R Tutorial Series: Simple Linear Regression. John M. Quick. (2009, november 26). Retrieved from [www.r-bloggers.com/r-tutorial-series-simple-linear-regression/](https://www.r-bloggers.com/r-tutorial-series-simple-linear-regression/) 

University of Michigan - Ann Arbor

In R, lm() is a function that can take many parameters. Common parameters include formula, which describes a model, and data, which contains a dataset. 
 

In simple linear regression in R, a formula parameter is written YVAR~XVAR, where XVAR is the predictor variable and YVAR is the response variable. 

A simple linear regression equation with data and formula parameters may look like:
``` R
lm(formula = YVAR~XVAR, data = datavar)
```


Simple Linear Regression in R: lm()

``` R
### start with assigning lm.fit to the model:
lm.fit = lm(XVAL~YVAL, data = datavar)
#1.  lm.fit provides “basic” information *such as* Coefficients
lm.fit
```
Below is an example of the type of output information you can get calling lm.fit (from Pg. 111 of Introduction to Statistical Learning with Applications in R).


lm.fit: Output Basic Statistical Information in R 

- predict() returns y-hat (estimate) based on your training model. 
- This method produces the confidence and prediction intervals for the prediction of YVAL given a value of the XVAL. In other words, for each training set, we have corresponding x and y values. 
- Now we have a new data set and we are passing a vector with one column from that new data and we want to predict the prediction/confidence intervals for that new data value based on the training data model.
```R
predict(lm.fit, data.frame(XVAL=(c(new_data_row_value1, new_data_row_value2), interval = “”)
#Example: 
predict(lm.fit, data.frame(XVAL=(c(5, 10,15)), interval = “prediction”)
	#Above, data.frame is included as an optional data frame that looks for variables to predict. Without it, fitted values are used.
	#interval = “confidence” , “none”, “prediction” are all options
        ```

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