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(a) Use the data from Exercise 2 to find the line of best fit for men s income as a function of women's income. (b) What is the slope of this line? (c) Does it predict that the earnings gap is widening or shrinking?

a)(b) 1.608(c) It is widening

Algebra

Chapter 1

Functions and their Applications

Section 8

Regression

Functions

Baylor University

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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Okay, so here we're gonna be using linear regression techniques to determine the line of best fit for median annual incomes between men and women. In this case, we want to determine specifically if the income gap is widening overtime. To do this, we're going to regress men's incomes as a function of women's incomes. So that is the women's incomes are going to be our X variable, our independent variable. Whereas men's very incomes are our dependent variable. Why so to do this, um, for your reference, I've put in the steps that I've taken using my graphing calculator, which is a t. I 84 to start. I went to stat edit in my l one and L two list. I entered the women's incomes and the men's incomes go into stat K elk and the fourth option going down of linear regression. Calculating that it outputs a result of y being equal to 1.608 x plus 6 51.9 to 1, there is our function of men's income regressed on women's income. Now what's interesting here is by taking a look at the slope, which, by the way, is 1.86 are slope here, 1.6 away in my bed? That is our slope. And what this is telling us is that for every increase in women's income, so for every increase in that X variable, men's income increases by 1.608 So when women's income increases by $1 if that's our unit of measurement, men will experience an increase of dollars 608 So that's quite disproportionate, actually, to see that they're earning that additional 60 cents on the dollar. This tells us that the income gap is widening, actually, which is a little interesting. There are other studies that we could do in order to determine exactly why that is, if we were to include other variables in this. But from here, we can see specifically that the slope of the line 1.608 tells us that in comparison to women's income, men's income is continuing to be greater. Therefore, the gap is widening

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