PowerPoint Presentation

SRHC Business Analytics: Module 4 & 5. Regression Analysis.

[Audio] Recognizing trends in data allows us to identify patterns and connections within our information. This skill is crucial when analyzing complex datasets. By detecting outliers, we ensure that our findings are accurate and reliable. Summarizing data sets concisely enables us to communicate our results effectively, making it easier to share insights with others. Analyzing relationships between variables helps us uncover hidden correlations and dependencies, ultimately leading to more informed decision-making..

[Audio] The statistical technique of linear regression models and analyzes the relationship between a dependent variable, which is often referred to as the response variable, and one or more independent variables, also known as predictors or explanatory variables. The objective is to discover the best-fitting straight line, also known as the regression line, that runs through the data points, thereby minimizing the disparity between observed values and predicted values. In simple linear regression, there is only one independent variable..

[Audio] Inferential statistical analysis enables us to infer properties about a population by analyzing a sample of data. This process involves testing hypotheses and estimating population parameters. Unlike descriptive statistics, which solely focuses on summarizing the characteristics of the observed data, inferential statistics makes assumptions about the larger population..

[Audio] Linear regression is a fundamental concept in many fields, including economics, finance, biology, and social sciences. It allows us to make predictions, identify trends, and understand relationships between variables. We must consider some underlying assumptions. The dependent variable, y, represents the outcome or result we're trying to predict. The independent variable, x, includes all the input variables that affect our outcome, each with its own variation, plus the inherent variation of the process itself. In multiple linear regression, we consider multiple independent variables. Understanding these concepts enables us to grasp the terminology used in regression analysis..

[Audio] A scatter plot is a powerful tool that allows us to visualize the relationship between two variables. By plotting one variable against another, we can see if there's a connection between them. This type of plot helps us identify whether there's a cause-and-effect relationship between the variables..

[Audio] When creating a scatter plot, we need to ensure that our data pairs up correctly in Excel. Each point on the graph represents a single observation or item, where we've measured two factors. For instance, if we're examining the connection between call length and broker's experience, each point would symbolize a unique call, accompanied by its corresponding duration and expertise level. Without suitable pairing, our diagram would be pointless, and we wouldn't be able to accurately visualize the data..

[Audio] Visualizing the data can be a powerful tool in our analysis. By using a scatter plot, we can see patterns emerge from the data, supporting or refuting our initial theories. This helps us refine our hypotheses and even predict what might happen if certain conditions were met. However, it's essential to remember that correlation doesn't necessarily mean causation. We need to be cautious when extrapolating our findings beyond the scope of the original data..

[Audio] When examining relationships between variables, it's essential to distinguish between correlation and causation. Just because two variables appear to be related doesn't mean one causes the other. There might be lurking variables influencing the outcome. To establish a cause-and-effect relationship, we need to consider additional factors and use techniques like regression analysis to isolate the impact of each variable. We'll explore these concepts further throughout this module..

[Audio] Scatter plots enable us to visualize how one factor influences changes in another. This graphical representation assists in developing and verifying our hypotheses. Furthermore, we can assess the strength of the relationship by examining the scatter plot's width or tightness. However, it is crucial to remember that correlation does not necessarily imply causation. We must exercise caution when interpreting these findings. Let's examine some examples. A no-correlation pattern signifies the absence of any apparent connection between the variables. Conversely, positive, curvilinear, and negative correlations indicate distinct types of relationships. By analyzing these patterns, we can derive valuable insights into the behavior of our data..

[Audio] The scatter plot shows a positive correlation between the delivery time per pizza and the number of pizzas delivered, suggesting that the number of deliveries may influence the customer's wait time. However, correlation alone cannot establish causality, and further analysis is required to confirm the relationship..

$2,136 per inch for males $955 per inch for females.

[Audio] Now we're introducing a new type of plot called a time series plot. This plot shows how a variable changes over time. We can use this plot to visualize patterns in our data and identify any unusual events or anomalies. By looking at this plot, we can see if there's a trend in the data, whether it's increasing or decreasing, and if there are any seasonal fluctuations..

[Audio] The time series plot shows the population of Salina increasing steadily over time, with occasional fluctuations. This type of visualization helps identify patterns and potential drivers of change. For instance, closer examination may reveal that the population grows faster during summer months when students are on break or that specific events or holidays influence the population. Analyzing these patterns provides valuable insights for informed decision-making..

[Audio] The time series plot depicts the historical price of gold in US dollars per ounce from July 2025 to November 2025, showcasing the opening, highest, lowest, and closing prices within this timeframe, with a range of $2,800 to $2,350..

[Audio] The correlation coefficient is a statistical measure that calculates the strength and direction of a linear relationship between two variables. Values ranging from -1 to 1 indicate the strength and direction of the relationship. A perfect positive correlation means that as one variable increases, the other also increases, while a perfect negative correlation means that as one variable increases, the other decreases. A value of zero indicates no correlation, meaning there is no linear relationship between the variables. This measure is a valuable tool in data analysis, allowing us to determine whether and how strongly pairs of variables are related. By calculating the correlation coefficient, we can test the power of our hypothesis and understand the influence of each factor on the outcome. We can also identify the vital few causes that have the most significant impact..

[Audio] I don't know.. Let's look at an example. Imagine you're studying the relationship between hours spent studying and exam scores among a group of students. Here are some fictional data points for five students:.

[Audio] When interpreting correlation coefficients, it's essential to understand that they fall within a range of -1 to 1. This scale allows us to determine the strength and direction of the relationship between two variables. A figure below -0.65 or above 0.65 indicates a meaningful correlation. On this scale, a perfect positive correlation is represented by a value of 1, while a perfect negative correlation is denoted by a value of -1. The Pearson Correlation Coefficient, also known as r, is used to calculate the square of the correlation coefficient, r2..

[Audio] Regression analysis enables us to comprehend how distinct variables correlate with one another. Examples include regression lines illustrating the connection between arm span and standing height, leg length and standing height, arm span and sitting height, and leg length and sitting height. These graphs demonstrate how alterations in one variable influence another variable. By scrutinizing these regression lines, we can derive insights into the associations between these physical attributes..

[Audio] The data indicates that there is a strong negative correlation between broker experience and call length. As broker experience rises, call length declines. The Pearson Correlation Coefficient, r, equals -0.896, signifying a robust connection..

[Audio] The scatter plot shows a strong correlation between the number of deliveries made by Six Sigma Pizza and the time customers wait. This suggests that as the number of deliveries increases, so does the waiting time. The Pearson Correlation Coefficient of 0.9144 further supports this relationship..

[Audio] Using this formula, we can make predictions about the future. Remember, it's based on a single variable, X, which helps us define or predict Y. The formula is y equals m times x plus b. This is called the slope-intercept form, where m represents the slope and b gives us the y-intercept..

[Audio] We have re-examined the issue with improved accuracy in mind. By switching from a linear equation to a second-order polynomial, we can capture more intricate connections within the data. This alteration has probably led to a closer match between our predictions and the actual outcomes, enabling us to make a more precise forecast about what would occur if we continued our investigation further..

[Audio] Approximately 83.6 percent of the variation in wait time can be attributed to the variability in deliveries. This means that if we were able to control for the variations in deliveries, we would expect to see a significant reduction in wait times..

[Audio] Multiple regression is a statistical technique used to understand the relationship between one dependent variable and two or more independent variables. By modeling this relationship, we can identify and quantify the effect of each independent variable while controlling for the others. This powerful tool allows us to make predictions and understand complex relationships in data..

[Audio] Regression analysis examines the connections between different variables. There are two main categories of variables: input variables, which are also referred to as predictor variables or independent variables. These are most effective when they are continuous, but can also be countable or categorized. Conversely, output variables, also known as response variables or dependent variables, represent what we aim to forecast and are typically most accurate when continuous, but can also be countable or categorized. The error term signifies the disparity between the observed value and the predicted value, a crucial concept in regression analysis..