2. Are rent rates influenced by the student population in a town? We, thus, wish to test the following relationship: log(rent) = Bo + B1 log(pop) + ß2 log(avginc) + Bzpctstu + u where log is the natural logarithm, rent is the average monthly rental paid on rental units, pop is the total city population, gyginc is the average city income and petstu is the student population as a percentage of the total population. Based on the above model the following equation is estimated: log(rent) = 0.043 + 0.066 log(pop) + 0.570 log(avginc) + 0.0056pctstu (0.081) (0.844) (0.039) (0.0017) n= 64, R² = 0.458 (standard errors in parentheses) a) Test the null hypothesis that the size of the student population has no ceteris paribus effect on the monthly rent against the alternative that there is an effect at 5% significance level. b) What signs do you expect for B1 and B2?

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.