Temple University
Department of Economics

Economics 615

Introduction to Analysis of Variance, Simple Regression
and Hypothesis Testing

1. (HT) In order to test whether four brands of gasoline give equal performance in terms of mileage, each of three cars was driven with each of the four brands of gasoline.  Then each of the (3x4=12) possible combinations was repeated four times. The number of miles per gallon for each of the four repititions in each cell is recorded in the table below.

 Brand of gasoline Car 1 2 3 4 1 21.0 14.9 16.3 20.0 15.8 19.4 17.8 17.3 16.2 18.8 15.2 21.6 14.5 14.8 18.2 20.4 2 20.6 19.5 15.5 16.8 16.6 13.7 18.1 17.1 20.8 18.9 17.4 19.4 18.2 16.1 21.5 19.1 3 14.2 13.1 17.4 18.1 15.2 16.7 16.3 16.4 16.8 17.4 16.4 16.9 17.7 18.1 17.9 18.8

The possible model of gasoline consumption is

i=1,2,3 cars

j=1,2,3,4 brands of gas

andis the interaction between car and brand.

Test the following hypotheses:
a.  The type of car does not matter.
b.  The type of gasoline does not matter.
c.  Neither the car nor the gasoline matters.
d. The interaction effect is zero.

2.  The data in capm.txt is an ASCII text file.  The first row has the variable names MARKET, RKFREE and Motor.  Market is the market rate of return as a weighted monthly average of the NY and American Stock Exchanges for January 1978 through December 1987 (120 months).  RKFREE is the return on 30-day U.S Treasury bills.  It is understood to be the risk free rate. Motor is the monthly return for Motorola.  By clicking you can retrieve a self-extracting file that contains this question set, the data, and a bit of MCD code which will read the data.
a.  Plot the observations for the last thirty six months (all 120 observations wouldn't look like much).
b.  Using the data construct Firm=Motor-RKFREE and MktIndex=Market-RKFREE.   Compute the sample means for Motor, MARKET, RKFREE, Firm and MktIndex.
c.  Annualize the monthly returns.
d.  Plot the annualized series for Firm and MktIndex for the last 36 months.
e.  Discuss the two plots you did.
f.  From the annualized data estimate the coefficients in the regression

g.  Using the least squares residuals from this regression compute an estimate of the error variance.
h. Compute estimates of  and .
i.  Test the hypothesis that the intercept is zero.
j.  Test the hypothesis that the slope is one.