Introduction to Regression Modeling

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Presentation transcript:

Introduction to Regression Modeling Check out the examples in Section 1.2 showing the relationship between a response variable and one or more explanatory variables The first is deterministic ; I.e. no random error is involved in the computation of payout (response) based on principal (P) and rate (R) and time (T)… The second is not deterministic since there is measurement error present and an unknown parameter (). Note how the model is then written: The third gives an example of empirical model building in the absence of theory; what are possible explanatory variables that might be used to predict the response a college professor’s annual salary?

Finally, let’s consider the “hardness data” ; hardness of the spring is the response and the temperature of the quench bath is the explanatory variable. The experiment is done with 4 levels of temperature (30,40,50,60) and the Rockwell hardness is measured for each trial… see the data and graph on p.5. How would you describe the relationship? ( discuss direction, strength, and form) Notice that hardness is not a function of temperature alone, since the same temp. gives various hardness values - there is error - but the relationship does appear to be linear in temperature. So we posit the following: Now add subscripts as in equation (1.4) on page 6 to represent the different trials and make the assumptions in equation (1.5) and we have our first linear model; I.e., the model is linear in the parameters  It’s very important to understand the meaning of the parameters in each application; 0 is the intercept and  is the slope. What do they mean in this problem? Explain…

Why do regression modeling? The general model we’ll consider this semester is given on page 15 in equations 1.10a and 1.10b. Note we assume the explanatory variables are measured without error (they are fixed) and the parameters i are interpreted as the change in E(y) when changing xi by one unit keeping all other explanatory variables the same. Why do regression modeling? usually gives a simple relationship between response and explanatory variables, where we know which explanatory variables are most effective in explaining the response. we can use the model to make predictions of the response for given values of the explanatory variables (“what if?) extrapolation? maybe… easy to measure variables can be used to explain one that is harder or more expensive to measure…

Homework: Google R and then install it on your computer – see if you can reproduce the plots in Figures 1.1 and 1.2 for next time. Make an effort to get to know R ... Also, go over the remaining examples in section 1.2 ... we’ll be working through the remainder of Chapter 1 next time...