Multiple Linear Regression | A Quick Guide (Examples)

Published on February 20, 2020 by Rebecca Bevans. Revised on June 22, 2023.

Regression models are used to describe relationships between variables by fitting a line to the observed data. Regression allows you to estimate how a dependent variable changes as the independent variable(s) change.

Multiple linear regression is used to estimate the relationship between two or more independent variables and one dependent variable. You can use multiple linear regression when you want to know:

  1. How strong the relationship is between two or more independent variables and one dependent variable (e.g. how rainfall, temperature, and amount of fertilizer added affect crop growth).
  2. The value of the dependent variable at a certain value of the independent variables (e.g. the expected yield of a crop at certain levels of rainfall, temperature, and fertilizer addition).
Multiple linear regression example
You are a public health researcher interested in social factors that influence heart disease. You survey 500 towns and gather data on the percentage of people in each town who smoke, the percentage of people in each town who bike to work, and the percentage of people in each town who have heart disease.

Because you have two independent variables and one dependent variable, and all your variables are quantitative, you can use multiple linear regression to analyze the relationship between them.

Continue reading: Multiple Linear Regression | A Quick Guide (Examples)

Simple Linear Regression | An Easy Introduction & Examples

Published on February 19, 2020 by Rebecca Bevans. Revised on June 22, 2023.

Simple linear regression is used to estimate the relationship between two quantitative variables. You can use simple linear regression when you want to know:

  1. How strong the relationship is between two variables (e.g., the relationship between rainfall and soil erosion).
  2. The value of the dependent variable at a certain value of the independent variable (e.g., the amount of soil erosion at a certain level of rainfall).

Regression models describe the relationship between variables by fitting a line to the observed data. Linear regression models use a straight line, while logistic and nonlinear regression models use a curved line. Regression allows you to estimate how a dependent variable changes as the independent variable(s) change.

Simple linear regression example
You are a social researcher interested in the relationship between income and happiness. You survey 500 people whose incomes range from 15k to 75k and ask them to rank their happiness on a scale from 1 to 10.

Your independent variable (income) and dependent variable (happiness) are both quantitative, so you can do a regression analysis to see if there is a linear relationship between them.

If you have more than one independent variable, use multiple linear regression instead.

Continue reading: Simple Linear Regression | An Easy Introduction & Examples

An Introduction to t Tests | Definitions, Formula and Examples

Published on January 31, 2020 by Rebecca Bevans. Revised on June 22, 2023.

A t test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another.

t test example
You want to know whether the mean petal length of iris flowers differs according to their species. You find two different species of irises growing in a garden and measure 25 petals of each species. You can test the difference between these two groups using a t test and null and alterative hypotheses.

  • The null hypothesis (H0) is that the true difference between these group means is zero.
  • The alternate hypothesis (Ha) is that the true difference is different from zero.

Continue reading: An Introduction to t Tests | Definitions, Formula and Examples

Choosing the Right Statistical Test | Types & Examples

Published on January 28, 2020 by Rebecca Bevans. Revised on June 22, 2023.

Statistical tests are used in hypothesis testing. They can be used to:

  • determine whether a predictor variable has a statistically significant relationship with an outcome variable.
  • estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data.

Statistical tests flowchart

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Guide to Experimental Design | Overview, Steps, & Examples

Published on December 3, 2019 by Rebecca Bevans. Revised on June 21, 2023.

Experiments are used to study causal relationships. You manipulate one or more independent variables and measure their effect on one or more dependent variables.

Experimental design create a set of procedures to systematically test a hypothesis. A good experimental design requires a strong understanding of the system you are studying.

There are five key steps in designing an experiment:

  1. Consider your variables and how they are related
  2. Write a specific, testable hypothesis
  3. Design experimental treatments to manipulate your independent variable
  4. Assign subjects to groups, either between-subjects or within-subjects
  5. Plan how you will measure your dependent variable

For valid conclusions, you also need to select a representative sample and control any extraneous variables that might influence your results. If random assignment of participants to control and treatment groups is impossible, unethical, or highly difficult, consider an observational study instead. This minimizes several types of research bias, particularly sampling bias, survivorship bias, and attrition bias as time passes.

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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans. Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

  1. State your research hypothesis as a null hypothesis and alternate hypothesis (Ho) and (Ha or H1).
  2. Collect data in a way designed to test the hypothesis.
  3. Perform an appropriate statistical test.
  4. Decide whether to reject or fail to reject your null hypothesis.
  5. Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Continue reading: Hypothesis Testing | A Step-by-Step Guide with Easy Examples