Karl Pearson Correlation and Regression

 Karl Pearson Correlation Coefficient

 Simply known as Pearson's r, it is a statistical measure used to calculate the strength and direction of the linear relationship between two variables, usually denoted as x and y.

WEATHER CONDITIONS DATA

The correlation is very weak (close to 0). 

The negative sign means that as x increases, $y$ tends to decrease slightly, but the relationship is extremely weak.

REGRESSION

Regression is a statistical method that models and analyzes the relationship between a dependent variable and one or more independent variables .

 Linear regression is the relationship between one independent variable  x and one dependent variable y.

Conclusion 

In this data, there is a very weak, negative relationship between $x$ and y. As $\mathrm{x }$increases, $\mathrm{y }$decreases slightly, but the relationship is not strong enough to make confident predictions.

Standard Deviation

 When analysing student spending habits, it’s not enough to just look at the average. Some students spend way more, others far less—so how spread out is this spending? That’s where standard deviation comes in. It helps us measure how much individual spending amounts differ from the average, giving a clearer picture of financial behavior on campus.

What is Standard Deviation?

Standard deviation is a measure of how spread out or dispersed a set of values is from the mean (average). A low standard deviation means that most values are close to the mean, while a high standard deviation indicates greater variability.

Standard Deviation for Grouped Data

We’ll use the standard deviation formula for grouped data:

Where:

• f = frequency
• x = midpoint of the class
• X = mean
• N = total frequency
• f(x - x})2 = squared deviation multiplied by frequency
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By calculating the standard deviation of student spending, we discovered just how varied their habits are. This measure adds depth to our understanding beyond just the average, helping campus businesses and planners see the bigger picture. In short, standard deviation tells us not just what students spend—but how differently they spend.

Positional Avarages

Breaking Down Student Spending: A Look Through Quartiles, Deciles & Percentiles

 

In an effort to understand how students spend money on campus, we conducted a survey focused on their weekly expenditure. With the data collected, we applied various statistical tools—not just averages, but also quartiles, deciles, and percentiles—to better interpret the spread and behavior of the data. These measures help reveal patterns that a simple average might miss, such as how spending varies across different groups of students.

University Survey Data For Student Total Expenditure

Quartile 

A quartile divides data into four equal parts.

• Q1 (First Quartile): 25% of the data lies below this point.
• Q2 (Second Quartile): This is the median (50% of the data below it).
• Q3 (Third Quartile): 75% of the data lies below this point.

 Decile

A decile divides the data into ten equal parts.

• For example, D1 marks the point below which 10% of data lies,
  D5 is the same as the 50th percentile or median,
  D9 marks 90% of the data.

 Percentile

A percentile splits data into 100 equal parts.

• For example, the 90th percentile (P90) means 90% of the data lies below that value.

Use: Often used in test scores, rankings, and performance comparisons.

By using quartiles, deciles, and percentiles, we gained a deeper understanding of student spending habits. For instance, the 90th percentile highlighted the top spenders, while the first quartile showed where the lighter spenders stood. These insights are vital for campus vendors, policymakers, or even students themselves, to better plan and respond to spending trends.