1. How could union members’ current annual incomes decline on net even if a long-lived strike induces a firm’s management to increase the hourly wage rate? 2. Sometimes union memberships coordinate work stoppages when all workers call in sick. From an economic standpoint, is there any difference between coordinated sick day work stoppages and strikes? Explain. Solution (1) This seems paradoxical, but even though hourly wages increase, a long strike will reduce the participant union members\' annual incomes. This is because, the annual income is a function of hourly wage - how many hours in the year a worker has worked. With an increased wage rate, the corresponding demand for labor will decrease (since, output will not increase due to the strike). As labor demand decrease, management will eventually cut down on workforce, thus quite a few workers will lose their job. Secondly, due to the strike, number of hours worked will also decline, and total income (wage mulplied by hours worked) will reduce as well. The total annual income of union members will therefore decline. (2) There is two differences between mass-scale sick day work stoppage & strikes. One, Federal labor law does not allow a strike unless there is a 60-day wait period, which the union must allow before the management refuses to agree to their terms & conditions. With a mass-scale sick day stoppage, this stipulation is not applicable. Two, even if all workers take sick leave, management is bound to pay them the wage even when productivity falls down to zero. But in case of a strike, the workers do not legally have a claim to get paid..

1. 1. How do correlation coefficients summarize the information in scatter-plot? What do scatter-
plots reveal that correlation coefficients do not?
2. What is the relationship between the correlation coefficient and R-squared?
Solution
1. They summarise the strength and direction of any potential linear relationship
between x and y. 2.In statistics, the coefficient of determination R2 is used in the context of
statistical models whose main purpose is the prediction of future outcomes on the basis of other
related information. It is the proportion of variability in a data set that is accounted for by the
statistical model. It provides a measure of how well future outcomes are likely to be predicted by
the model. There are several different definitions of R2 which are only sometimes equivalent.
One class of such cases includes that of linear regression. In this case, if an intercept is included
then R2 is simply the square of the sample correlation coefficient between the outcomes and
their predicted values, or in the case of simple linear regression, between the outcomes and the
values of the single regressor being used for prediction. In such cases, the coefficient of
determination ranges from 0 to 1. Important cases where the computational definition of R2 can
yield negative values, depending on the definition used, arise where the predictions which are
being compared to the corresponding outcomes have not been derived from a model-fitting
procedure using those data, and where linear regression is conducted without including an
intercept.