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REVISION LECTURE

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Addie McCall

on 6 April 2016

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Transcript of REVISION LECTURE

Linear Regression
REVISION LECTURE:
Case Study: Hours of Sleep vs GPA
Recap: What is linear regression?
In statistics we say that linear regression describes the linear relationship between "x" variables and the corresponding "y" variables.

DATA
The Experiment
15 high school students were used in this theoretical study. Their average number of hours slept each night was recorded as well as their current GPA. A linear regression was then conducted, and a graph and table were tabulated.
Linear Equation: y= bx + a

What linear relationship can be established between x and y? Linear regression analysis can tell us!
Image from: http://onlinestatbook.com/2/regression/intro.html
GRAPH
Example:
The "best fitting line" / regression line could then be incorporated into the graph using Excel or the calculated values above.
Recall: Y= bx + a (regression line)
Find values for "b" and "a" using the following equations:
b=sp/ssx
b= 17.6/64
b= 0.275
b
a
a= y-bar - b*(x-bar)
a= 3.1 - (0.275)*(5)
a= 1.711
Therefore the equation for the regression line is:
y = 0.275x + 1.711
* Values calculated in Table 1.1 *
Table 1.1 Theoretical Data: Hours Slept vs GPA
Figure 1: Graph showing relationship between average hours slept and GPA of
Assumptions

1) Linearity
2) Normality
3) Little or No Multicollinearity
4) Independence
5) Little or No Autocorrelation
6) Homoscedasticity


Types of Linear Relationships
Image from: https://www2.palomar.edu/users/rmorrissette/Lectures/Stats/Correlation/Correlation.htmmage from
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Full transcript