Which of the following situations would have data sets or plots that could have a regression line with a positive slope? Select all that apply
A.) The cumulative number of ships launched by ship builders as a function of the number of months since the start of the year
B.) The number of cars produced as a function of the number of days since the end of the last strike
C.) The total shipping orders that are backlogged as a function of the number of ships docked
D.) The number of back orders as a function of the number of assembly workers in a manufacturing company that makes the product
The correct answer and explanation is:
The correct answers are:
A) The cumulative number of ships launched by ship builders as a function of the number of months since the start of the year
B) The number of cars produced as a function of the number of days since the end of the last strike
D) The number of back orders as a function of the number of assembly workers in a manufacturing company that makes the product
Explanation:
A regression line with a positive slope implies that as the independent variable (on the x-axis) increases, the dependent variable (on the y-axis) also increases. In other words, there is a direct or positive relationship between the two variables.
Option A describes the cumulative number of ships launched by ship builders over time (in months). As months pass, it is reasonable to assume that the number of ships launched would increase, making this a scenario where a positive slope is expected. The number of ships launched tends to grow as time progresses, assuming continuous production.
Option B refers to the number of cars produced as a function of days since the end of a strike. Once the strike is over, car production is likely to increase over time as workers return to work, leading to more cars being produced. This relationship would also show a positive slope, where the number of cars produced rises as the number of days increases.
Option D examines the relationship between back orders and the number of assembly workers. In general, as more workers are added to an assembly line, production tends to increase, which would reduce back orders. However, if production cannot keep up with demand, back orders may still increase, but a positive correlation can often be assumed where more workers would lead to fewer back orders over time, depending on the context.
Option C, on the other hand, describes backlogged shipping orders as a function of the number of ships docked. A negative relationship is likely here because more ships docked should reduce the backlog, assuming those ships are unloading cargo. Therefore, the regression line in this case would likely have a negative slope.