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In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables).
- Assumptions of Simple Linear Regression
- How to Perform A Simple Linear Regression
- Interpreting The Results
- Presenting The Results
- Can You Predict Values Outside The Range of Your Data?
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Simple linear regression is a parametric test, meaning that it makes certain assumptions about the data. These assumptions are: 1. Homogeneity of variance (homoscedasticity): the size of the error in our prediction doesn’t change significantly across the values of the independent variable. 2. Independence of observations: the observations in the da...
Simple linear regression formula
The formula for a simple linear regression is: 1. y is the predicted value of the dependent variable (y) for any given value of the independent variable (x). 2. B0 is the intercept, the predicted value of y when the xis 0. 3. B1 is the regression coefficient – how much we expect y to change as xincreases. 4. x is the independent variable ( the variable we expect is influencing y). 5. e is the errorof the estimate, or how much variation there is in our estimate of the regression coefficient. L...
Simple linear regression in R
R is a free, powerful, and widely-used statistical program. Download the dataset to try it yourself using our income and happiness example. Dataset for simple linear regression (.csv) Load the income.data dataset into your R environment, and then run the following command to generate a linear model describing the relationship between income and happiness: This code takes the data you have collected data = income.data and calculates the effect that the independent variable income has on the de...
To view the results of the model, you can use the summary()function in R: This function takes the most important parameters from the linear model and puts them into a table, which looks like this: This output table first repeats the formula that was used to generate the results (‘Call’), then summarizes the model residuals (‘Residuals’), which give...
When reporting your results, include the estimated effect (i.e. the regression coefficient), standard error of the estimate, and the p value. You should also interpret your numbers to make it clear to your readers what your regression coefficient means: It can also be helpful to include a graph with your results. For a simple linear regression, you...
No! We often say that regression models can be used to predict the value of the dependent variable at certain values of the independent variable. However, this is only true for the rangeof values where we have actually measured the response. We can use our income and happiness regression analysis as an example. Between 15,000 and 75,000, we found a...
If you want to know more about statistics, methodology, or research bias, make sure to check out some of our other articles with explanations and examples.
Learn how to use simple linear regression to estimate the relationship between two quantitative variables. Find out the formula, assumptions, steps, and how to interpret the results with examples and R code.
Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.
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