MATH 11 Regression Inference

response variable

value of the variable y that we want to predict

explanatory variable

the variable x we want to predict y from

linear

the relationship between x,y needs to be _____

scatterplot, residuals

to check linearity assumption, check ____ for linearity and ____ for random scatter

patterns

for independence assumption, check that there are no _____ in the residual plot

even spread

for homoschedasticity and equal variance, check if the residuals have _____ around the line in residual plot

normal probability plot

to check for normal distribution, check _____ of residuals

T = b1/SE(b1)

test statistic for HT for B1

mean response

ex: average college GPA of all students with SAT score 900 is...

individual response

ex: college GPA of a specific student with a SAT score of 900 is...

smaller, smaller

the more data, the ____ the standard error and the ___ the CI

easier

the more data we have the ____ it will be to predict the mean response

prediction interval

____ for the value of the response variable of a specific observation with explanatory variable fixed at x*

greater, individual repsonse

the standard error of y-hat should be ____ than the standard error of mu because there is more uncertainty in predicting an _____ and we need to take into account epsilon*

uncertainty

no matter how much data we have there is going to be a lot of uncertainty in predicting an individual response