STATS 500 Lecture 4: STATS 500 – Lecture 4

31 views3 pages

crimsonwalrus133

19 Oct 2016

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Linear regression -estimation: the normal linear model. Assume the linear model y is the n x 1 random response vector (observed) X is the fixed n x p matrix of predictor variables (observed) Is the p x 1 vector of fixed and unknown parameters ( not observed. Is the n x 1 random vector of error terms (not observed) This is how it looks like in matrix form: linear versus nonlinear model. A linear model is linear in the parameters ( for example). A nonlinear model: brief overview of least squares estimation. Assuming x has rank p, the unique solution is: the fitted values and residuals. P=x (cid:894)x"x(cid:895)-1x is the li(cid:374)ear tra(cid:374)sfor(cid:373)atio(cid:374) represe(cid:374)ti(cid:374)g the orthogo(cid:374)al projectio(cid:374) of (cid:374)- dimensional euclidean space: properties of least squares estimates. The gauss-markov theorem states that is the best linear unbiased estimate (blue) of (i. e. it has minimum variance in the class of unbiased estimators)

Related Questions

A salesperson makes four calls per year. A sample of 100 days given the following frequencies of sales volumes.

Number of Sales	Observed Frequency (days)
0	30
1	32
2	25
3	10
4	3
TOTAL	100

Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial distribution. The Binomial distribution is represented by:

For this exercise, assume that the population has a binomial probability distribution with n=4, p=0.30 and x= 0, 1, 2, 3 and 4.

(a) Compute the expected frequencies for x=0, 1, 2, 3 and 4 by using the binomial probability function. Combine categories if necessary to satisfy the requirement that the expected frequency is five or more for all categories.

(b) Use the goodness of fit test to determine whether the assumption of a binomial probability distribution should be rejected. Because no parameters of the Binomial probability distribution were estimated from the sample data, the degrees of freedom are k-1 .