Entry Task Write the equation in slope intercept form and find the x and y intercepts. 1. 4x + 6y = 12

Chapter 2.5: Using Linear Models Target: I can write linear equations that model real world data and make predictions from linear models.

Scatter Plot A scatter plot is a graph of a collection of ordered pairs (x,y). The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

Positive Correlation If the x-coordinates and the y-coordinates both increase, then it is POSITIVE CORRELATION. This means that both are going up, and they are related.

Positive Correlation If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation. Age Height “

Negative Correlation If the x-coordinates and the y- coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION. This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.

Negative Correlation If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative correlation. Age of car Value$30,000$27,000$23,500$18,700$15,350

No Correlation If there seems to be no pattern, and the points looked scattered, then it is no correlation. This means the two are not related.

No Correlation If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.

Scatterplots Which scatterplots below show a linear trend? a) c)e) b) d)f) Negative Correlation Positive Correlation Constant Correlation

Year Sport Utility Vehicles (SUVs) Sales in U.S. Sales (in Millions) x y Year Vehicle Sales (Millions) Objective - To plot data points in the coordinate plane and interpret scatter plots.

x y Year Vehicle Sales (Millions) Trend is increasing. Scatterplot - a coordinate graph of data points. Trend appears linear. Positive correlation. Predict the sales in 2001.

x y Year Vehicle Sales (Millions) Scatterplot - a coordinate graph of data points. Write the equation of the trend line. Step 1 choose 2 points on the trend line. (1992, 1.1) and (1997, 2.4) Step 2 write an equation in slope intercept form Step 3 use the equation to predict the trend for 2001.

Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis.. Student Time Spent Watching TV Time Spent on Homework Sam Jon Lara Darren Megan Pia Crystal 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 90 min.

Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis. TVHomework 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 120 min. 90 min. Time Watching TV Time on Homework

Describe the relationship between time spent on homework and time spent watching TV. Time Watching TV Time on Homework Trend is decreasing. Trend appears linear. Negative correlation.

Let’s do it with a Calculator! Make a scatterplot, draw the trend line and write the equation of the trend line. Directions are on page 95 but watch here first (2,58),(6,105),(8,88),(8,118),(12,117), (16,137),(20,157),(20,169)

1. Enter the Data into Lists Press STAT. Under EDIT, select 1: Edit. Enter x-values (input) into L1 Enter y-values (output) into L2. After data is entered in the lists, go to 2nd MODE to quit and return to the home screen. Note: If you need to clear out a list, for example list 1, place the cursor on L1 then hit CLEAR and ENTER.

2. Set up the Scatterplot. Press 2nd Y= (STAT PLOTS). Select 1: PLOT 1 and hit ENTER. Use the arrow keys to move the cursor down to On and hit ENTER. Arrow down to Type: and select the first graph under Type. Under Xlist: Enter L1. Under Ylist: Enter L2. Under Mark: select any of these.

3. View the Scatterplot Press 2nd MODE to quit and return to the home screen. To plot the points, press ZOOM and select 9: ZoomStat. The scatterplot will then be graphed.

4. Find the regression line. Press STAT. Press CALC. Select 4: LinReg(ax + b). Press 2nd 1 (for List 1) Press the comma key, Press 2nd 2 (for List 2) Press ENTER.

5. Interpreting and Visualizing Interpreting the result: y = ax + b –The value of a is the slope –The value of b is the y-intercept –r is the correlation coefficient –r 2 is the coefficient of determination

5. Interpreting and Visualizing Write down the equation of the line in slope intercept form. Press Y= and enter the equation under Y1. (Clear all other equations.) Press GRAPH and the line will be graphed through the data points.

Homework Homework – p. 96 #7,8,11,12,13,14,15,16,18,20 Challenge - # 19