population as a percentage of the total population. One model to test for a relationship is log(rent) = Bo + ß1 log(pop) + B2 log(avginc) + B3 pctstu + u. i) State the null hypothesis that size of the student body relation to the population has no ceteris paribus effect on monthly rents. State the alternative that there is an effect. ii) The equation estimated using 1990 data for 64 college towns is log(rent) = .0443+.066 log(pop) + .507 log(avginc) + .0056 pctstu (.844) (.039) (.081) (.0017) R² = 0.458. iii) What is wrong with the statement: “A 10% increase in population is associated with about a 6.6% increase in rent"? iv) Test the hypothesis stated in part(i) at 1% level of significance. v) Give interval estimators for ß1, B2 and B3 and interpret them.
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.
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