Linear Regression, Hypothesis Testing and Probability
1. The basic assumption in linear regression is that the
relationship between variables can be approximated by linear relation. Can you
think of examples of such relations that you expect to be linear relations?
2. Pick one of the feature hypothesis tests and explain it
in everyday language.
3. Consider rolling a pair of dice. What is the probability
of rolling two faces such that their sum is an odd number or 3 is one of the
faces?
4. Assume that the probability of the number of breakdowns
of a cell phone of a certain make in the first year of service is a Poisson
distribution and the standard deviation of that distribution is 2. What is the
probability that a phone of that make will break down between 2 and 4 times in
the first year of service.
5. The following is a list pairs of numbers consisting of
amounts invested in recent movies (in millions) and the revenues generated by
the movies. (2,2), (4,5), (6,7), (18,15), (20,18), (24,30). Calculate the
regression equation for the data and the correlation coefficient. Is there good
evidence of a linear relation between investment and revenue?
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