STAT312 : Stat 312 Course Notes, 140 pages done in LaTeX

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silverseal471

28 Dec 2011

School

University of Alberta

Department

Statistics

Course

STAT312

Professor

Yassir Rabhi

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Interpretation of e[y|x] in the two treatment a &b . The spanning set of the columns of a matrix . 2. 7 changing matricies (for fun and pro t) . 2. 9. 4 computation of , y, h, and 2, in terms of the qr decomposition . 2. 9. 5 expectation, variance, and covariance in a linear regression model . Expectation, variance, and covariance with random variables . Expection, variance, and covariance with vectors and matricies . Important formulas for linear regression with hat matricies . 4. 3 distribution of a function of a random variable . 5. 4. 2 finding new power series from old ones . 5. 3. 2 applications: kth moment of a random variable x: e(cid:2)x k(cid:3) . Properties of riemann integrals on bounded variation functions . 6. 2. 2 review of common integrals of trig functions . Proof of weak law of large numbers by tchebyche inequality . 8 convergence of sequences and series of functions. Matrix algebra is essential for applications of probability in various elds:

Related Questions

Opeele Kyinkafa sells different used 2005 GM cars in excellent condition. The value or the retail price (Price) of a car is dependent on a variety of characteristics such as number of miles the car has been driven (Mileage), manufacturer of the car (Make) such as Buick, Cadillac, Chevrolet, Pontiac, SAAB, and Saturn. The car price is also influenced by the body type (Type) such as sedan, convertible, coupe, hatchback and wagon. It is also affected by number of cylinders (Cylinders) in the engine, the engine size (Liter), cruise control which is an indicator variable representing whether the car has cruise control (yes) or no otherwise and Sound indicator representing whether the car has upgraded speakers (yes) or no otherwise. All cars in this data set were less than one year old when priced and considered to be in excellent condition. Determine which major variables are dummies and are dynamic? Identify 3 potential unobserved heterogenous factors in this dataset. Display the full descriptive statistics of the data in R. Why do you think some variables are starred (*)? What is the median for “price”, standard deviation for “mileage”, skewness for “cylinder” and mean for “sound”? Test if “price” is normally distributed using histogram, kernel density plot and the shapiro wilk test. Create a red scatterplot matrix of price, mileage, cylinder, liter, make. From your graph, is the correlation between price & mileage positive or negative? What’s the pearson correlation coefficient between price & mileage and between “cylinder” & “liter” correct to 2 d.p Create a correlation matrix of the dataset by finding the apt R command for converting all string/dummy variables From the matrix, identify 2 potentially good predictors? Identify 3 pairs of variables that are mostly multicollinear. Which 2 pairs of variables are least correlated? Identify 3 pairs of variables most highly correlated with Cylinder Generate a simple regression plot of price on mileage with a re fitted line. Run the whole multiple regression model (label the equation as "regprice") & use it to answer the other questions. Specify the regression model for the whole data keeping the exact names of the variables. Write the estimated regression equation. In one sentence, which variables are significant and which are not? Justify Is the regression model justifiable? Explain Interpret the coefficient of Mileage, MakeCadillac, TypeSedan, Cylinder, & Cruiseyes. Compare the price of a car with 130,000 mileage, 6 cylinders, 3.8 liters, with cruise and sound, was manufactured by Pontiac with a convertible body type with that of the price of a car with four cylinders, 120,000 mileage, 3.8 liters, without cruise nor sound, was manufactured by Cadillac with a hatchback body type. Which factor(s) appears to be causing a comparative difference (if any)? Using only the VIF, which one of the pairs of variables selected to be multicollinear may be deleted? Justify?

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STAT312 : Stat 312 Course Notes, 140 pages done in LaTeX

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