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Analyze Scatterplots Causation versus CorrelationCausation versus Correlation

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43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to interpret linear models. - Interpret slope in context of data. - Write the line-of-best-fit for a scatter plot. - Distinguish between correlation and causation. - Use technology to calculate correlation coefficient. The student will be able to: - Determine if a scatter plot has positive or negative correlation and if the correlation is weak or strong. - Use the correlation coefficient to interpret the strength of a correlation. With help from the teacher, the student has partial success interpreting linear models or scatter plots. Even with help, the student has no success understanding the concept of a linear models. Learning Goal #2 for Focus 4 (HS.S-ID.C.7, 8 & 9, HS.S-ID.B.6, HS.F-IF.B.6): The student will be able to interpret linear models.

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Scatterplots… Scatterplots show the relationship between two sets of data. Scatterplots show the relationship between two sets of data. The correlation coefficient tells the strength of the relationship. The correlation coefficient tells the strength of the relationship. Correlation just means there is a relationship. Correlation just means there is a relationship. Causation means that one set of data CAUSED the other to happen. Causation means that one set of data CAUSED the other to happen. In today’s lesson, you will determine if the scatterplot or set of data is correlated and if one set of data caused the other to happen. In today’s lesson, you will determine if the scatterplot or set of data is correlated and if one set of data caused the other to happen.

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Correlation tells us how closely two sets of information or data are related. For example: Look at the US highway fatality rate and care it to the metric tons of fresh lemons imported from Mexico. For example: Look at the US highway fatality rate and care it to the metric tons of fresh lemons imported from Mexico. We can see that this set of data has a strong correlation with an r-value of 0.97. We can see that this set of data has a strong correlation with an r-value of 0.97. However, does the importing of lemons CAUSE traffic fatalities in the United States? However, does the importing of lemons CAUSE traffic fatalities in the United States?

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Is it Causation or Correlation? 1.A recent study showed that college students were more likely to vote than their peers who where not in school. 2.Principal Verrill noticed that there was more trash in the hallways after 2 nd period than 1 st period. 3.You hit your little sister and she cried.3.You hit your little sister and she cried. Causation Correlation Correlation

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Causation: The act or process of causing; the act or agency which produces an effect. A Causal Relationship between two things exists if one occurs because of the other. A Causal Relationship between two things exists if one occurs because of the other. For example: If you work less hours, you will earn less money. For example: If you work less hours, you will earn less money. In many cases, the direction of the cause and effect matters. In many cases, the direction of the cause and effect matters. For example: If you earn less money, doesn’t necessarily mean you worked less hours. It could mean that the job pays less. For example: If you earn less money, doesn’t necessarily mean you worked less hours. It could mean that the job pays less. Another example: If you are obese, you will have diabetes. Another example: If you are obese, you will have diabetes. However, the reverse isn’t necessarily true. If you have diabetes, you will be obese. However, the reverse isn’t necessarily true. If you have diabetes, you will be obese.

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Proving causation is a major challenge. There are no set rules or criteria for saying that a correlation is causation. There are no set rules or criteria for saying that a correlation is causation. The more robust the correlation, the more LIKELY they are to imply causation. The more robust the correlation, the more LIKELY they are to imply causation. For example: smoking and cancer. For example: smoking and cancer. Enough research has been conducted and the correlation between cancer and smoking is strong enough to be considered a causal relationship. Enough research has been conducted and the correlation between cancer and smoking is strong enough to be considered a causal relationship. This means smoking causes cancer. This means smoking causes cancer. (The reverse isn’t true: cancer leads to smoking.) (The reverse isn’t true: cancer leads to smoking.)

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Does this data show causation? Is the divorce rate in Maine really caused by how much margarine is consumed? Is the divorce rate in Maine really caused by how much margarine is consumed? Graph from: http://www.fastcodesign.com/3030529/infographic-of-the-day/hilarious-graphs-prove-that-correlation-isnt-causation#1

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Does this data show causation? Are the number of people who drowned by falling into a swimming pool caused by the number of Nicolas Cage films that were made? Are the number of people who drowned by falling into a swimming pool caused by the number of Nicolas Cage films that were made? Graph from: http://www.fastcodesign.com/3030529/infographic-of-the-day/hilarious-graphs-prove-that-correlation-isnt-causation#1

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Does this data show causation? Does consumption of mozzarella cheese cause more people to earn civil engineering doctorate degrees? Does consumption of mozzarella cheese cause more people to earn civil engineering doctorate degrees? Graph from: http://www.fastcodesign.com/3030529/infographic-of-the-day/hilarious-graphs-prove-that-correlation-isnt-causation#1

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Does this data show causation? Is the number of people who die by being tangled in their bed sheets caused by how much revenue was generated by skiing facilities? Is the number of people who die by being tangled in their bed sheets caused by how much revenue was generated by skiing facilities? Graph from: http://www.fastcodesign.com/3030529/infographic-of-the-day/hilarious-graphs-prove-that-correlation-isnt-causation#1

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Causation or Correlation The manager of a toy store hires one new worker, Stacy, in December. The manager of a toy store hires one new worker, Stacy, in December. After Stacy is hired, the store’s sales shoot up by 300%. After Stacy is hired, the store’s sales shoot up by 300%. “Wow!” the manager says to himself. “That Stacy is a fantastic sales worker! I haven’t hired anyone else but Stacy. Still, since I hired her, our sales have tripled! I’d better give her raise!” “Wow!” the manager says to himself. “That Stacy is a fantastic sales worker! I haven’t hired anyone else but Stacy. Still, since I hired her, our sales have tripled! I’d better give her raise!” Is the manager’s conclusion logical? Why or why not? Is the manager’s conclusion logical? Why or why not? Image from Iclipart.

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Newspaper Headlines Many newspapers have headlines that make the reader BELIEVE that the relationship is based on causation. Many newspapers have headlines that make the reader BELIEVE that the relationship is based on causation. Check out these titles: Check out these titles: Lack of sleep may shrink your brain Early language skills reduce preschool tantrums, study finds Dogs walked by men are more aggressive Straight A's in high school may mean better health later in life Eating brown rice to cut diabetes risk Deep voiced men "have more kids“ Eat sweets, live longer Image from Iclipart.

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Remember, correlation does mean causation.

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Lesson 6.1 & 6.2. Learning Goal for Focus 2 (HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3): The student will create equations from multiple representations.

Lesson 6.1 & 6.2. Learning Goal for Focus 2 (HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3): The student will create equations from multiple representations.

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