Inference for Slope

Population regression line

Population regression line

a regression line calculated form every value in the population

Sample regression line

a regression line is calculated from a sample

Sampling distribution of a slope

mean

standard deviation

shape of b is approximately normal

Conditions for regression

• Linear - the true relationship of x and y is linear

• Independent - individual observations are independent of each other and when sampling without replacement use 10%

• Normal - for any particular value of x, the response y varies according to the normal distribution

• Equal SD - the standard deviation of y is the same for all values of x

• Random - the data come from a random sample from the population of interest or a randomized experiment