### Reading Scatter Plots and Understanding Correlations.

Due Sunday 9/22/13 by 11:59pm

__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)

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Click on graphs to enlarge.

Correlation Coefficient -0.07 |

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?

Correlation Coefficient +0.47 |

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?

Correlation Coefficient -0.34 |

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? What third variable which is not shown on the graphs might be causing the relationship between shoe size and hair length? Does correlation imply causation? Why or why not?

## 14 comments:

Key P.

Hair length vs. height

In this scatter plot of hair length vs. height we find a negative correlation. As height increases hair length decreases. The correlation is weak because there are a lot of outliers. You could assume from our data that the students are mostly male. Males tend to be taller and have shorter hair. If you were to eliminate the outliers the data would have a strong negative correlation. To make the information we have more accurate you would need more students.

Shoe size Vs. Height

This scatter plot shows a relationship between height and shoe size. As height increases so does shoe size. There is a very strong positive correlation. Height increases shoe size. If you are very tall and have small feet you will not be able to balance your body in equilibrium and therefore you will tip over.

Shoe Size Vs. Hair length

In this scatter plot there is somewhat a relationship between shoe size and hair length. The correlation is weak and negative. If a third variable were to occur it would probably be gender. Correlation does not imply causation. Causation is the reason why two variables are related. Correlation shows how two variables are related or how they are being compared.

In the graph, hair length vs. height, we can tell that height isn’t effected by how long or short your hair is. There is a negative correlation between hair length and height and the correlation is weak. This information about the students in my class tells me that most people who are short have short hair in and some that are taller have long hair. The point at the very top is the one that’s separated from the rest of the clustered points. If we were to get rid of the point at the top I think the correlation wouldn’t change much.

In the graph, shoe size vs. height, we can tell that there is a relationship between the two because the points are all around the same area and as height increases so does shoe size. There is a positive correlation and it is very strong. Height causes shoe size to change because as people get taller their shoe size gets bigger.

In the graph, shoe size vs. hair length, there is a correlation between the two. It is a strong but not an immensely strong negative correlation. Correlation does not cause causation because the correlation between two variables does not necessarily imply that one causes the other.

-Ashley L.

From the hair length and height you are available to tell that there is a correlation between it. It is a weak negative correlation. And there are a few outliers in this graph, people who have long hair aren’t always short or in between, there’s one person who have short hair don’t always tend to be tall. Maybe what will help to understand this data would be to figure out if it was a male or female. Now in the shoe vs. height graph we see a strong positive correlation. I it’s understandable that the taller you are the bigger feet you will have. That way you balance yourself. There are some outliers that just don’t make sense like small people with average in between the data shoe size.

In the last graph it is shoe size vs. hair, there is a negative somewhat strong relationship. I think that the third variable in this chart would be if it was a male or a female. Because male usually (not always) have shorter hair, and are typically taller than women. Correlation does not cause causation, because there are variable that you did not plan to come across or things that you did not expect that alter the results.

Jocelyn M.

On the scatter plot of hair length vs. height, we can see that the points are all scattered because people from different height, all had different hair lengths. In this graph there is a correlation but the correlation isn’t strong. The correlation is negative and weak because the line goes down which means negative but the points are all scattered so this makes the graph weak. This graph tells me that the students in our class that were short had the biggest hair length from the class and the students that were taller had shorted hair length. There are only two points in the graph that are “outliers”. If we through this two points out then the whole graph will change because these points are important points that make the graph and if they are removed then everything will change. Maybe the graph will change to positive but weak graph.

On the scatter plot of shoe sizes vs. height, we can tell that the points are scattered from each other because people that were different heights, some students had the same size shoes. In this graph there is a correlation and the correlation is strong. The correlation is positive and strong because the line goes up which means positive and some points are lining up with the line which makes it strong. In the graph it shoes that shoe size cause height to change because as the shoe sizes started to increase so did the height the taller the students, the bigger shoe size. Also height caused shoe size to change because the taller the student, the bigger shoe size which means that the bigger shoe size were boys and boys are also taller.

On the scatter plot of shoe sizes vs. hair length, we can tell that the points are scattered from each other there were students with different hair lengths and shoe sizes.in this graph there is a correlation but the correlation isn’t strong. The correlation is positive and weak because the line shows that the graph is negative and then mostly all the points are scattered in the beginning of the graph which explains that the graph is weak. The third variable that is a negative and weak relationship between hair length and shoe size is that there isn’t enough data to show good graph because if we had more students than the graph could shoe a good graph. Correlation does not imply causation when you use a logical fallacy to illustrate the point.

-Roberto R.

On the hair length vs. height graph, the correlation is negative but it's so weak that it's practically nonexistent. This tells me that just because a person has long hair doesn't mean that they are tall. On the other hand, just because a person has short hair doesn't mean that they are short in height. There are a few outliers on the graph and I think that if we removed them, the correlation wouldn't really change. It would be helpful to know if the test subject is a male or female.

On the shoe size vs.height graph, there is a evident relationship between shoe size and height. The correlation is positive and it is kind of strong but towards the middle. It seems to be the case that as the shoe size gets bigger, the height gets bigger and vice versa.

On the shoe size vs. hair length graph, there is a negative correlation between the variables. This correlation is somewhat strong, but more towards the weak side. I believe that the 3rd variable that isn't mentioned that has a huge effect on this study is gender. So in this and every other case, correlation does not equal causation. Even though this study revealed the relationship between shoe size and height , what it did not reveal is what other variables could be causing this relationship to exist.

-Briana B

In the graph titled "hair length vs. height", we can see that there is a weak negative correlation. As the hair length increases the height decreases. The graph shows us that the students with longer hair tend to be shorter. This is likely to be because the girls in the class have longer hair and are shorter compared to the boys. There are a few outliers in the data. If you were to throw them out the data would probably lean a little more towards being negative. It would be helpful if we had a larger amount of students to test and if the male and female ratio were equal.

In the shoe size vs. height graph shoe size increases as the height increases. This means that its a strong positive correlation. Shoe size does not cause height to change but height can cause shoe size to change because the taller you are the more base support you need, cause taller people to have bigger feet.

In the shoe size vs. hair length graph there is a strong negative correlation. The third variable that is not shown that may be causing the strong negative correlation is that there are very few males in the class compared to females. Correlation does not imply causation because Correlation is the relationship between two variables. While causation explains why the two variables are related.

-Alexandra I.

1. what i see from the scatter plot above is that as height increases hair length decreases. there is a weak negative correlation in this data. the information given in this data is that there are far more students with shorter hair and taller length. there are a few outliers and that caused the correlation to be weak, but if they were to be thrown out then it would only change by a small amount. other information that would better interpret this data would be the genders; male or female.

2. The relationship I see is that as height increases shoe size increases as well. Yes, the correlation for this graph is positive and strong. In my opinion I think that it can be both, shoe size causes height to change and height causes shoe size to change. My reasoning for this would be that there are a lot of tall students with larger shoe size, but that doesn’t mean there aren’t tall students with smaller sizes or shorter students with larger sizes. Height wouldn’t really affect shoe size in this case or vice versa.

3. The correlation between hair length and shoe size is negative and somewhat strong. in this study the third variable that is not shown that causes an effect to this graph is gender as stated in my first answer. In this case correlation does not equal causation as well as in other cases, because the two variables in this experiment do not imply that they caused something to one another.

-Alondra C.

Eliza C (Liza Lizard)

Hair length vs. Height correlation would be viewed as a negative and weak graph. We notice that this scattered plot shows a few “out liners” but also shows a group together. This little group shows that the students who are in this class had the same amount or averaged height but not the same hair length causing the plot to be scattered. If we were to take out the “out liners” out I would conclude that the graph will represent a negative yet strong plot. Other information that would be helpful in this case would be gender identification.

As we continue shoe size vs. height the correlation would be viewed as a positive and a weak plot. We notice a small relationship between the amounts of the same shoe size as they stack next to each other. In this graph it is hard to say whether what is changing what because the tallest (176) has a shoes size of (26). While this person has the biggest foot (27) he is a smaller height of (160). Basically saying that either or has an effect. Being tall does not affect show size and having a big foot does not have an effect on height. All in all it can go both ways.

To finalize shoe size vs. hair length has a correlation of negative and kind of strong graph. What I believe the third variable missing would definitely be the gender identifications. I found this to be the most brought up question and source of information I would look for when observing these graphs. As taught in class correlation does not cause causation in any case at all. Two variables can be seen as a relationship but it does not show the other variables that take part in this to exist. Ending up with a third variable that was not supposed to exist in the experiment is an example.

We can see from the scatter plot of hair length vs. height that almost most of the taller people had the shortest hair length. In this scatter plot there is a correlation. The correlation is not strong. It is a negative correlate. This graph informs me that probably the students with the shorter hair and was males, and the students with longer hair were females. There are a few outliers. If I throw them out of the data set the correlation would still look like a weak negative correlation.

The data collected on our shoe size vs. our height I can see a relationship. There is a correlation. The correlation is strong. It also is a positive correlation. This graph shows me that the bigger the shoe size is the person is taller and the taller the person the bigger the shoe size is.

On the graph showing the relationship between shoe size and hair length there is a correlation. The correlation is negative. The correlation is not strong but not so weak. The third variable which is not shown on the graphs that might be causing the relationship between shoe size and hair length is if it’s a female or male. Correlation does not imply causation. One thing does not necessarily mean that it causes something else to happen.

-Yariel G.

Graph 1- The correlation is negative and It is also very very weak as if its not even there. There are few outliners here. As height increases hair length decreases. You could assume by the data shown that the test subject could be male. Though this is incertan it might be a female and we can not be bias.

Graph 2- The correlation here is positive and strong. As height increases so does the shoe size. Neither one effects the other but it just happens to be that when one grows so does the other.

Graph 3- The correlation here is negative and somewhat strong but more weak so to say in my opinion. Also this correlation does not equal causation. Gender which is the third variable which causes a major effect. We are unsure wether or not the variables are related.

-Precious A.

Height v.s hair length

In the graph of height v.s hair length, we see that the taller people are the shorter hair they have. It is not so strong, because it's not a complete diagonal line, just slightly slanted. The graph is pretty negetave. This graph tells me that in or phychology class the people are the shorter a hair they have. Except for maybe a couple people that are tall wi long hair. It would help to know which dots represent a girl or boy.

Height v.s Shoe size

-yes, the relationship seems to be that the bigger the shoe size the taller they are. The correlation seems positive and very strong. The shoe size does not cause height to change, but it's only logical that height causes our shoe size to change.

Shoe size v.s Hair length

-the correlation of this shoe size and hair length graph seems to be negetave, and it is somewhat strong. The third variable not shown on the graphs would be gender. Correlation does not imply causatren because this research data does not shown how one variable caused, changed or effect the other.

-Gema M.

The graph hair length vs. height, there is a weak negative correlation. As the hair length increases the height decreases. The graph shows that the students with longer hair are shown to be a little shorter. This is most accurate because the girls in class have longer hair and are shorter than to the boys. There are a few outliers in the data. If you were to take them out then the data would show a negative change. If we had a larger group of students that we tested this on then it would’ve been quite more better results.

In the shoe size vs. height graph shoe size increases as the height increases. This means that it’s a strong positive correlation. Shoe size does not cause height to change but height can cause shoe size to change. The reason is because the taller you are the more support you need; also tall people have longer and bigger feet.

Shoe size vs. hair length graph there is a strong negative correlation. The third variable isn’t shown that could be causing the strong negative correlation. Correlation is the relationship between two variables. While causation explains why the two variables are the same.

On the hair vs. height graph, there is barely any correlation. It is a weak and negative. This graph tells me that not all short people have long hair and not all tall people have short hair. This is probably because of the amount of “outliers” in our data (I’m one of the outliers for being short with short hair). I think that if we were to throw the outliers out, the correlation would definitely be stronger. I think this date is pretty easy to understand, but getting rid of the outliers would be better.

For the shoe size vs. height graph there is definitely a relationship. Height and shoe size seem to be increasing together. The correlation is positive and strong. I can’t tell if shoe size is causing the height to change or if the height is causing the shoe size to change. However, it can be either one.

On the shoe size vs. hair length graph, there is a negative semi-strong correlation. The third variable that might be causing their relationship is might be gender. Correlation does not imply causation. In this case, we don’t know which variable is causing the other change.

-Daniela V.

-Linda S.

Hair Length v. Height

The hair length v. height graph shows us that when a person is taller their hair is shorter. There is a correlation, it’s a weak and negative. It tells us that the students in our classroom are tall with short hair while short students have longer hair. There is outliners, one student is tall while he/she has long hair, it seems unsual because every other tall student has short hair while this student has long hair. If that student was taken out the correlation would be more equal in both sides, negative and positive.

Shoe Size v. Height

Yes I see a relationship, when someone is taller they have larger shoe size. There is a correlation. The correlation is strong and positive too. The height doesn’t change shoe size because theres short people who have large feet and tall people who have smaller feet. Shoe size doesn’t change height because the shoe size doesn’t matter when it come to height.

Shoe Size v. Hair Length

There is a correlation in the graph shoe size v. hair length. The correlation is negative and its not fully strong. The variable might be the gender of the people that took this experiment, because usally males have shorter hair while they have larger feet and there might not have been enough males to test it out. Correlation does not apply causation because causation shows the relationship between two variables.

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