Statistical Analysis of the Nfl

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Michael Freiberg
Statistics Mid-Term #2
1.)
A.) X2 Male=0; Female =1 X3 No PhD=0; Having a PhD=1
Benchmark Equation= Y=Bo+B1*(X1i)+Ei
B.) B1= With each additional year of experience on Average an instructors annual salary would increase or decrease by B1, HOLDING ALL ELSE CONSTANT B2=When instructors are females, on Average their annual salary would increase or decrease by B2 HOLDING ALL ELSE CONSTANT B3= When instructors have a PhD On average their annual salary would increase or decrease by B3, HOLDING ALL ELSE CONSTANT C.)

X4= X1*X3
Yi=Bo+B1*(X1i)+ B2*(X2i)+B3*(X3i)+B4*(X4i)+Ei
With a PhD(X3=1); Y=Bo+B1*(X1i)+B2*(X2i)+B3*(X3i)+B4(X3i*X1i)+Ei With NO PhD(X3=0); Y=Bo+B1*(X1i)+B2*(X2i)+ Ei
2.)
A) Rsquared= SSR/SST= 1.9683/1.9798= .99421
B) Adjusted Rsquared= 1-[(1-Rsquared)*((n-1)/(n-k-1))]
Adjusted Rsquared= 1-[(1-.9942)*((100-1)/(100-2-1))]= .99408 C) Residual Df= n-k-1=100-2-1 Residual Df=97
D) Regression F= MSR/MSE= .984152/.000118= 8340.27
E) t-Stat of X2 = Coefficient X2/Standard Error of X2= -.0396/.0028797= -13.75

3.)
A) B1= On average a dogs ranking according to urban inhabitants will go up by 1.98 units for every additional inch in height they are, HOLDING DOG WEIGHT CONSTANT B2= On average a dogs ranking according to urban inhabitants will go down by .0396 units for each additional pound they weigh, HOLDING DOG HEIGHT CONSTANT B) It is silly to interpret due to the fact that it is impossible for a dog to have a height of 0 inches and a weight of 0 pounds. In addition I would assume the values of 0,0 to be excluded from the relevant range from this made up set of data therefore making the equation inaccurate with these x, y value. 4.) Ho=B1=B2=0

Unrestricted= Yi=Bo+B1*(X1i)+B2*(X2i)+B3*(X3i)+ Ei
Restricted = Yi= Bo+ B3*(X3i)+Ei
A) Number of restrictions=M=2
B) Denominator degrees of freedom=n-k-1=200-3-1=196
C) RSquared Unrestricted= .9977
D) Rquared Restricted=.9848
E)...
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