Question

1. For each of the following regression models, write down the X matrix and 3 vector. Assume in both cases that there are four observations (a) Y BoB1X1 + B2X1X2 (b) log Y Bo B1XiB2X2+ 2. For each of the following regression models, write down the X matrix and vector. Assume in both cases that there are five observations. (a) YB1XB2X2+BXE (b) VYBoB, X,a +2 log10 X2+E regression model never reduces R2, why 3. If adding predictor variables to a not just include all the available predict or variables in the model? Also, remark on the meaning of Rd adj 4. Recall the simple correlation coefficient r is signed. Why is it not meaning ful to include a sign on the coefficient of multiple correlation (or coefficient of determination) R2? The data set called mtcars is included in the basic R installation and contains information on 1973-74 model automobiles, including miles per gallon, number of cylinders, displacement (cubic inches), gross horsepower, read axle ratio, weight (in lbs/1000), quarter mile time in seconds, v- or straight (V-0, straight 1), transmission (coded so 0 = automatic and 1 manual), number of forward gears, and number of carburetors. This data set came from the 1974 Motor Trend magazine. You can see the data set by simply typing mtcars at the prompt: mtcars Use this data set to answer the remaining questions. I have included R code to help you 5. Make a scatterplot matrix of the mpg, dips, drat, and wt variables, indi- cating the numbers of gears like this library (car) scatterplot.matrix ( "mpg+ disp+ drat +wt | cyl, main-"Three Cylinder Options") data-mtcars, The plots along the diagonal are of course not scatterplots (if they were, they would all be straight lines), but show estimated density functions for each variable, color-coded for the number of cylinders. Each of the scatterplots includes a fitted regression line, as well as a lowess-smoothed trend curve (which is There are also rug plots in the cell margins. Comment generally on a few things that you observe about these five variables based on the scatterplot matrix, specifically about the trends between the quantitative variables and also if the mumber of cylinders seems to be a factor. Note the legend for the numbers of cylinders is located in one of the plots. more sophisticated way of estimating trends). a 6. Get a sample correlation matrix of the same four quantitative variables from the previous part like this: attach (mtcars) d data.frame (mpg, disp, drat, vt) cor(d) Which variable pairs seem most correlated now? Also, explain the mag- nitude and direction of the correlations. 7. Fit a GLM that attempts to predict mpg based on disp, wt, and drat. Use planar model of the form mipg bo + b x disp+b2 x wt +bs x drat: a 1m(mpg disp drat t) out

Answer 1

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