PreCalculus 1-7 Linear Models

Our goal is to create a scatter plot to look for a mathematical correlation to this data

Linear Models Open a list and spreadsheet window

Linear Models Enter “depth” and “pressure” in the top rows of the first two columns

Linear Models Enter the data from the table

Linear Models To see this data in a scatter plot, go to home, and open a Data & Statistics window

Linear Models Select “depth” on the x-axis, and “pressure” on the y-axis

Linear Models Does this data appear to have a correlation?

Vocabulary Positive Correlation – data where the dependent variable tends to increase with the independent variable Negative Correlation – data where the dependent variable tends to decrease with the independent variable No Correlation – data where the dependent variable is not related to the independent variable

Linear Models – Quick Questions Examples of real world items with.. Positive correlation? Negative correlation? No correlation?

Linear Models Without a calculator, scatter plots can be done by hand On a TI-84, use the list feature

Linear Models If data has a correlation, then we can approximate the data with a straight line

Linear Models Add a line and pick two points to find the line’s equation

Linear Models Let the calculator add a line, and move it to a place you like Menu > 4 > 2

Linear Models Compare slopes and intercepts for the equations Menu > 4 > 2

Linear Models Write down your results, and clear the line on your screen ctrl - Z

Linear Models Let the calculator find the “best fit” line Menu > 4 > 6 > 1

Linear Models – Quick Questions What makes one model better than another? How might we compare the quality of the different lines? Positive versus negative approximations?

Vocabulary Sum of the squared differences – method to compare quality of best fit lines. Error amounts for each data point are squared then added together A smaller sum demonstrates a “Better” fit

Vocabulary Least Squares Regression Line – The model with the lowest sum of square differences

Linear Models

Vocabulary Correlation coefficient – statistical measure of the accuracy of a model to data. The closer the value of |r| is to one, the better the fit

Linear Models Calculators give the “r” value for comparison of different regression models

Linear Models y = x cm

y = x – cans

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