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The following $(x, y)$ pairs give the advertising dollars (in millions) spent on direct mail and newspaper advertisements respectively for the same years. (a) Find the line of best fit and the regression coefficient. (b) Roughly speaking, how do the two expenditures relate to one another? (c) Do you think that advertising people believe that one of these forms of advertising can substitute for the other. Data: $(10.3,17.7),(8.9,16.5),(7.6,14.8),(4.1,8.2),(2.8,5.7),(1.8,3.7).$

Algebra

Chapter 1

Functions and their Applications

Section 8

Regression

Functions

Missouri State University

McMaster University

Baylor 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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here we are given a set of X Y coordinate points, which describe the amount in millions that's spent on direct mail advertisements and newspaper advertisements, respectively. You can see the key written down in blue for X and Y coordinates. We want to determine the line of best fit for these coordinate points and their regression coefficient. To do this in your stat edit on your graphing calculator and lists L one and l two, you can just enter these X and y coordinate points and then we will go to stat, calculate and calculate a linear regression calculating the linear regression we find that we have see him. Looks like our calculator gives us a linear function of y is equal to 1.70 x plus 1.1 We can interpret the 1.70 here as our regression coefficient. What this tells us is that for each increase in X, so as our direct mail advertisements go up by one, our newspaper advertisements will go up instead by 1.7. So it looks like there is not an equal representation of the two. It looks like newspaper advertisements are greater than direct mail advertisements by about 70%. It looks like if we wanted to determine the relationship here, I suppose I just kind of explain that for you again So we could have We could state this in terms if we wanted. As let's see, direct mail increases by one newspaper increases by 1.7. Okay, so that's all you really need to do in order to explain this relationship here. And it would be a positive relationship to because our regression coefficient is positive. We would end up with a line that look something like this. And if you were to graph all of these points a scatter plot, you would see something similar to that determining whether or not they are substitutes for one another. Again, this goes back to our interpretation that they were an uneven increments. So as direct mail increases by one newspaper increases by 1.7, this suggests that these, uh, advert these people in advertising making the decisions about how much to spend on direct mail newspaper advertisements. It looks as though they believe that newspaper advertisements are actually more worth their while considering that they spend more on that. So we have no, they are not substitutes, and it's simply because of our interpretation

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