Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Biostats > Chapters 34 and 35-Models > Flashcards

Chapters 34 and 35-Models Flashcards

1
Q

What is a model?

A

A mathematical model is an equation(s) that

describe or represent a physical state or process.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What does the equation of a model describe?

A

The equation of a model describes the outcome of a function of one or more independent variables, parameters, and/or constants.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is the outcome otherwise known as as that the equation of a model describes?

A

It’s also known as the dependent variable.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is an example of a model?

A

The dependent variable is insulin sensitivity. The independent variable is the percent of C20-22 fatty acids. The two parameters are the slope and intercept. There are no constants in this example, but some might make the intercept a constant at zero.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

In statistics, the model will likely also have a
____________ in the response and possibly
the independent variable(s).

A

random component.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What is the simplest model?

A

The mean.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

The mean is estimated from what?

A

The mean is estimated from the data.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What could be predicted from the data?

A

New samples could be predicted from the mean.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the formula used to predict new samples from the mean?

A

Yi = μ + εi

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What does the “μ” stand for in Yi = μ + εi?

A

It means the population mean.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What does the “ε” stand for in Yi = μ + εi?

A

It means the error.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Each Y and ε has a different value, but there is

only…

A

one true mean (μ).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What does “μ” stand for?

A

It stands for the expected value of Y.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What accounts for the random error in each Y?

A

ε accounts for the random error in each Y.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What do you include for the Linear Regression Model?

A

The random component is included.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the formula for the Linear Regression Model?

A

Y = intercept + slope · X + scatter

17
Q

What does the Linear Regression Model describe?

A

It describes a straight line.

18
Q

What is the formula for the Linear Regression Model?

A

Yi = β0 + β1

· Xi + εi

19
Q

What are the parameters for the Linear Regression Model?

A 
β0 = intercept
β1 = slope
20
Q

There are both _____ in the Linear Regression Model.

A

There are both X and Y variables.

21
Q

The straight line model of the Linear Regression Model is unlikely to be what?

A

It’s unlikely to be accurate outside of the range of X values.

22
Q

The straight line model is unlikely to be

accurate outside of the range of X values. What is an example of this?

A

It might predict values that are not possible like 100%.

23
Q

What does Linear Regression find?

A

Linear regression finds the values of the slope and intercept parameters.

24
Q

How does linear regression find the values of the slope and intercept parameters?

A

It does this by minimizing the sum of the squared of the vertical distances of the points from the line.

25
Q

What does it mean if the scatter (ε) in Y is Gaussian for a linear regression model?

A

If it is Gaussian, then this finds the maximum likelihood estimate of the true relationship between X and Y (assuming that the relationship is a straight line).

26
Q

List other kinds of relationships that can be represented using models.

A
  1. Nonlinear
  2. Multiple independent variables
  3. Discrete variables: binary and Poisson
  4. Survival time
27
Q

How do you determine the model for the data?

A

There should be a scientific (not just statistical) criterion, and models won’t be perfect.

28
Q

What should you consider linear regression?

A

You should consider linear regression as a comparisons of two models.

29
Q

What is the null hypothesis for linear regression?

A

The null hypothesis is a horizontal line.

30
Q

The null is a linear model in which β1=? and β0=?

A

β1 = 0
β0 = the mean of Y. (recall: Yi = β0 + β1
· Xi + εi
)

31
Q

Or an even simpler model with only one parameter for linear regression:

A

Yi = μ + εi

μ: the mean of Y, ε: error

32
Q

Why are the parameters chosen in a best fit line of a linear model?

A

It’s chosen to minimize the sum of squares.

33
Q

The sum of squares is higher for…

A

a horizontal line.

Biostats (21 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions