Correlations and Line of Fit Students will explore the line of fit/correlations of data sets without having to create a scatterplot.

Explanatory/Response Variables FFor the following variables, please decide if they are random variables or explanatory/response, and if they are explanatory/response…decide which one is which. AA family’s income and the years of education their eldest child completes. YYour pay and the type of job you have. YYour IQ test score and your school GPA TThe age you start crawling and when you stopped eating baby food.

Correlation  What is a brief definition of correlation?  Draw a scatterplot that would have a correlation of exactly 1.  Draw a scatterplot that would have a correlation of exactly -1.  Draw a scatterplot that has a correlation of 0.  Draw a scatterplot that has a correlation of -0.7 and another at 0.5

Line of fit  Instead of calling the line of fit, the line of fit, we are going to call the regression line.  The regression line helps us predict what will happen in the future.  We can use our calculator to find it.  Y = a + bx where b is the slope and a is the y-intercept.

Practice finding the regression line Age x in months Height y in centimeters  Use your calculator to find the regression line.  Predict the height of someone at 32 months.  Predict the height of someone at 240 months.  If someone is 90 centimeters, how old are they?

What does it mean?  Explain what the slope and y-intercept means to each problem in the real world.  SAT math score = 572 – 1.04 x percent taking the test  Pay at your job = x years on the job  Weight of soap = 54 – 2.38 x days