Part 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables
Linear Regression Linear correlation Significance Tests Multiple regression
ESS210B Prof. Jin-Yi Yu
Linear Regression
Y=aX+b
Dependent Variable
Independent Variable
? To find the relationship between Y and X which yields values of Y with the least error.
ESS210B Prof. Jin-Yi Yu
Predictor and Predictand
In meteorology, we want to use a variable x to predict another variable y. In this case, the independent variable x is called the "predictor". The dependent variable y is called the "predictand"
Y = a + b X
the dependent variable the predictand
the independent variable the predictor
ESS210B Prof. Jin-Yi Yu
Linear Regression
We have N paired data point (xi, yi) that we want to approximate their relationship with a linear regression:
The errors produced by this linear approximation can be estimated as:
a0 = intercept a1 = slope (b)
The least square linear fit chooses coefficients a and b to produce a minimum value of the error Q.
ESS210B Prof. Jin-Yi Yu
Least Square Fit
Coefficients a and b are chosen such that the error Q is minimum:
This leads to:
covariance between x and y
Solve the above equations, we get the linear regression coefficients:
b=
where
variance of x
ESS210B Prof. Jin-Yi Yu
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- chapter 2 frequency distributions and graphs or making
- frequency distributions university of notre dame
- susceptibility to cracking of different lots of cdr35
- gg313 g d a soest
- uniform or rectangular distribution
- part 2 analysis of relationship between two variables
- one way analysis of variance new jersey institute of
- us bl 84 instructions usgs
- characterizing the effects of disorder in metamaterial
- aiha proficiency analytical testing programs
Related searches
- correlation between two variables examples
- when two variables have a negative correlation
- limit of two variables calculator
- relationship between two numbers
- no of days between two dates
- calculate percentage of difference between two numbers
- types of relationship between people
- line of intersection between two planes
- total of days between two dates
- number of days between two dates calculator
- letter of agreement between two parties
- function of two variables graph