# Positive relationship between dependent and independent variables

### Correlation and Regression

of relationship between a set of independent variables and the dependent variable. Independent variables are characteristics that can be measured directly (example The company expects that there is a positive relationship between the. I want to know the relationship between a dependent variable and an independent variable has a positive/negative small/big deviation from. Statements about association are usually stated in terms of a relationship between an independent and a dependent variable. The idea is that one variable is.

In regression analysis, the dependent variable is denoted Y and the independent variable is denoted X.

## Introduction

When there is a single continuous dependent variable and a single independent variable, the analysis is called a simple linear regression analysis. This analysis assumes that there is a linear association between the two variables.

If a different relationship is hypothesized, such as a curvilinear or exponential relationship, alternative regression analyses are performed.

The figure below is a scatter diagram illustrating the relationship between BMI and total cholesterol.

### Analyzing Relationships Among Variables

Each point represents the observed x, y pair, in this case, BMI and the corresponding total cholesterol measured in each participant. Note that the independent variable BMI is on the horizontal axis and the dependent variable Total Serum Cholesterol on the vertical axis.

BMI and Total Cholesterol The graph shows that there is a positive or direct association between BMI and total cholesterol; participants with lower BMI are more likely to have lower total cholesterol levels and participants with higher BMI are more likely to have higher total cholesterol levels. For either of these relationships we could use simple linear regression analysis to estimate the equation of the line that best describes the association between the independent variable and the dependent variable.

**Biology: Independent vs. Dependent Variables**

The simple linear regression equation is as follows: The Y-intercept and slope are estimated from the sample data, and they are the values that minimize the sum of the squared differences between the observed and the predicted values of the outcome, i. These differences between observed and predicted values of the outcome are called residuals. The estimates of the Y-intercept and slope minimize the sum of the squared residuals, and are called the least squares estimates.

That would mean that variability in Y could be completely explained by differences in X. In business, a well-dressed man is thought to be financially successful.

A mother knows that more sugar in her children's diet results in higher energy levels. The ease of waking up in the morning often depends on how late you went to bed the night before.

## Analyzing Relationships Among Variables

Quantitative regression adds precision by developing a mathematical formula that can be used for predictive purposes. For example, a medical researcher might want to use body weight independent variable to predict the most appropriate dose for a new drug dependent variable. The purpose of running the regression is to find a formula that fits the relationship between the two variables.

Then you can use that formula to predict values for the dependent variable when only the independent variable is known. A doctor could prescribe the proper dose based on a person's body weight.

### Correlation and Linear Regression

The regression line known as the least squares line is a plot of the expected value of the dependent variable for all values of the independent variable.

Technically, it is the line that "minimizes the squared residuals". The regression line is the one that best fits the data on a scatterplot.