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2-5: Using Linear Models Algebra 2 CP

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Scatterplots & Correlation Scatterplot ◦ Relates two sets of data ◦ Plots the data as ordered pairs ◦ Used to tell the strength of a relationship (correlation) Correlation ◦ How close the data points fall along a line ◦ The closer the points fall to a line: 1.The stronger the relationship 2.The stronger the positive or negative correlation.

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Positive Correlations Negative Correlations No Correlation Complete Got It? #1 p.93 a.Strong negative b.About $170

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Linear Regression Function TI-84 1. Enter the data into STAT EDIT (L 1, L 2, L 3, etc.) 2. Press STAT; move the cursor to CALC and press 4:LinReg(ax+b) 3. Enter the lists followed by commas; press VARS 4. Move the cursor to Y-VARS; press 1:Function 5. Choose Y 1 6. Press ENTER Complete Got It? #2 p.94

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1. Create a scatterplot of the data using your graphing calculator. 2. What type of correlation do you see in the graph (positive, negative, or none)? 3. Draw a line of best fit using the LinReg function on your calculator. What is the equation of this line? 4. Use this equation to predict the number of traffic deaths in the United States in 1990. There were approximately 143.5 million cars in the US in 1990. Country Cars (Millions) Traffic Deaths Argentina4.33,054 Australia7.74,210 Belgium3.81,937 Bulgaria1.31,409 Canada12.64,210 France23.610,198 Israel0.8439 Italy27.38,717 Japan34.914,398 W. Germany30.77,435

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Correlation Coefficient The _______ number from the linear regression model is called the ________________________. This number is from ______ to _____. The absolute value of the r number indicates the ______________ of the ___________ relationship. When |r| = ____, there is a perfect linear relationship. When |r| = ____, there is a no linear relationship. r correlation coefficient 1 1 linear strength 0

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Correlation Coefficient The closer the number is to ___, the stronger the linear relationship between the variables. The closer the number is to ____, the ________ the linear relationship between the variables. The sign of the r-value indicates a positive or negative slope for the linear regression. In this case the sign is __________, therefore a _________slope indicated. 1 weaker 0 positive

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Below is the population of Kansas based on census data for the years 1900 through 1990. a. Create a scatterplot of the data. b. What type of correlation do you see in the graph (positive, negative, or none)? c. Draw a line of best fit using the LinReg function on your calculator. What is the equation of this line? d. Use this equation to predict the population of Kansas in 2010. Year Population (thousands) 19001,480 19101,690 19201,780 19301,890 19401,800 19501,920 19602,190 19702,250 19802,350 19902,490

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Homework: p. 96 #7-11 odd, 14 (a-c), 19 (a-d), 20-23, 27-29

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