Question

This topic is tricky for me and I just need some guidance in answering this question:

Simple linear regression looks at the relationship between an independent and a dependent variable. Can you give a real-world example of two variables that have this special relationship?

Be sure that you answer the following questions:

(a) What is the independent (predictor) variable? Explain.

(b) What is the dependent (explanatory) variable? Explain.

(c) What is the nature of the independent and dependent variable relationship that you are exploring? Are we dealing with proportional or non-proportional behavior? Explain.

Answer 1

We all know that regression is a functional relationship between a dependent and at least one independent variable.

Simple linear regression model is expressed as

Y = a + bX +e

where a is the intercept and B is the slope coefficient.

Y is the dependent and X is the independent variable

e is the error term follows iid normal distribution.

For example,

In current world, many countries problem is to save the environment. So, environment may be affected the quality of air. So, we consider the data of air quality index (AQI) that affect by the following pollutant concentrations of NO₂, CO, O₃, PM_2.5, PM₁₀ and SO₂. As my study, PM₁₀ is the most affected variable of the quality air. So, fit a linear regression model and compute the correlation.

(a) The independent variable is PM10

(b) The dependent variable is air quality index

(c) The nature of the independent and dependent variable relationship that you are exploring is non-proportional behavior because we do not know how much change in independent variable is approximately change the dependent variable.

Answer 2

We all know that regression is a functional relationship between a dependent and at least one independent variable.

Simple linear regression model is expressed as

Y = a + bX +e

where a is the intercept and B is the slope coefficient.

Y is the dependent and X is the independent variable

e is the error term follows iid normal distribution.

For example,

In current world, many countries problem is to save the environment. So, environment may be affected the quality of air. So, we consider the data of air quality index (AQI) that affect by the following pollutant concentrations of NO₂, CO, O₃, PM_2.5, PM₁₀ and SO₂. As my study, PM₁₀ is the most affected variable of the quality air. So, fit a linear regression model and compute the correlation.

(a) The independent variable is PM10

(b) The dependent variable is air quality index

(c) The nature of the independent and dependent variable relationship that you are exploring is non-proportional behavior because we do not know how much change in independent variable is approximately change the dependent variable.