Quantitative Analysis #2 : 1 page memo
Some notes on what you want out of the data:
Moth analysts want some kind of confirmation from simple regression before they accept the multi-linear regression results.
Test each variable to make sure that on your own they are explanatory.
There is only one dependent variable.
Maximize your r squared while at the same you are minimizing the number of independent variables. The reason why that is difficult is because your r squared will go up if you include a variable that has absolutely nothing to do with it.
Minimize your significant f value. (the p value of the f)
Notes:
Y values salary (HH Inc)
X = Age
Regression backwards…and then I click ok
Look at the significance f
Significant f: It’s the same.
Why? Because you can always write a linear equation to make the other variable on it’s own.
How is x dependent on y? They may or may not be.
If there is a difference…if there is a relationship between y and x there relationship x and y.
But there are a couple of things that can change.
For example: Your coefficients are different. The line has different slope and a different y intercept. However your p values are the same…as your significant (f) is…and your r squared is the same.
There is clearly a relationship. The model as a whole has explanatory power because that significant (f) is below .05
The variable salary does have a relationship with (HH Inc) because that is a logical statistic. And it has the same level of predictability.
In other words, the data, distance from the line is still what it is. The line has changed though.
Multi-regression: (using the alpha .05)
When choosing which one is 0 and which one is 1:
You want to make each category a separate dummy variable.
If you have more than two categories you can’t really have a 0, 1, 2. Because you have a 0 and a 2, but your regression can come up with a 1.
Type in excel…
DATA
ANALYSIS
What are my independent (y) variables? You need to select all of them.
How many independent variables are there? Ok now that you have them, you select all of them.
Make labels:
MLR1…and then click OK.
NOTE! The only thing you highlight is the dummy variable.
MAJOR QUESTION TO CONSIDER: Is the model as a whole meaningful? Is there a explanatory relationship between the (x) and the (y)
Now look at your p values. You will notice that your p values are no longer the same as that significance (f).
The significance (f) is the model as a whole.
The p values represent the importance of each independent variable. Has we look at the p value, we do not care about the intercept. The intercept is the outgrowth of the line.
Which categories are an explanatory value? Why? Because the p value is below the explanatory line.
Your p value has to be below your alpha!!! (.05)
Peers notes:
You do not want a high intercept.
Get your lowest p value.