Regression Analysis

Perform linear regression analysis.

Linear Regression

def linregress(
	yobs:_Iterable, 
	factor:_Iterable[_Iterable], 
	intercept=True, 
	alpha=0.05)->simple_linregress|multiple_linregress:
"""
Performs simple/multiple linear regression

yobs: Dependent data 
factor: independent data (must be 2D)
intercept: True if there is intercept
alpha: significance level
"""


class simple_linregress:
   def compute(self)->list:
   def summary(self)->linregressResult:	
   def residuals(self)->tuple:		


class multiple_linregress:
   def compute(self)->list:
   def summary(self)->linregressResult:
   def residuals(self)->tuple:


class linregressResult:
   @property
   def R2(self):

   @property
   def stderr(self):

   @property
   def pvalue(self):

   @property
   def fvalue(self):

   @property
   def intercept(self):

   @property
   def ANOVA(self):

   @property
   def coeffstat(self):

Example

Do the following data (Data from: Larsen & Marx, An Introduction to Mathematical Statistics and Its Applications) support the suspicion that smoking contributes to CHD mortality?

Cigarette Consumption: [3900, 3350, 3220, 3220, 2790, 2780, 2770, 2290, 2160, 1890, 1810, 1800, 1770, 1700, 1680, 1510, 1500, 1410, 1270, 1200, 1090]
Mortality per 100000: [256.9, 211.6, 238.1, 211.8, 194.1, 124.5, 187.3, 110.5, 233.1, 150.3, 124.7, 41.2, 182.1, 118.1, 31.9, 114.3, 144.9, 59.7, 126.9, 43.9, 136.3]

factor = [3900, 3350, 3220, 3220, 2790, 2780, 2770, 
    2290, 2160, 1890, 1810, 1800, 1770, 
    1700, 1680, 1510, 1500, 1410, 1270, 1200, 1090] 

response = [256.9, 211.6, 238.1, 211.8, 194.1, 124.5, 187.3, 
    110.5, 233.1, 150.3, 124.7, 41.2, 182.1, 118.1, 31.9, 114.3, 144.9, 
    59.7, 126.9, 43.9, 136.3] 
 
slm = st.linregress(response, factor) 
slp_inter = slm.compute()
print("Coefficients:", slp_inter)

summary = slm.summary()
print("p-value:", summary.pvalue)
"""
Coefficients: [0.0601, 15.771]
p-value: 0.0002
"""