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

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

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

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

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)

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

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.

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

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

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.

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)