1. Objective: To write linear equations that model real-world data. To make predictions from linear models. Bell Ringer: Write 3 ways you used math over your weekend. Using Linear Models Name Class/Period Date

2. Vocabulary A scatter plot is a graph that relates two sets of data by plotting the data as ordered pairs. You can use a scatter plot to determine the strength of the relationship, or the correlation. Open you books to page 103 to view: Strong negative correlation Weak negative correlation No correlation Weak positive correlation Strong positive correlation

3. Vocabulary The line that gives the most accurate model of related data is called the line of best fit. The correlation coefficient, r, indicates the strength of the correlation. You can find these numbers by doing a linear regression.

4. How to Use a Graphing Calculator to Find Correlation Correlation Coefficient and Line of Best Fit 1. Turn the calculator on. 2. Hit the STAT button and then ENTER to edit lists. 3. Use the information in the table on p. 104 to fill in your table. L1 will be your average temperatures and L2 will be your electricity bill numbers. 4. Hit STAT, then the right arrow (>) to highligh CALC, then hit 4: LinReg (ax + b) 5. Make sure that Xlist: L1 and Ylist: L2 then highlight Calculate and hit ENTER If you do not see a number listed for a, b, r 2, and r, raise your hand

5. What does this mean? Your line of best fit will be y = ax + b So it should be y = 4.15x + - 117.68 (I rounded a and b) R is the correlation coefficient. Since it is close to +1 the correlation is a strong positive correlation. It should be.9146 … Let ’ s check to make sure: 1. Hit Y =, highlight Plot1 and hit enter so that it is in a black box, enter our line of best fit y1 = 4.15x + -117.68 2. Hit WINDOW, make Xmin = 50, Xmax = 100, Xscl = 5, Ymin = 100, Ymax = 300, Yscl = 10 3. Hit GRAPH. Do the points seem to follow closely to the line?

6. Exit Ticket Does a negative slope for the line of best fit mean the correlation coefficient will be negative? Why or why not? Homework P. 108 #8-10, 12, 14