Essential Understanding: Sometimes it is possible to model data from a real-world situation with a linear equation. You can then use the equation to draw conclusions about the situation. Objectives: Students will be able to write linear equations that model real world data make predictions from linear models of data define and identify various types of correlation
Algebra A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Functions F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship★ F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ F-BF.1. Write a function that describes a relationship between two quantities.★
What is a scatter plot? A graph that relates two sets of data by plotting the data as ordered pairs. Can be used to determine strength of a relationship. The closer the points fall together the stronger the correlation(Correlation does not mean causation)
The following table shows the number of hours students spent online the day before a test and the scores on the test. Make a Scatter Plot and describe the correlation. What would you predict the test score to be of someone who was online for 2.5 hours? Computer Use and Test Scores # of 0 0 1 1 1.5 1.75 2 2 3 4 4.5 5HoursOnlineTest 100 94 98 88 92 89 75 70 78 72 57 60Scores
Trend Line: a line that approximates the relationship between the variables, or data sets, of a scatter plot. You can use a trend line to make predictions from the data You can pick to two points in the scatter plot to represent the equation of a trend line
The table shows median home prices in California. What is the equation for a trend line that models the relationship between time and home prices? California Median Home PricesYear 1940 1950 1960 1970 1980 1990 2000Median 36,700 57,900 74,400 88,700 167,300 249,800 211,500Price ($)
Line of Best Fit: trend line that gives the most accurate model of related data This is the linear regression (LinReg) function on your calculator Correlation Coefficient: r, indicates the strength of the correlation. The closer the data is to 1 or -1, the more closely the data resembles a line and the more accurate your model is.
The table lists the cost of 2% milk. Use a scatter plot to find the equation of the line of best fit. Based on your linear model, how much would you expect to pay for a gallon of 2% milk in 2025? Cost of 2% Milk Year 1998 2000 2002 2004 2006 2008Avg Cost for 1 gal 2.57 2.83 2.93 2.93 3.10 3.71 ($)