Brianna Heggeseth
February 4, 2015
At what temperature does it become unsafe to launch a space shuttle?
What is the best way to train for a marathon?
What should be the sale price for a house going onto the market?
What factors impact biological growth?
All could be addressed with a model!
A formalization of relationships between one or more random variables and other non-random variables in the form of assumptions, probability distributions, and mathematical equations.
We use them to describe how we think the “data were generated” and to explain observed variation.
We also use them to make predictions for new individuals.
Every model that we use is wrong in that it does not fully describe the true relationship existing in the universe.
Rather, good models approximate these relationships to help us understand the relationship.
What do you think makes a good model?
A Normal model with mean 150 lbs. and standard deviation 20 lbs.
\[ Weight = 150 + \epsilon\text{ where }\epsilon \sim N(0,20) \]
Two Normal models, one for Males and one for Females, with different means 160 lbs. for males and 140 lbs. for females and same standard deviation of 13 lbs.
\[ Weight = 160- 20\times Female + \epsilon\text{ where }\epsilon \sim N(0,13) \]
A linear model with intercept -140 and slope 4 and standard deviation of errors 10 lbs.
\[ Weight = -140 + 4\times Height + \epsilon\text{ where }\epsilon \sim N(0,10) \]
Almost all of the statistical models that you have learned in the past can be written as Data = Function + Error, or in mathematical notation, \[ Y = f(X) + \epsilon \]
Data table
Case
Quantitative variable
Categrical variable
Response variable
Explanatory variable
Population
Parameters
Sample
Statistic
Experiement
Observational study
Random Variable
Probability Model
Expected Value
Variance
Properties of Expected Value and Variance
Sampling Distribution
Statistical Inference
Confidence Interval
Margin of Error
Hypothesis Test
P-value