STEP 1
a. In this problem we are tasked to generate a scatter plot. You can use any tool you are familiar of but for this answer I will use SPSS, a statistics software. I have uploaded a screenshot of the scatter plot the software generated and you can find it below.
b. For this part, we really need to use a computing software to aide us in our calculations since doing it manually would take a lot of time. For this one I used the same SPSS software and the equation I got is shown below:
c. In this sub-item we just do the same thing that we did in the previous two. The scatter plot for the data for women has also been attached in this answer and you can find it below. As for the equation, the results from SPSS show the following:
STEP 2
a. For this data, we can clearly see from both scatter plots that the linear model fit it very well since the trend of the data is linear. Also, the regression calculator gives us the r correlation value and both data for male and female got a value of 0.99, indicating a strong positive linear relationship.
b. A slope is defined as the "rise over run", or the dependent variable divided by the independent variable. In this case, the slopes of both functions would be the increase in the number of citizens per year. For this item we round off the slopes to the nearest whole number since there is no such thing as half a person.
Slope of M: 20 males per year
Slop of F: 28 females per year
c. As stated in the previous item, these slopes represent the increase in the number of US citizens that earn a bachelor degree every year. Thus, it means that for every succeeding year, the number of males who earn a bachelor degree increases by 20 while the number of females increases by 28.
Step 3.
a. For this item I will make use of Desmos' online graphing calculator to graph the two equations we generated earlier. These two equations should overlap at one point. This point will be the solution to the system. A screenshot of the graph is also attached below.
b. To answer this, we just look at the intersection in our graph. Luckily, Desmos highlights the intersection and it is the one with the displayed coordinates. Looking at it, we can say that the solution to the system is the coordinate pair (-23.442, 41.846).
c. For this item we will equate the two functions and we will solve for the solution using algebra. I will show the step-by-step solution below:
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Using algebra, we arrived at the ordered pair (-23.44, 41.8) which is identical to the one we got by using the graphing calculator.
d. The x value in the solution of the system represents the number of years before 2000 (since it's negative) where the number of men and women who earned a degree is equal (since we equated both equations).
This would mean that there was an equal number of men and women who earned a bachelor degree some time in 1977. Clearly, our answers support the opening paragraph because as we can see from the graph, the line representing the women degree-earners rose in number compared to the men's after equaling them, thus it would make sense that women started outnumbering men in college during the early 1980s.
