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Table 6 shows the median incomes, in dollars, of men and women in the United States for the years 1974 through 1980 . (a) Find the line of best fit for women's incomes versus time and (b) the line of best fit for men's income versus time. (c) Plot both lines on the same set of axes. (d) Is the gap widening or shrinking? (e) What would this data predict about the earnings gap in $1986 ?$ (The actual gap in 1986 was $25,256-16,232=9024$ ).

a)b)c)(d) Widening(e) $\$ 9,810$

Algebra

Chapter 1

Functions and their Applications

Section 8

Regression

Functions

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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04:16

The following table lists …

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Table 2.9 shows the median…

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The accompanying graph sho…

02:48

01:19

The Gender Gap The followi…

11:27

02:27

(a) Use the data from Exer…

00:34

The wage gap is used to co…

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01:46

Median Family Income The f…

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The scatterplot shows the …

00:55

okay. Using linear regression analysis here we are going to be determining the line of best fit for the data set that we have here, which is describing median incomes in dollars between men and women between the years of 1974 1980. For the purpose of our regression, we're going to make our X values equal to year, and we're going to do it by number, starting at one ending at seven. Rather than doing the actual name of the year itself to begin, let's find the line of best fit for women, In which case what we need to do is plug in the year values and the values. The meeting that comes for the women into your graphing calculator. I am personally using a T I 84 calculator, and for me to do this, I start by going to my staff button, go to edit, and then I can enter my l one and L two values l one being the year L to being the median incomes for women. After doing that, you can go back to your staff button and make your way over to go over to your calculate button At least that's how I'm doing. I suppose yours might be somewhat different, but most graphing calculators are at least somewhat similar. Once you get there, you're fourth option or my fourth option is the linear regression button. By doing that, I end up finding that for women, it produces a linear regression equal to 687.928 x plus 6 92.142 Now, if we wanted to determine the line of best fit for men's median incomes, you would do the same process. But in your l two changer that women's values to the men's values all the same the same process that calculate linear regression. By doing that, it will produce a linear regression for men's median incomes equal to 1007.785 x plus 10,442 0.428 From here, you could plot these if you would like go to your y equals on your graphing calculator plot Both of these on the same axis, you'll see something that looks similar to the graph I have up in the right hand corner of the screen here You can see that over time the gap has widened between the incomes. We have a gap right in here and all the way up here. It looks appears to be much larger. Um, maybe a little concerning, but not the point of the discussion from here. If we wanted to predict the income gap in a future year, we can do that. Let's say that we want to know what the what the earnings gap in the year 1986 was or will be. If we are predicting we can just plug in whatever year 1986 would be within our data set and here it would be 13. So we're gonna equal to X, which is equal to 13 plugging 13 in for each of our X values. You'll end up finding that women in 1986 are predicted to earn one 15 oh, 35.206 and men are predicted to earn 24843 633 So women are projected to earn about $15,000 while men are predicted to earn almost $25,000 to determine the income gap. Here we just take our upper value so we can take the men's income and subtract the women's income. And that ultimately gives us a gap equal to about $9810 in the year of 1986.

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