Tuesday, October 13, 2015

Shoe Size, Height, Hair Length: Do They Correlate? Due Mon. 10/19 Before Class.

In a comment to this post, please discuss each of the graphs below. Be sure to address the questions under each graph. Please don't copy the questions or number your answers, rather, you should write a paragraph or two in complete sentences so your reader knows what you are talking about. Be sure to sign in as "anonymous" but put your first name and last initial in the post so I know to whom to give the credit. If you have any questions please e-mail me. Review the "how to e-mail a teacher" post on my blog before you send your e-mail.(click on the graphs to enlarge)

I strongly suggest you write the comment in Word or another program and then copy and paste it into the comment section below. This way, if the comment doesn't go through or is accidentally deleted you'll have a record of your work. Please also remember that I have to approve all comments, so it may take a while for it to show up on the blog. You don't need to resubmit it over and over. 

Click on graphs to enlarge. 

Hair Length vs. Height
Correlation Coefficient -0.58 

What can we see from the above scatter plot of hair length vs. height? Is there a correlation? How strong is it? If so, is it positive or negative; strong or weak?

What information about the students in our class does this graph give you? Are there a few "outliers" or extreme data points that seem unusual? If you throw them out of the data set what does the correlation look like? What other information would be helpful to interpret the data? FYI - I eliminated the 5 serious outliers which had heights between 16 and 52 cm.. These were clearly mistakes and they skewed our data severely. 

Height vs. Shoe Size
Correlation Coefficient 0.72

Above is the data we collected about our shoe sizes vs our heights. Can you see a relationship? Is there a correlation? If so, is it positive or negative? How strong is it?  Does shoe size cause height to change? Does height cause shoe size to change? What about the foot that's 38 cm long? 

Shoe Size vs. Hair Length
Correlation Coefficient -0.49

Finally, the above graph shows the relationship between shoe size and hair length. Is there a correlation?  If so, is it positive or negative? How strong is it? The points clustered in an interesting way. What third variable which is not shown on any of the graphs might be causing the relationship between shoe size and hair length?  Does correlation imply causation? Why or why not? How about that high value for Shoe Size? 

And a video about ice cream and polio... 


Anonymous said...

What we can say about the hair length vs. height is that taller people have shorter hair than shorter people who have longer hair. There is a correlation in the hair length vs. height graph therefore it is strong and negative. In the height vs. shoe size graph I see that the taller the people are the bigger feet they have and vise-versa. This correlation is positive and strong. Here, the height causes the shoe size to change. The foot that’s 38 cm long is really tall and has big feet. Finally, in the shoe size vs. hair length graph. Its correlation is negative and weak. Height should be another variable in that graph to show what causes the relationships. I believe that correlation does not imply causation because the correlation between two variables does not imply that one causes the other. –By: ChristianP

Anonymous said...

Valeria G.

In the scatter plot of hair length vs. height there is a negative correlation since it is going downwards. It is also weak since the diagram shows that it is getting closer to “0” anything close to zero is considered to be weak. This graph shows that having a larger height can have a large chance of having a short hair yet with having a shorter height one can conclude that person can have around the same length of “long” hair. Yet there are still some point on the graph that are out of place farther away from groups of points. Also showing that height and hair length can vary but also show that with the other points can have an average based on the people.

Yet in our shoe sizes vs. height graph most points are either close by or on the correlation except one since it was a greater shoe size. The graph also shows a positive and strong correlation since it is going upwards and away from zero. Based on the graph I would say that there was an average since that was a group of point between 155-170 cm of height and 20-25 cm of shoe size. To me height can cause shoe size to be bigger but it can also be the opposite for example a person with a height of 150 cm had a shoe size of 22.5 cm yet a person had the same shoe size but a different height of 161 cm, Showing that height can cause some effect to the shoe size but not always. With the point that has a height of 178 cm and a shoe size of 38 cm it can be determined that with a height it can cause the shoe size to become bigger since it does have a higher height than the rest.

In the final graph between shoe size vs, hair length the correlation is negative and weak since it gets closer to zero rather than farther away in order to become a strong correlation. The graph even if some points are grouped together in order to determine a better understanding we would have to add height since it would a different perspective since with the shoe size of 38 their hair length is only one. While other shoe sizes between 21-23 had an average hair length between 30- 40 cm. It still would be off data since the 38 shoe size had a hair length of one cm. In all these graph correlation does not imply with causation since correlation is between two variables. In the end all graphs had a different result two had a negative correlation while the other had a positive one showing the different types of ways a correlation can form just by seeing the different values of data.

Anonymous said...

From the hair length and height graph you can see different scatter plots.There is no correlation between hair length and height.Therefore,the graph is neither strong nor weak nor negative or positive.I interpreted from the graph that the students in our class have different measurements for hair length and height.There are no extreme outlier since the data is scattered around.It would helpful to know which students have cut there hair before and which students have never cut there hair .Many people cut there hair, so there isn't any correlation between there height.
There is a strong relationship between shoe size and height.There is a correlation and it’s strong and positive.Height does cause shoe size to change.The foot that is 38 cm long is also 180 cm tall.If a person is tall they usually have bigger feet and vice versus.
The final graph is hair length and shoe size.There is a correlation between the two and it’s weak and negative.The third variable that is not shown on the graph is gender , usually men cut their hair very short ,but they still have large feet.correlation doesn’t imply causation because hair length and shoe size are not affecting each other.The highest value for the shoes size ,explains how a person with short hair can still have big feet.

Melody M.

Anonymous said...

Jose M

Hair Length vs. Height
In this graph we see a weak, negative correlation. It’s hard to detect any “outliers” in this graph because all the data seems correct. Many students have different kinds of hairstyles that call for different hair lengths, regardless of their height. We can't assume there is any correlation between height and hair length based on the data in this graph.

Height vs. Shoe Size
In the “Height vs. Shoe Size” graph there is a positive correlation. It’s a strong correlation but it might be because of the outlier that has 38 cm shoe size. one possible explanation for the data of this graph may be that the taller you are, the bigger your foot needs to be in order to maintain balance. We cannot, however, assume that height causes shoe size to increase, or vice versa. We can only determine possible explanations.

Shoe Size vs. Hair Length
In this graph we see a weak and negative correlation. There is a gap between the two clusters of points. A third variable may be causing this gap in the data. One possible variable maybe gender. Males tend to have larger shoe sizes than females while having much shorter hair. The graph could be showing us the two different genders with a few exceptions in both clusters.

Anonymous said...

Gabriel S.
From the "Hair Length vs Height" graph, we can see from the best fit line that students with longer hair are shorter while students with short hair are taller. The best fit line has a negative slope which means there's a correlation, or relationship, between the variables. The correlation coefficient is -0.58 which tells us how strong the relationship is; the further away from zero the absolute value of the coefficient is, the stronger the correlation is. A coefficient of -0.58 means the correlation is about average. Of course the plots on the graph aren't perfect, there are a few students that are short and have short hair or vice versa.
The "Height vs Shoe Size" graph shows that taller students have longer feet while shooter students have shorter feet. The correlation coefficient is 0.72 which means that this relationship is pretty strong. Obviously our feet is what helps us stay balanced when walking so this relationship is correct; there is one plot that states that one student has a foot that is 38 cm long. If we were to eliminate this point, I assume the correlation would be much more stronger.
Finally, the "Hair Length vs. Shoe Size" graph has a correlation of -0.49. This is the weakest correlation coefficient of the three graphs. The slope tells us that the students with longer feet have longer hair. There is a big cluster between 30 cm and 50 cm on the x-axis, and they all have about the same shoe size which helps prove that correlation does not mean causation; in other words, we cannot state that students with longer feet have shorter hair. One thing to consider on these graphs is that the gender of the student was not accounted for which means this is a variable that might've affected our data.

Anonymous said...

In the first correlation graph “Hair Length vs Height” the correlation is negative. As height increases, hair length decreases. the correlation is semi-strong at -0.58. I’m assuming that the students with shorter hair are boys because boys are usually taller with shorter hair, and that the students with longer hair are girls because they are usually shorter than boys.. there are a couple of outliers with a plot scattered unusually. if we remove these outliers it wouldn't matter the correlation would continue to be negative.

In the second correlation graph “Height vs Shoe Size” the correlation is positive. As shoe size increases, Height increases. This correlation is really strong at 0.72. shoes size does not cause height to change or height does not cause shoe size to change, but i is more normal for a big person to have a bigger foot as a smaller person with a smaller foot. The foot that is 38 cm long doesn't matter, if we was to completely cross it out the correlation would continue to be positive.

In the third correlation graph “Shoe Size vs Hair length” the correlation is negative. As Hair length increases, Shoe size decreases. The correlation is semi-week at -0.49. the points are clustered that way with a blank space between around 12 to around 28 is because it goes straight from boys to girls in the drop. there are a couple outsiders with girls with short hair and guys with long hair but the correlation remains negative. correlation does imply causation because shoe size and hair length does not have any relation.

Sergio G.

SB said...

In the scatter plot of hair length vs. height, I can see that someone with long hair had a short height and someone who was tall or had a taller height had shorter hair. There is a correlation between hair length and height. It’s negative and strong. I don't believe there was a few outliers in hair length wise because some girls actually have really long hair.. To me the data was helpful. In the scatter plot of height vs shoe size, there is relationship between the two. The correlation is positive and strong. Height causes shoe size to change. The more you grow, the bigger your foot grows along with your height.bI don't think there's a foot that is 38 cm long unless you're like an ogre. In the scatter plot of shoe size vs hair length, there is a correlation, but it negative and weak. The third variable MIGHT be gender that causes the relationship between shoe size and hair length. The hair length particulates to girls because girls mainly let their hair grow out rather than boys. Correlation does not cause causation because you can't say one variable causes the other. It's just a relationship between the two. Again someone probably made a mistake about their shoe size and was not paying attention.

Anonymous said...

Eleana G.
In the “hair length vs. height” graph, the best fit line indicates that the taller the students are, the shorter hair they’ll have. The line’s slope is negative which means that there is a relationship between the variables. Some of the points on the graph show that there is a couple of students who are short with short hair and tall with long hair. The coefficient of the graph is -0.58, which shows that the correlation is strong; the farther away from zero the stronger the correlation is.
In the “height vs. shoe size” graph, the taller students are the ones with longer feet, and shorter students have shorter feet. This graph has a pretty strong coefficient, which means that the relationship between the variable is really strong. Some of the points were off on the graph; they were probably mistakes but they threw off the data, so maybe the correlation coefficient could’ve been way more stronger than it already was.
The “hair length vs. shoe size” graph is the weakest of all three graphs. it was a coefficient of -0.49. the best fit line shows that students with longer feet have longer hair; however, there is a big cluster between 30 cm and 40 cm on the x-axis which shows hair length. This shows us that correlation does not mean causation because the shoe sizes are all about the same. Gender is a variable that might cause the relationship between the two variables. The correlation might’ve gotten a higher coefficient than expected because of the extremely high value in shoe size. The student might’ve measured wrong, or made some type of error that caused the data for this graph to be thrown off.

Lenny Weston said...

In the first graph there is a negative correlation. The relationship between the X and Y is that the taller you are the shorter your hair. For the second graph there is a positive correlation. The relationship for the graph is that if you are taller you have bigger feet and if you are shorter you have smaller feet. Height causes shoe size to change because you can't be tall with too small of feet you wouldn't be able to hold carry yourself. And for the last graph there is a negative correlation. It's weak too. I feel like comparing the two proves nothing because people cut thier hair so that it tells you nothing. I feel like the points clusters bare the females in the class considering the hair length and shoe size.

Anonymous said...

The first scatter plot with the variables of height and hair length, shows that the taller the person the shorter their hair will be. This scatter plot shows that there is a negative correlation; this correlation would be considered a strong correlation.The information the graph gives me, about the students, is that majority of the boys are taller than the females and those boys had shorter hair. In our class data some of the short students had longer hair but is didn't mess up the data.
In the second scatter plot the relationship I see between the two variables, height and shoe size, is that the taller the person the bigger their feet tend to be.This scatter plot shows that there is a positive correlation; this correlation would be considered a strong correlation as well. The information from the data showed that the height caused the shoe size to change.

Tyra L.
The last scatter plot with the variables of shoe size and hair length, shows that there is a negative correlation and it is also a weak correlation . The correlation does not imply causation because the hair length doesn't really effect the shoe size. Based on the Previous scatter plots, we can imply that the hair length was longer because there could have been more girls than boys, but we really don't know if that's true based off of this correlation. For this correlation we cannot say that the hair length effects the shoe size.

Anonymous said...

In the first scatterplot there is No correlation because as the graph shows,as height goes up,it does not necessarily follow that hair length goes down.Removing the outliers would reveal a neg correlation,however, this would only happen if all boys had short hair and girls long hair.

There is no correlation in the shoe length/ height graph because there was no general trend. The 38cm shoe size belongs to a tall person ,yet, this dot is not a part of a line going upward.

For the third graph, there is no general trend. It would seem that gender could be the third variable actions behind the scenes but, gender neither suggests hair length or shoe size contrary to popular belief.markus we lander