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Conclusions Causal relationship: ~one variable’s change causes a change in another's. Note~ Quiz this Friday Unit Test Next Friday (2 weeks)

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Accidents vs. Precipitation Frequency of accidents amount of precipitation What conclusion could you make??

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Be careful Frequency of ice cream sales No. layers of clothing What conclusion could you make??

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Conclusion: heavy clothes cause people to not want ice cream Does the evidence support this conclusion? What other factors may contribute?

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Scatter Plot Plot pairs of values using a single point:Plot pairs of values using a single point: Speed (km/h)Stopping Distance (m)Speed (km/h)Stopping Distance (m) 25102510 35153515 45214521 55275527 60336033

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Stopping distance speed Independent Variable~ Speed Dependant Variable~ Stopping Distance As the speed increases the ________ ________ Strong Positive Correlation Correlation~ The apparent relationship between 2 variables

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Types of correlation Strong Positive Linear Correlation Strong Negative Linear Correlation Weak Positive Linear Correlation Weak Negative Linear Correlation No Correlation If the data points are in a strait line, we call it perfect correlation.

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The Correlation Coefficient r r has a value between -1 and 1 r= 1 indicates perfect positive correlation r=0 indicates no correlation r= -1 indicates perfect negative correlation

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Classifying the Strength of r |r| > 0.67 ~ Strong Correlation 0.67>|r|>0.33 ~ Moderate Correlation 0.33>|r| ~ Weak Correlation

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Calculating r manually: Notice that the x and y deviations are being multiplied. If they are uncorrelated, r is zero as positive and negative deviation products cancel out. When the correlation is strong and positive, x and y deviations of the same sign are multiplied together more often. In the case of strong negative correlation, positive x deviations are multiplied by negative y deviations and vice versa leading to an overall negative sum. The denominator scales the value down to the range between -1 and 1. You do not have to calculate it manually but examining this closely helps you understand what r means.

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Home Work (in class you can use technology to calculate r) Page 168Page 168 1,2,3,5,6,81,2,3,5,6,8 Using Excel type =pearson(X-data,Y-data) (watch an example)Using Excel type =pearson(X-data,Y-data) (watch an example) Using Fathom Enter X and Y data as attributes to a collection. Create a scatter graph and show graph info. They give you r 2, take its square root. (watch example)Using Fathom Enter X and Y data as attributes to a collection. Create a scatter graph and show graph info. They give you r 2, take its square root. (watch example)

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Figure 15-3 (p. 512) Examples of positive and negative relationships. (a) Beer sales are positively related to temperature. (b) Coffee sales are negatively.

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