Here is our sample data on height
and weight.
Observation Height (H or X) Weight (W or Y)
1.Jackie 64 130
2. Philip D. 75 210
3. Bryan 76 230
4. Rita 67 190
5. Shane 68 175
6. Keith 75 190
7. Kelsie 65 145
8. Di 72 185
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Sample Data - Applied Regression Analysis - Lecture Slides, Slides of Data Analysis & Statistical Methods
It is the Lecture Slides of Applied Regression Analysis which includes Perfect Multicollinearity, Overall Significance of Equation, Recap, Population of Students etc. Key important points are: Sample Data, Jackie, Philip, Bryan, Rita, Shane, Keith, Kelsie, Formulas, Email Attachment
Typology: Slides
2012/2013
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Download Sample Data - Applied Regression Analysis - Lecture Slides and more Slides Data Analysis & Statistical Methods in PDF only on Docsity!
Here is our sample data on height
and weight.
Observation Height (H or X) Weight (W or Y) 1.Jackie 64 130
- Philip D. 75 210
- Bryan 76 230
- Rita 67 190
- Shane 68 175
- Keith 75 190
- Kelsie 65 145
- Di 72 185
Assignment 1(Carries 30 points
and is due before noon on
Thursday, September 6 )
- Use the data set on the previous slide and the formulas on Page 8 (1-5 and 1-6) to estimated the coefficients β 0 ^ and β 1 ^ in the equation below W = β 0 ^ + β 1 ^ H
- Make sure to show your work.
- Do the estimated coefficients make sense to you?
- What is the meaning of the estimated coefficients?
Note:
- The following notes are not going to take
the place of the discussions covered in
your text books
- First read the book
- Then look at the notes
Total, Explained and Residual Sum
of Squares (PP11-13)
- Remember our height/weight example
- What is the average weight of the
class?
- Duplicate the graph on Page 12 where
Y is the weight and X is the height
- The Fitted Line will be upward sloping
- The Average Line (average weight) will be horizontal
Remember we have 8 observations
in our sample
- Some of our weights are below average
and some are above average.
- Look at Equation 1-8, Page 12
- The reason why we square (Y – Ybar), (Y^ - Ybar) and (Y – Y^) is because we do not want the positive differences to cancel the negative differences
- Note: the best fitted line will be the one
with the lowest (Y – Y^) 2
Multiple Regression Model
(Chapter 2, PP20-29)
- Is height the only factor affecting weight?
- Of course not.
- What are some other factors affecting an individual’s weight? - Age - Calorie in take per day - ……
The meaning of the estimated
coefficients
- Our estimated equations will be
- Y^ = β 0 ^ + β 1 ^ X 1 + β 2 ^ X 2 + β 3 ^ X 3
- Bonus: Can someone tell me why didn’t I put an “e” at the end of the above equation?
- β 1 ^ measures the effect of one more inch of height on weight, holding the age and the calorie intake constant and ignoring the effect of all other variables on weight.
- Similarly β 2 ^ measures the effect of one more year of age on weight , holding the weight and the calorie intake constant and ignoring the effect of all other variables on weight.
How big should the sample be?
- The bigger the sample the closer the β^
will be to β.
- Rule of thumb: Degrees of Freedom >
- Degrees of Freedom = n- k-
- Where n is the sample size and k is the number of independent variables.
Assumption 1
The regression equation
- Is linear in coefficients (not linear in
variables)
- Is correctly specified (right functional
form, no omitted variables, no irrelevant
variables)
- Has additive error term
Assumption 2
Two or more independent variables are not perfectly correlated with each other.
- If violated Perfect Multicollinearity
- Example
- Consumption = f (inflation, real interest rate, nominal interest rate, ….) - Since real interest = nominal interest – inflations, - The 3 independent variables are perfectly and linearly correlated with each other. When one independent variable changes, the others change too. OLS can not capture the effect of one variable in isolation
Assumption 4
- The error terms are uncorrelated with
each other
- What if it is violated?
- Then we have autocorrelation (serial
correlation) problem
- Example: Consumption = f (…., income)
- Suppose we use time series data on the US economy to estimate the above model. - Suppose that in 5 years of our study there was a war and consumption dropped significantly even though income didn’t. So, we will get negative errors during those years and they all seem to be correlated with each other. Docsity.com
Assumption 5
- The error term must have a zero mean
- What if this assumption is violated
- This is not a big deal: the intercept will pick
up the mean of the error term
Assumption 7 (Not Necessary)
- The error term is normally distributed
- What is a normal distribution?
- Symmetric, continuous, bell shaped
- Can be characterized by its mean and variance
- Must know if it is violated
- If violated, some statistical tests are not applicable
- As the size of sample goes up the distribution becomes more normal