11/16/10 Week 13
Inference About Regression
Why are you not the same weight as the person sitting next to you?
Why doesn’t everyone get the same grade?
Effort put into the class
Attendance in class
Completion of activities
Use unit quiz scores to predict exam scores
Simple Linear Regression
Simple because we only consider one predictor variable or also called an explanatory variable
We use linear regression when we have a response or outcome we want to predict and this
outcome is a quantitative variable
Y= mx + b y= dependant m= slope x= independent b=yintercept
Y= B o B X +1e Y= response or outcome B o population y
B 1 population slope X= explanatory or predictor variable e= error in 1 prediction
Error= observed prediction
The software finds the best line by minimizing what is called the squared error where error is the
difference between what we observed and what we predicted. Example; say we use height to
predict weight. From out regression we predict a weight of 215 pounds for someone 72 inches.
Wiesner: 225 lbs Student X: 190 lbs
Wiesner Error: 225215=10 Student X Error: 190215=25 Following the software’s calculations we set a best fit line
Yhat= b + bo X 1 Yhat= fitted or predicted value b = eotimated yintercept
b 1 estimated slope x= predictor or explanatory
How can we tell if two variables have a significant linear relationship?
2. Slope tested against zero
Slope test= H :oB 1 0 Ha: B1 ≠ 0
If there is no relationship between x and y we would have no slope (horizontal
Zero would represent no relationship
Any number that differs from zero implies a relationship
Provide a value to represent strength and direction of a linear relationship