Bernard Szlachta at 03:13, 6 March 2016

2016-03-06T03:13:28Z

New page

[[Category:Intro to R|084]]
{{Cat|Forecasting}}

'''Linear regression''' is an approach to modelling the relationship between a dependent variable ''y'' and one or more explanatory variables ''X''.
* One explanatory variable -> ''simple regression''
* Many explanatory variables -> ''multiple regression''
* Multiple correlated dependent ''y'' variables are predicted -> ''multivariate linear regression''

Linear regression is usually used for:
* Prediction/forecasting
* Quantify the strength of the relationship between ''y'' and the ''X''<sub>''j''</sub>

Implementation:
* Least squares
* Least absolute deviations
* Ridge regression

== Regression Model==
<math>
y_i = \beta_1 x_{i1} + \cdots + \beta_p x_{ip} + \varepsilon_i
</math>

== Hours Studying and GPA ==

"How well does the average number of hours studying predict GPA?"

* Predictor variable - Hours
* Response (criterion) variable - GPA
<source lang="rsplus">
# Read the data
gpa <- read.table("http://training-course-material.com/images/8/86/Study-time-gpa.txt",h=T)

# Pearson correlation
cor(gpa)

# Draw a scatter plot
plot(gpa)

# Create a model
m <- lm(GPA ~ Hours, data=gpa)

# Show the model
m

# Validate the model
summary(m)

# Draw the model
abline(m)

# What would be a score for studding for 34 hours
p <- predict.lm(m,data.frame(Hours = c(34)))
p
</source>

:[[File:ClipCapIt-160306-111233.PNG]]

== Exercises ==
Using linear regression, find the predicted post-test score for someone with a score of 43 on the pre-test.

http://training-course-material.com/images/8/84/Pre-post-test-scores.txt

R - Regression - Revision history

Bernard Szlachta at 03:13, 6 March 2016