Question

1. Consider a city in which urban density averages five housing units per acre. The city is fully circular with the CBD at the center. The distance between CBD and the city border is 30 miles. Land at 10 miles from CBD costs $500,000 per acre and land at 20 mile from CBD costs $300,000. Calculate annual transportation cost per mile assuming the city is currently neither growing nor shrinking.

Answer 1

To solve this question just input those variables which are to be used in logistic regression, as the question talks about using two variables only that is total loans and leases to total assets & total expenses/ total assets, so we will not input total cap/assets as an input variable in our excel, here we go

As one can see, we have taken only two variables , total exp/assets and total lns & leases/ assets in calculation, follwing steps have been followed to construct the above table

1. Assume logit= b0+ b1* independent variable1+ b2* independent variable 2 , take values of b0=0.1, b1=0.1, b2=0.1, note that these values of b0, b1 and b2 are just taken for calculation, one could assume any values here for bo , b1 and b2

2. Calculate exponential of logit in the next column by using exp (value in previous column)

3. Calculate probability by using formula, probability= exp (logit)/ { 1+ exp(logit)} in the next column

4. In next column, calculate log likelihood by using formula : financial condition value (i.e. 1 or 0) * LN( probability calculated in previous column) + (1- financial condition value)* LN( 1- probability calculated in previous column)

5. take the total of the column values of log likelihood

6. use solver function in excel to change this total by putting max value of 0 and changing the variable cells containing assumed values of b0, b1 and b2 , by clicking on solve, you will get actual values of b0, b1 and b2

which comes out to be b0=-14.72, b1=89.83, b2= 8.37

therefore you will get logit as

-14.72+ 89.83* Total exp/assets+8.37*Total lns & lsses/ assets

With values given in the question as total exp/ assets= 0.11 and total loans & leases/ assets= 0.6 , we get

logit as -14.72+ 89.83* 0.11+ 8.37*0.6= 0.1833

exp (logit) = 1.20

Probability= 0.546

Loglikelihood= 1*LN(0.546)+0*LN(1-0.546)= LN(0.546)= -0.605