	0.5
1.3. Load and inspect parental age data	0.5	0.5
1.4. Join counts with ages into a merged table	0.5	0.5
2.1. Scatter plots for maternal and paternal DNMs vs. parental age	1	1
2.2. Fit and interpret maternal OLS model	1	1
2.3. Fit and interpret paternal OLS model	1	1
2.4. Predict paternal DNMs for age 50.5	0.5	0.5
2.5. Plot distributions of maternal vs. paternal DNMs	1	1
2.6. Paired t-test (`t.test` and `lm(diff ~ 1)`) and interpret results	1.5	1.5
3.1. Choose and document TidyTuesday dataset	0.5	0.5
3.2. Produce exploratory figure(s)	0.5	0.5
3.3. Pose and test a linear-model hypothesis and interpret results	1	1

As you can see, you nailed every exercise! The consistency in performance is truly impressive. Now, let's zoom in on each section to appreciate the work done and the key concepts explored during the week. Understanding the details behind each exercise can further enhance your skills.

Detailed Exercise Breakdown

Section 1: Data Loading, Inspection, and Preparation

In the first part of this journey, we focused on the very core of data analysis: loading, inspecting, and preparing the data. The goal was to ensure you're comfortable with the initial steps required to kick off any data project. This foundational work sets the stage for everything that follows, so getting it right is crucial. The tasks in this section aimed to equip you with the fundamental skills for handling data effectively.

1.1. Load and inspect DNM data (0.5/0.5 points): This involved loading the DNM (De Novo Mutation) data and taking a close look at it. This exercise emphasizes the importance of understanding your data from the get-go. Inspecting the data helps you get a feel for its structure, missing values, and any initial patterns. Think of this as getting to know your data before you start analyzing it. This initial step is vital for ensuring the accuracy and reliability of any further analysis, ensuring that you're well-prepared for more complex analytical tasks.
1.2. Create per-proband maternal and paternal DNM counts (0.5/0.5 points): Here, the objective was to calculate the counts of DNMs for both maternal and paternal sides. This involves grouping the data by proband (the individual being studied) and summing up the mutations. This step is essential because it transforms the raw data into a more usable form for analysis. Creating these counts provides a clearer picture of the data, helping to see differences or trends that might not be immediately apparent. By summarizing the data in this manner, you gain a better handle on the key metrics, making it easier to identify patterns and draw meaningful conclusions. This process is like creating a summary table to highlight important information.
1.3. Load and inspect parental age data (0.5/0.5 points): This exercise focused on loading parental age data, which is an important factor in the analysis. This step ensures that you have access to the necessary information for the subsequent analyses. Understanding parental age is crucial because it's often linked to the occurrence of DNMs. Like with the DNM data, understanding the parental ages allows you to identify trends or associations between parental age and mutation rates.
1.4. Join counts with ages into a merged table (0.5/0.5 points): The last task in this section involved merging the DNM counts with the parental age data. This combines the two datasets into one, which is essential for conducting further analysis. Merging the data brings together all the relevant information into a single table. This makes it possible to investigate the relationship between DNM counts and parental age. This step is a critical preparation for the next stage of the analysis, where you'll start modeling the relationship between these variables.

Section 2: Building and Interpreting Linear Models

Now, let's explore the exciting world of linear models! Section 2 dives deep into building, interpreting, and applying linear regression models. This part is where we see how to use data to make predictions and understand the relationships between different variables. You'll not only learn to build these models but also how to interpret their results, ensuring you can make informed decisions based on your data. This section provides the foundation for using linear models in more complex real-world scenarios.

2.1. Scatter plots for maternal and paternal DNMs vs. parental age (1/1 point): In this exercise, the goal was to create scatter plots to visualize the relationship between DNMs and parental age. Visualizing the data through scatter plots is crucial because it allows you to see the relationships between variables at a glance. By plotting DNM counts against parental age, you could look for patterns like an increase or decrease in mutations as parents get older. This step is critical because it visually explores the data and aids in determining whether a linear model is appropriate. The scatter plot allows for the quick identification of potential trends or outliers. This step provides a visual foundation for building your models.
2.2. Fit and interpret maternal OLS model (1/1 point): Here, you built an Ordinary Least Squares (OLS) model for maternal DNMs. This involves estimating the parameters of a linear equation to fit the data. The interpretation of the model is critical. It involves understanding the coefficients and their meaning. For example, how does the maternal age affect the number of DNMs? This task demonstrates how to build and understand the linear models. Knowing how to interpret the results will allow you to make conclusions based on the data. This skill is useful when trying to infer the impact of different factors on the outcome variables.
2.3. Fit and interpret paternal OLS model (1/1 point): Similar to the previous exercise, you created an OLS model but this time for paternal DNMs. This reinforces the concepts covered and ensures you know how to apply these techniques to different datasets. Understanding the paternal data helps in creating a comprehensive analysis. By comparing the results of the maternal and paternal models, you can draw more robust and detailed conclusions. This comparison helps in understanding if different factors affect the DNMs. The models will help to determine if paternal age has the same effect as maternal age.
2.4. Predict paternal DNMs for age 50.5 (0.5/0.5 points): Using the paternal model, you were tasked with predicting the number of DNMs for a father aged 50.5 years. This exercise shows how to use the model to make predictions. By inputting the specific age, you can predict what the model suggests for the outcome variable. This exercise is practical because it directly applies the developed models for real-world scenarios. It allows you to visualize how the model works. This step is essential in the practical application of linear regression, showing how to derive actionable insights from your models.
2.5. Plot distributions of maternal vs. paternal DNMs (1/1 point): This exercise focused on plotting the distributions of maternal and paternal DNMs. Creating visualizations of the distribution of both maternal and paternal DNMs provides a clear visual comparison of their occurrence. By comparing the distributions, you can identify any differences in the data, which may not be obvious from a numerical analysis alone. This provides a visual representation of the datasets that can highlight patterns, outliers, and skewness, all of which are essential in interpreting the results. The comparison gives valuable insights into the data.
2.6. Paired t-test (t.test and lm(diff ~ 1)) and interpret results (1.5/1.5 points): This exercise involved conducting a paired t-test to assess the differences between maternal and paternal DNMs. Both the t.test and the linear model approach (lm(diff ~ 1)) were used to reinforce the understanding of hypothesis testing in linear models. This test is designed to measure whether the mean difference between two related groups is significantly different from zero. The interpretation of these results is critical, allowing you to determine if there is a statistically significant difference between maternal and paternal DNMs. This skill is critical when comparing two different datasets and determining whether the differences observed are likely due to chance or a true underlying effect.

Section 3: Exploring and Testing with a TidyTuesday Dataset

Let's get creative! In the last section, we applied the linear modeling techniques to a TidyTuesday dataset. This is a brilliant way to explore real-world data and solidify the concepts you've learned. It challenges you to pose your own questions, build hypotheses, and test them. It's all about taking what you've learned and applying it to something new.

3.1. Choose and document TidyTuesday dataset (0.5/0.5 points): This is where you picked a TidyTuesday dataset, and the first step was to choose a dataset and document it. This allows for exploration of different topics. Selecting a dataset and documenting it shows that you can independently find and document relevant data sources. This step sets the stage for any analysis.
3.2. Produce exploratory figure(s) (0.5/0.5 points): The next step was to create exploratory figures. Creating figures helps in exploring and understanding the data. Exploratory figures are used to visually explore the dataset. These figures help you to understand the data's characteristics, identify patterns, and reveal potential areas of interest. This ensures a more informed approach.
3.3. Pose and test a linear-model hypothesis and interpret results (1/1 point): The final task involved posing a hypothesis and testing it using a linear model. This is where you apply all the skills you've acquired to answer a specific question using a linear model. Interpreting the results is crucial. This helps in drawing conclusions and assessing the validity of your hypothesis. It brings all the elements together, from data selection to interpretation.

Final Thoughts and Next Steps

Overall, you all did an amazing job! I'm genuinely impressed with your understanding of linear regression and your ability to apply these concepts. The feedback I provided aims to highlight the areas where you excelled and provide insights on refining your approach. As you move forward, keep practicing, keep exploring, and keep challenging yourselves. The skills you've developed are incredibly valuable, and with continued effort, you'll become even more proficient in data analysis and linear regression.

Keep up the great work, and I'm looking forward to seeing what you accomplish in the future. Don't hesitate to reach out if you have any questions or need further clarification. Let's keep the learning going, guys!