# Linear Regression Concept and with R

In “linear regression concept and computations with R series”, videos alternate between focussing on explaining statistical ideas and concepts, and on implementation of ideas using R.

Linear regression is a linear approach to study the relationship between a dependent variable and one or more predictor, explanatory or independent variables . If there is only one explanatory variable it is called simple linear regression. For more than one explanatory or independent variables , it is called multiple linear regression. Simple linear regression (SLR) is a way of modeling the linear relationship between a single quantitative explanatory variable (X) and a single quantitative outcome variable (Y). Multiple linear regression (MLR) is a method for modeling the linear relationship between a quantitative outcome variable (Y) and many explanatory variables (many X's).

In this series of 15 videos you will first learn what a linear regression model is used for, what regression model coefficients are and how to interpret them. We run through an example of linear regression, and while we do present the linear regression formulas, we focus on a conceptual understanding of the model. Then we show how to fit a simple linear regression model in R, what all of the model output is, and how to interpret the model output and model coefficients (parameters). Next, we discuss the linear regression assumptions as well as how to check the linear regression assumptions using R. After this, we discuss the different approaches we may take to dealing with a non-linearity in a linear regression model (if the linearity assumption is not met). Then we show how to implement a few of the different solutions for dealing with a non-linearity in R; namely we present polynomial regression models in R, as well as converting X to a factor (categorical variable). Regarding converting X to a factor, we show how to change which category is the reference category in R, as well as provide an introduction to what a dummy variable is (indicator variable, dummy-coded-predictor), as dummy variables are how factors are included in a linear regression model. We then show how to fit and interpret a multiple linear regression model in R, and how to interpret all of the model coefficients (parameters). We make sure to cover the interpretation of the model intercept, and the regression reference group this refers to. This is followed by a large conceptual overview of exactly what R squared (the coefficient of determination) is measuring, and how it is doing so. This is followed by two videos focussing specifically on how factors (categorical or qualitative variables) are included in a linear regression model. Then we present how to fit a multiple linear regression with interaction model, including a discussion of the interpretation of the model coefficients, and exactly what interaction implies about the relationship between the variables in the regression model. Finally, we conclude with a discussion of how to compare nested models using the partial F test, in order to select (add or remove) variables from a regression model (variable selection).

1. Simple Linear Regression Concept https://youtu.be/vblX9JVpHE8
2. Simple Linear Regression in R https://youtu.be/66z_MRwtFJM
3. Checking Linear Assumptions in R https://youtu.be/eTZ4VUZHzxw
4. Nonlinearity in Linear Regression Concept https://youtu.be/tOzwEv0PoZk
5. Polynomial Regression in R https://youtu.be/ZYN0YD7UfK4
6. Changing Numeric Variable to Categorical Variable in R https://youtu.be/EWs1Ordh8nI
7. Change Reference/Baseline Category for a categorical Variable in Regression Model in R https://youtu.be/XJw6xdBYG7c
8. Dummy Variable or Indicator variable in R https://youtu.be/2s8AwoKZ-UE
9. Multiple Linear regression in R https://youtu.be/q1RD5ECsSB0
10. R Squared or Coefficient of determination Concept https://youtu.be/GI8ohuIGjJA
11. Categorical Variable or Factors in Linear Regression in R https://youtu.be/KHTBwTBkCzg
12. Categorical Variable or Factors in Linear Regression in R continued https://youtu.be/ZtBmMhGkx
13. Multiple Linear Regression with Interaction in R https://youtu.be/8YuuIsoYqsg
14. Interpreting Interaction in Linear Regression in R https://youtu.be/vZUtDJbzFRQ
15. Variable Selection in Linear regression Using Partial F-Test in R https://youtu.be/G_obrpV70QQ

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Our Team:
Content Creator: Mike Marin (B.Sc., MSc.) Senior Instructor at UBC.

These videos are created by #marinstatslectures to support a course at The University of British Columbia (UBC) (#RTutorial and #IntroductoryStatistics for Health Science Research), although we make all videos available to the public for free.
In “linear regression concept and computations with R series”, videos alternate between focussing on explaining statistical ideas and concepts, and on implementation of ideas using R.

Linear regression is a linear approach to study the relations...