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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0 5 10 15 20Time

Wei

ght i

n gr

ams

Chick Weight Over Time

yi = a + bxi + ei

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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

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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 5 10 15 20Time

Wei

ght i

n gr

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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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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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Rea

ctio

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Reaction Times by L2 Proficiency Level

0 1

yi = a + bxi + ei

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Rea

ctio

n tim

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ms

Reaction Times by L2 Proficiency Level

0 1

yi = a + bxi + ei

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ctio

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Reaction Times by L2 Proficiency Level

0 1

yi = a + bxi + ei

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ctio

n tim

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Reaction Times by L2 Proficiency Level

0 1

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ctio

n tim

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Reaction Times by L2 Proficiency Level

0 1

yi = a + bxi + ei

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Rea

ctio

n tim

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Reaction Times by L2 Proficiency Level

0 1

yi = a + bxi + ei

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Rea

ctio

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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