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?
This solution gives examples of linear regression in a company's profit equation, provides a null and alternative hypothesis and also calculates the probability of the cell breakdown, regression equation and correlation coefficient. All steps are shown in a clear manner with brief explanations.