# What Investors Need to Know About Regression Analysis  Do you ever wonder how the price of a house is affected by things like its size, number of bedrooms, and location? Well, there's a cool thing called regression analysis that helps us figure that out.

In regression analysis, we have two types of things we look at: the price of the house (what we want to understand better) and the factors that might influence the price, like the size, number of bedrooms, and location (we call these the "independent variables").

The goal of regression analysis is to create a special math formula, kind of like a secret code, that helps us predict the price of a house based on its size, number of bedrooms, and location. This secret code considers how these factors are connected and tries to find the best way to guess the price.

So, by using regression analysis, we can find out how the price of a house changes when its size, number of bedrooms, or location change. It helps us make predictions and understand how these factors affect the price we're interested in.

There are different types of regression models we can use depending on the situation. If we only have one independent variable, like the size of the house, we can use a simple linear regression. But if we have multiple independent variables, such as size, number of bedrooms, and location, we use multiple linear regression.

Regression analysis helps us understand how changes in the independent variables affect the dependent variable, the price of the house in our example. It gives us insights into the relationships and patterns in the data. By using this method, we can make predictions and understand how different factors influence the outcome we're interested in, which is the price of the house.

In summary, regression analysis is a way to study the connections between variables, like how the size, number of bedrooms, and location of a house affect its price. It helps us create a model that can predict prices based on these factors and gives us a deeper understanding of how different factors impact the outcome we're investigating.

## Simple Linear Regression

Imagine you're curious to know if the time you spend studying has any effect on your test scores. Well, there's a cool thing called Simple Linear Regression that can help us find out!

In Simple Linear Regression, we look at two things: the time you spend studying (that's the independent thing) and your test score (that's the dependent thing). We want to see if these two things are related.

Simple Linear Regression makes a special equation, like a secret code, that tries to guess your test score based on how much time you study. It's like having a smart friend who can predict how well you might do on a test if you study for a certain amount of time.

It looks like this:

Test Score = β0 + β1 * Study Hours + ε

Here's what each part means:

Test Score is the dependent variable, the thing we want to predict or understand better.

Study Hours are the independent variable, the factor we think might influence the test score.

β0 is the intercept or constant, which represents the expected test score when you haven't studied at all.

β1 is the slope coefficient, which tells us how much the test score is expected to change for each additional hour of study.

ε is the error term, accounting for any random or unexplained factors that affect the test score.

To estimate the values of β0 and β1, we use a method called least squares. It helps us find the line that minimizes the difference between the predicted test scores and the actual test scores from our data.

The formula for β1, the slope coefficient, looks like this:

β1 = Σ((Study Hours - )(Test Score - )) / Σ((Study Hours - )^2)

Here's what each part means:

Σ means adding up all the values.

Study Hours and Test Score represent the individual values from our data.

is the mean (average) of the Study Hours.

is the mean of the Test Score.

To find β0, the intercept, we use the following formula:

β0 = - β1

Once we have the values of β0 and β1, we can use the equation to predict your test score for any number of study hours.

Hypothesis testing is another important step. We want to determine if the slope coefficient (β1) is statistically significant. We compare it to zero to see if there is a meaningful relationship between study hours and test scores.

We calculate a t-statistic using this formula:

t = (β1 - 0) / (SE(β1))

SE(β1) is the standard error of the slope coefficient, which measures how much it can vary.

With the t-statistic, we calculate the p-value, which tells us the probability of observing the relationship between study hours and test scores by chance alone.

If the p-value is smaller than a chosen level of significance (e.g., 0.05), we conclude that there is a statistically significant relationship between study hours and test scores.

In simpler terms, Simple Linear Regression helps us understand if studying more hours leads to higher test scores. We use math and data to find a formula that predicts test scores based on study hours. Then, we check if the relationship we found is real or just a coincidence.