A.     What is the dependent variable? What is the independent variable? What are the conditioning variables?

B.     How much do the ages overlap? Note that upper bound of one age is the midpoint of the next age and the lower bound of the next age.

C.    The graph has 12 panes. Explain what the graph in the top row and second column from the left shows. (A one sentence explanation is sufficient.)

D.    The lowess curves match the regression lines at higher education levels but lie above the regression lines at lower education levels. What does this imply?

E.     What group has a stronger relation of wages to education level: women age 38 to 54 or women age 23 to 38?

F.     What group has a stronger relation of wages to education level: women age 38 to 54 or men age 38 to 54?

 

 

 

 

I'm not sure I understand this homework assignment.  Is education the independent variable, wages the dependent variable and sex and ages the conditioning variables?  What does the lowess curve represent (part D)?  Is there a typo in part E- there is no 23-28 grouping?  Thanks.

[NEAS: Correct for the variables. The lowess curve is like a regression line that is not constrained to be a straight line. Yes, the previoust post had a typo in the ages. The second age group is 23-38, which was the intended figures.]

What is part B asking? Is it just looking for the actual age ranges? Is it that simple, and I am just reading too much into it?

[NEAS: It is hard to read the exact ages of each group from the plot, but it is clear that each group shares 50% of its points with the next higher group and the other 50% of its points with the next lower group. That is all that Part B asks.

I'm also confused by part B.  Could someone please clarify the following sentence from part B: "Note that the upper bound of one age is the midpoint of the next age and the lower bound of the next age." 

For example, the second age range is 23-38, so its upper bound would be 38.  The next (third) age range is from 28-44.  It's midpoint would therefore be (44-28)/2 = 36.

[NEAS: Suppose one wants to examines ages 10 - 20; 20 - 30; 30 - 40; etc. A lowess curve won't fit well at the ends of the age points. So the graph uses ages 5 - 25; 15 - 35; 25 - 45; etc. The lowess curves fit well for the ages 10 - 20, 20 - 30; 30 - 40; etc.

Part D states: "the lowess curves match the regression lines at higher education elvels but lie above the regression lines at lower education levesl. What does this imply?"

Is it just that the relationships are closer to linear ath the higher education levels where the data is less sparse?

[NEAS: Many reasons are possible, depending on the scenario. It means the higher education levels have a pattern that seems linear, but the lower education levels have a pattern (if any) that does not seem linear. Sparsity of data is not necessarily the cause.]

Are parts E and F just asking which of the two regression lines has the steepest slope?

[NEAS: Correct; the homework assignment sees if you can relate the panes of the graph to the age groups.]

I am confused on what part B is looking for. When it asks "how much do the ages overlap" is it asking for an answer with a numerical explanation? like what the age groups are or is it looking for a descriptive answer, which would be more so using the "note" part of the question.

The "note" part has me somewhat confused though...
as the endpoint for the fifth age group does not look like the midpoint of the sixth age group...
Maybe I am looking at the graph in the wrong way... any thoughts?

[NEAS: Ages overlap to 50% of the points in the next group. The last group is skewed, since it has some old ages.]

Regarding part E and F, is it correct to say that the more positive correlation exists on the graph (as indicated by a steeper positive slope), the stronger the relationship between the variables?

[NEAS: Yes, but always be careful with units of measurement. The units are the same by age and sex here, so your statement is correct. If we change the units of measurement, the slopes change, so we cant compare different explanatory variables.]

In regard to the reply on the question on E and F, I am slightly confused why the answer would be that the steeper slope would indicate a stronger relation. I think of the slope more as a rate of change. I would think the closer the lowess curve and regression line were to each other the stronger the relation. If you had a less steep slope but all points fell on the regression line, wouldn't this indicate a stronger relation than a graph with points points all over but yielding a regression line with a steeper slope?

[NEAS: The word “strong” is not the beststatistical term. Suppose each additional year of experience raises the average salary for workers 10% in Country A and 5% in Country B. We would say thatexperience has a stronger relation with salary in Country A than in Country B.You note that the significance of the relation between experience and salarymay be greater in Country B, depending on how closely the regression line fitsthe empirical data.]

For part C, am I suppose to tell the exact age group? It's really not clear to read from the graph, or can I just say that this graph shows the relationship between wages and years of experience for males of age 30-42 (roughly read)?

[NEAS: The exact figures are not required; show that you understand what the graph shows.]