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Using Scatter Plots to Identify Relationships Between Variables LG: I can create a scatter plot LG: I can interpret a scatter plot by identifying the dependent and independent variables LG: I can distinguish between causation and correlation

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Minds On What’s the difference between one- and two- variable data sets? One-variable: you know ONE attribute about each subject Two-variable: you know TWO attributes about each subject

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Exit Card (from yesterday) Identify whether these situations use one- variable or two-variable sets of data – 1) Noah researches annual hours of sunshine in Canadian cities – 2) A study compared the length time children spent playing video games and the time they spent reading – 3) Kurt looked up stats on baseball players to decide whether arm length influenced how far the pitchers could throw.

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…but what IS a variable, anyway? A variable is an attribute that can be measured. A quantity Its root word is vary because the variables change (or we don’t know what they are yet, until we make some decisions or define one of them)

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In two-variable data sets, one variable MAY depend on the other one. For example: Students were surveyed and asked to report their average grade for semester 1 and the number of hours they spent studying What are the two variables in this data set? Which of these two variables is dependent on the other?

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When we plot data…. we ALWAYS plot the __________________ variable on the x-axis, and the ___________________ variable on the y-axis. independent dependent x independent y dependent

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EXAMPLE 1Designing and Conducting an Experiment A group of rock climbers want to investigate the effects of practice and the time it takes to climb a wall. The results of the experiment are provided. (1) When organizing the results, what would be the variable There are two variables - Trial number - Time (2) Why would displaying the results using a scatter plot be the most appropriate for this experiment? We are dealing with two variables

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EXAMPLE 1Designing and Conducting an Experiment (3) Display the data on a scatterplot Trial Number Time (in minutes) # of Trials vs. Time

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EXAMPLE 1Designing and Conducting an Experiment (4) Analyse the data. What can you conclude about the data collected? As the participants had more practice, their times were faster Improved performance Trial Number Time (in minutes) # of Trials vs. Time

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So let’s say you’ve worked really hard and conducted some experiment where you measured two variables… How will you know if there’s a relationship between the two variables you measured? A CORRELATION is a relationship between two variables. A Positive Correlation means that the variables _______________________. A Negative Correlation means that one variable ________________ while the other ________________. increase together increases decreases Like this!

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So how will you know if the correlation is weak or strong? Weak positiveStrong positive No correlation Points are spread out? WEAK Points appear to lie on a line? STRONG Points are scattered/ No visible trend? NO CORRELATION

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Analyzing Data with a Scatter Plot Davis conducted an experiment comparing a person’s leg length and how long it takes the same person to walk 100 m. His data is plotted here in the scatter plot.

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Analyzing Data with a Scatter Plot (a) Does the data suggest a relationship between leg length and time taken to walk 100 m? If so, describe the relationship. Yes; negative correlation The time it takes to walk 100 m decreases as leg length increases.

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Analyzing Data with a Scatter Plot (b) Use the graph to estimate the time it would take a person with legs that are 85 cm long to walk 100 m. Where x = 85, y = 63 Therefore, someone with legs that are 85 cm long might take about 63 seconds to walk 100 m.

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Considering Possible CAUSE & EFFECT Where there is a cause and effect relationship, changes in the independent variable cause changes in the dependent variable. Observing a relationship between two variables does NOT necessarily mean that change in one variable CAUSES change in the other. Other factors may be involved, or the correlation may be a coincidence.

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Considering Possible CAUSE & EFFECT State whether each claim is reasonable. A scientific study showed a negative correlation between aerobic exercise and blood pressure. It claimed that the increase in aerobic activity was the cause of the decrease in blood pressure. REASONABLE, but… There may be other factors involved. Because it’s a scientific study, we can assume they probably controlled for other factors by choosing subjects of the same age and fitness level.

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Considering Possible CAUSE & EFFECT State whether each claim is reasonable. Mila discovered a positive correlation between gasoline price and average monthly temperature. She concluded that temperature determines the price of gasoline. NOT REASONABLE More likely, it’s increased demand for gas that raises the price. Why would demand for gas increase with temperature? People travel more in the summer time (cottage, air travel, etc), using more gasoline

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Considering Possible CAUSE & EFFECT State whether each claim is reasonable. Since the 1950s, the concentration of carbon dioxide in the atmosphere has been increasing. Crime rates in many countries have also increased over this time period. Does more carbon dioxide in the atmosphere cause people to commit crimes? NOT REASONABLE More likely, the correlation is coincidental, or is due to other factors. For example, increasing populations could have caused both changes.

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Group Activity 1) Read the information above 2) With your group: – Identify the two variables being discussed – What type of relationship is being suggested in the reading; positive or negative? Explain. – Decide whether it is reasonable to think that a ‘causal’ relationship (not just a correlation) exists between these variables? Why? – Do you agree with the dietary recommendations? Why or why not? Share your ideas with the class! A group of scientists were trying to determine some risk factors for heart disease. They performed multiple blood tests on 5000 people and then tracked these people for 20 years to determine which ones developed heart disease. They found that those people with the highest levels of triglyceride (fat) in their blood were most likely to develop heart disease. Based on these observations, it has been recommended that Canadians opt for a diet low in fat to reduce risk of heart disease.

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Homework: Pg. 142-147 # 1-6, 8, 9, 13, 15

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