Download - Multiple linear regression
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What is a Multiple Linear Regression?
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Welcome to this learning module onMultiple Linear Regression
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In this presentation we will cover the following aspects of Multiple Regression:
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In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA
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In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable
![Page 6: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/6.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time
![Page 7: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/7.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle
![Page 8: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/8.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
![Page 9: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/9.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
![Page 10: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/10.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
In this presentation we will cover the concept of Partial Correlation.
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In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
After going through this presentation look at the presentation on Analysis of Covariance and consider what multiple regression and ANCOVA have in common.
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In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
What is a Partial Correlation?
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Partial correlation estimates the relationship between two variables while removing the influence of a third variable from the relationship.
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Like in the example that follows,
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Like in the example that follows, a Pearson Correlation between height and weight would yield a .825 correlation.
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Like in the example that follows, a Pearson Correlation between height and weight would yield a .825 correlation. We might then control for gender (because we think being female or male has an effect on the relationship between height and weight).
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However, when controlling for gender the correlation between height and weight drops to .770.
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However, when controlling for gender the correlation between height and weight drops to .770.
Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female)A 73 240 1B 70 210 1C 69 180 1D 68 160 1E 70 150 2F 68 140 2G 67 135 2H 62 120 2
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However, when controlling for gender the correlation between height and weight drops to .770.
Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female)A 73 240 1B 70 210 1C 69 180 1D 68 160 1E 70 150 2F 68 140 2G 67 135 2H 62 120 2
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However, when controlling for gender the correlation between height and weight drops to .770.
Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female)A 73 240 1B 70 210 1C 69 180 1D 68 160 1E 70 150 2F 68 140 2G 67 135 2H 62 120 2
&
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However, when controlling for gender the correlation between height and weight drops to .770.
Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female)A 73 240 1B 70 210 1C 69 180 1D 68 160 1E 70 150 2F 68 140 2G 67 135 2H 62 120 2
&
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However, when controlling for gender the correlation between height and weight drops to .770.
Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female)A 73 240 1B 70 210 1C 69 180 1D 68 160 1E 70 150 2F 68 140 2G 67 135 2H 62 120 2
& controlling for
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However, when controlling for gender the correlation between height and weight drops to .770.
Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female)A 73 240 1B 70 210 1C 69 180 1D 68 160 1E 70 150 2F 68 140 2G 67 135 2H 62 120 2
& controlling for
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However, when controlling for gender the correlation between height and weight drops to .770.
Individual Height (inches) Weight (pounds) Sex (1 – male, 2 – female)A 73 240 1B 70 210 1C 69 180 1D 68 160 1E 70 150 2F 68 140 2G 67 135 2H 62 120 2
& controlling for = .770
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This is very helpful because we may think two variables (height and weight) are highly correlated but we can determine if that correlation holds when we take out the effect of a third variable (gender).
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While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable.
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While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Independent or Predictor Variables
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While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Independent or Predictor Variables
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While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Independent or Predictor Variables
![Page 30: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/30.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Independent or Predictor Variables
![Page 31: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/31.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Independent or Predictor Variables
![Page 32: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/32.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
![Page 33: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/33.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
![Page 34: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/34.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Weight
![Page 35: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/35.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Weight
all have an influence on . . .
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While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Weight
all have an influence on . . .
![Page 37: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/37.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Weight
all have an influence on . . .
![Page 38: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/38.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Weight
all have an influence on . . .
![Page 39: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/39.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Weight
all have an influence on . . .
![Page 40: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/40.jpg)
While in partial correlation, only two variables are correlated while holding a third variable constant, in multiple regression several variables are grouped together to predict an outcome variable
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
![Page 41: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/41.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
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Essentially, the group of predictors are all covariates to each other.
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
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Meaning,
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
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Meaning, for example,
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
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Meaning, for example, that it is possible to identify the unique prediction power of height on weight
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
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Meaning, for example, that it is possible to identify the unique prediction power of height on weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . . Height
Weight
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Meaning, for example, that it is possible to identify the unique prediction power of height on weight after you’ve taken out the influence of all of the other predictors.
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . . Height
Weight
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Meaning, for example, that it is possible to identify the unique prediction power of height on weight after you’ve taken out the influence of all of the other predictors.
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . . Height
Weight
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For example,
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
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For example, here is the correlation between Height and Weight without controlling for all of the other variables.
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . . Height
Weight
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For example, here is the correlation between Height and Weight without controlling for all of the other variables.
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . . Height
Weight
Correlation = .825
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However,
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
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However, here is the correlation between Height and Weight after taking out the effect of all of the other variables.
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
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However, here is the correlation between Height and Weight after taking out the effect of all of the other variables.
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight
Height
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However, here is the correlation between Height and Weight after taking out the effect of all of the other variables.
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . . Height
Weight
Correlation = .601
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However, here is the correlation between Height and Weight after taking out the effect of all of the other variables.
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight
Correlation = .601
So, after eliminating the effect of gender, age, soda, and exercise on weight, the
unique correlation that height shares with weight is .601.
Height
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Even though we were only correlating height and weight when we computed a correlation of .825,
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Even though we were only correlating height and weight when we computed a correlation of .825, the other four variables still had an influence on weight.
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Even though we were only correlating height and weight when we computed a correlation of .825, the other four variables still had an influence on weight. However, that influence was not accounted for and remained hidden.
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With multiple regression we can control for these four variables and account for their influence
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With multiple regression we can control for these four variables and account for their influence thus calculating the unique contribution height makes on weight without their influence being present.
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We can do the same for any of these other variables. Like the relationship between Gender and Weight.
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We can do the same for any of these other variables. Like the relationship between Gender and Weight.
Height
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight
Gender
![Page 64: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/64.jpg)
We can do the same for any of these other variables. Like the relationship between Gender and Weight.
Height
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight
Gender Correlation = .701
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But when you take out the influence of the other variables the correlation drops from .701 to .582.
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BEFORE
Height
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight
Gender Correlation = .701
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AFTER
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AFTER
Height
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight
Gender
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AFTER
Height
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight
Gender Correlation = .582
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Here is the correlation between age and weight before you take out the effect of the other variables:
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Here is the correlation between age and weight before you take out the effect of the other variables:
Height
Gender
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight Age
![Page 72: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/72.jpg)
Here is the correlation between age and weight before you take out the effect of the other variables:
Height
Gender
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight Age Correlation = .435
![Page 73: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/73.jpg)
The correlation drops from .435 to .385 after taking out the influence of the other variables:
![Page 74: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/74.jpg)
The correlation drops from .435 to .385 after taking out the influence of the other variables:
Height
Gender
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight Age
![Page 75: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/75.jpg)
The correlation drops from .435 to .385 after taking out the influence of the other variables:
Height
Gender
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight Age Correlation = .385
![Page 76: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/76.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
![Page 77: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/77.jpg)
Beyond estimating the unique power of each predictor,
![Page 78: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/78.jpg)
Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors.
![Page 79: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/79.jpg)
Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors.
![Page 80: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/80.jpg)
Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors.
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
![Page 81: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/81.jpg)
Beyond estimating the unique power of each predictor, multiple regression also estimates the combined power of the group of predictors.
Height
Weight
Gender
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Combined Correlation
= .982
![Page 82: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/82.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
![Page 83: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/83.jpg)
Multiple regression can estimate the effects of continuous and categorical variables in the same model.
![Page 84: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/84.jpg)
Multiple regression can estimate the effects of continuous and categorical variables in the same model.
Height
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Age
Soda Drinking
Exercise
Gender
Weight
![Page 85: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/85.jpg)
Multiple regression can estimate the effects of continuous and categorical variables in the same model.
Height
Independent or Predictor Variables
Dependent, Response or Outcome Variable
Age
Soda Drinking
Exercise
Gender
Weight
Height is represented by continuous data – because height can take on any value between two points in inches or centimeters.
![Page 86: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/86.jpg)
Multiple regression can estimate the effects of continuous and categorical variables in the same model.
![Page 87: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/87.jpg)
Multiple regression can estimate the effects of continuous and categorical variables in the same model.
Height
Age
Soda Drinking
Exercise
Independent or Predictor Variables
Dependent, Response or Outcome Variable
all have an influence on . . .
Weight
Gender Gender is a represented by categorical data – because gender can take on two values (female or male)
![Page 88: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/88.jpg)
In this presentation we will cover the following aspects of Multiple Regression:- Connection to Partial Correlation and ANCOVA- Unique contribution of each variable- Contribution of all variables at the same time- Type of data multiple regression can handle- Types of relationships multiple regression
describes
![Page 89: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/89.jpg)
Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales:
![Page 90: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/90.jpg)
Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales:
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
Average Monthly Ice Cream Sales
Ave
Mon
thly
Tem
pera
ture
![Page 91: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/91.jpg)
Multiple regression can describe or estimate linear relationships like average monthly temperature and ice cream sales:
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
Average Monthly Ice Cream Sales
Ave
Mon
thly
Tem
pera
ture
Linea
r Rela
tionsh
ip
![Page 92: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/92.jpg)
It can also describe or estimate curvilinear relationships.
![Page 93: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/93.jpg)
For example,
![Page 94: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/94.jpg)
For example, what if in our fantasy world the temperature reached 100 degrees and then 120 degrees. Let’s say with such extreme temperatures ice cream sales actually dip as consumers seek out products like electrolyte-enhanced drinks or slushies.
![Page 95: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/95.jpg)
Then the relationship might look like this:
![Page 96: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/96.jpg)
Then the relationship might look like this:
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
Average Monthly Ice Cream Sales
Ave
Mon
thly
Tem
pera
ture
![Page 97: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/97.jpg)
Then the relationship might look like this:
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
Average Monthly Ice Cream Sales
Ave
Mon
thly
Tem
pera
ture
This is an example of a Curvilinear
Relationship
![Page 98: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/98.jpg)
In summary,
![Page 99: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/99.jpg)
In summary, Multiple Regression is like single linear regression but instead of determining the predictive power of one variable (temperature) on another variable (ice cream sales) we consider the predictive power of other variables (such as socio-economic status or age).
![Page 100: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/100.jpg)
With multiple regression you can estimate the predictive power of many variables on a certain outcome,
![Page 101: Multiple linear regression](https://reader035.vdocument.in/reader035/viewer/2022062419/55847919d8b42a6b4d8b51f9/html5/thumbnails/101.jpg)
With multiple regression you can estimate the predictive power of many variables on a certain outcome, as well as the unique influence each single variable makes on that outcome after taking out the influence of all of the other variables.