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Consider the Auto  dataset consisting of 392 observations on 9 variables Mpg: miles per gallonCylinders: Number of cylinders between 4 and 8Displacement: Engine displacement (cu. inches)Horsepower: Engine horsepowerWeight: Vehicle weight (lbs.)Acceleration: Time to accelerate from 0 to 60 mph (sec.)Year: Model year (modulo 100) Origin: Origin of car (1. American, 2. European, 3. Japanese) Name: Vehicle nameMpg01: 1 if mpg above median mpg, 0 otherwise We wish to predict whether a given car gets high or low gas mileage (mpg01). We used LDA on train data to predict mpg01. R output is provided below.> lda.fitCall:lda(mpg01 ~ cylinders + displacement + weight, data = Auto.train) Prior probabilities of groups:       0        10.5068027 0.4931973 Group means: cylinders    displacement  weight0 6.637584    266.1946  3588.7321 4.213793    118.0552  2358.386 Coefficients of linear discriminants:                          LD1cylinders        -0.371188396displacement      -0.000695555weight            -0.001015639 > lda.predict = predict( lda.fit, newdata=Auto.test )> CM = table( predicted=lda.predict$class, truth=Auto.test$mpg01 )> print( CM )               truthpredicted        0  1            0   42  1            1   5  50Report the values of the prior probabilities and explain briefly their meaning (in context).Using the Math Editor in Blackboard UltraWhen you need to show a calculation or mathematical expression:Click in the answer box.Select the + (Add Content) button in the editor.Select Math to open the Math Editor.Enter your equation or calculation and select Insert.Continue typing your explanation in the answer box.  

Suppose n=2, p=2, x11=x12,  x21=x22 and  y1+y2=0 and x11+x21=0 and  x12+x22 =0. Write out analytically the lasso optimization problem in this setting.  HINT. Start with the general lasso objective function. Since p=2 write the prediction for observation i using the two predictors. Then expand the summation for n=2. You do not need to solve for the betas.

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Where _____ may be present in an agricultural building, enclosures and fittings shall have corrosion-resistance properties suitable for the conditions.

Where there is more than one driving machine in an elevator machine room, the disconnecting means shall be numbered to correspond to the identifying number of the _____.

Where an equipment grounding conductor is installed underground within an agricultural building, it shall be _____.

Which of the following wiring methods are permitted in an assembly occupancy of fire-rated construction?

Threaded conduits or fittings installed in hazardous (classified) locations shall be made wrenchtight to _____.

In Class I hazardous (classified) locations, sealing compound shall be used in Type MI cable termination fittings to _____.

Electric vehicle supply equipment includes the conductors and electric vehicle connectors, _____ installed specifically for the purpose of transferring energy between the premises wiring and the electric vehicle.