Lesson 2: Linear Regression
Learn about linear regression
This Lesson’s Goals
Summarise results in an R Markdown document
Do a linear regression in R
Make a figure for data from a linear regression
Math
yi = a + bxi + ei
yi = specific y value (dependent variable)
a = intercept
b = slope
xi = specific x value (independent variable)
ei = random variance or the residual
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0
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200
300
0 5 10 15 20Time
Wei
ght i
n gr
ams
Chick Weight Over Time
yi = a + bxi + ei
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0
100
200
300
0 5 10 15 20Time
Wei
ght i
n gr
ams
Chick Weight Over Time
yi = a + bxi + ei
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0
100
200
300
0 5 10 15 20Time
Wei
ght i
n gr
ams
Chick Weight Over Time
yi = a + bxi + ei
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0
100
200
300
0 5 10 15 20Time
Wei
ght i
n gr
ams
Chick Weight Over Time
yi = a + bxi + ei
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0
100
200
300
0 5 10 15 20Time
Wei
ght i
n gr
ams
Chick Weight Over Time
yi = a + bxi + ei
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0
100
200
300
0 5 10 15 20Time
Wei
ght i
n gr
ams
Chick Weight Over Time
yi = a + bxi + ei
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0
100
200
300
0 5 10 15 20Time
Wei
ght i
n gr
ams
Chick Weight Over Time
yi = a + bxi + ei
categorical?
yi = a + bxi + ei
continuouspredictors
categoricalpredictors
x = a set of continuous data points
a + bx
x = a set of binary/categorical data points
a = the value of y when x is 0
a = the value of y when the x is the default level
b = the change in y for one change in x
b = the change in y when x is the non-default level
yi = a + bxi + ei
●
900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
yi = a + bxi + ei
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900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
yi = a + bxi + ei
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900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
yi = a + bxi + ei
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900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
yi = a + bxi + ei
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900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
yi = a + bxi + ei
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900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
yi = a + bxi + ei
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900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
yi = a + bxi + ei
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900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
yi = a + bxi + ei
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900
950
1000
1050
1100
high lowProficiency in L2
Rea
ctio
n tim
es in
ms
Reaction Times by L2 Proficiency Level
0 1
R Code
yi = a + bxi + ei
lm(weight ~ Time)
yi = a + bxi + ei
lm(rt ~ type)
Lab
Dataset: Baby names per year from USA Social Security Administration
Continuous Predictor: Does your name get more or less popular between the years of 1901 and 2000?
Categorical Predictor: Is your name more or less popular with females or males?
yi = a = b = xi = ei =
frequency of name? - will get from model? - will get from modelyear? - will get from model
yi = a = b = xi = ei =
frequency of name? - will get from model? - will get from modelsex? - will get from model
Continuous Predictor Categorical Predictor
source: R package “babynames”
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−5.5
−5.0
−4.5
1925 1950 1975 2000Year
Prop
ortio
n of
Peo
ple
(log
base
10
trans
form
ed)
Proportion of People withthe Name 'Page' Over Time
End of Lesson Food for Thought
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−5.5
−5.0
−4.5
1925 1950 1975 2000Year
Prop
ortio
n of
Peo
ple
(log
base
10
trans
form
ed)
Proportion of People withthe Name 'Page' Over Time
End of Lesson Food for Thought
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−5.5
−5.0
−4.5
1925 1950 1975 2000Year
Prop
ortio
n of
Peo
ple
(log
base
10
trans
form
ed)
Proportion of People withthe Name 'Page' Over Time
End of Lesson Food for Thought