Section 5.4 Guided Notes

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Reading Notes – Complete Outside of Class Section 5.4 – Linear Regression and Correlation Pages 295-301 1) The ________________________________-________________________________ regression line for a set of bivariate data is the line that minimizes the sum of the squares of the vertical distances from each data point to the line. 2) To determine the strength of a linear relationship between two variables, statisticians use a statistic called the linear ________________________________ ________________________________. 3) The linear correlation coefficient r is a real number between _________ and _________, inclusive.  If all of the ordered pairs lie on a line with positive slope, r = 1 .  If all of the ordered pairs lie on a line with negative slope, r =− 1 .  If r = 0 , it indicates that the two variables cannot be modeled by a linear function.  For any set of ordered pairs, the linear correlation coefficient r and the slope of the least-squares line bot have the same sign.

Lecture Notes – Complete During Class Section 5.4 – Linear Regression and Correlation How to Turn on Your Correlation Coefficient r : Option 1 Option 2 1. Click MODE 2. Scroll to STAT DIAGNOSTICS 3. Highlight ON 4. 2 ND MODE will take you to the home screen 1. Click 2 ND 0 (zero) 2. Click ALPHA X -1 3. Scroll to DiagnosticOn 4. Press ENTER twice How to Find a Least-Squares Regression Line 1. Click STAT and ENTER on your calculator. Enter the data from the table into L 1 and L 2 . 2. Click STAT and move the arrow over to CALC 3. Scroll to 4: LinReg (ax+b) and press ENTER 4. Scroll to Store RegEQ and press VARS / Y-VARS / ENTER / ENTER 5. Scroll to Calculate and press ENTER Example 1: Stride Lengths of Adult Men Stride Length (m) 2.5 3.0 3.3 3.5 3.8 4.0 4.2 4.5 Speed (m/s) 3.4 4.9 5.5 6.6 7.0 7.7 8.3 8.7 a) Equation of the least-squares regression line (round to the nearest thousandth): ___________________________________________________ b) Find the linear correlation coefficient. Round to the nearest hundredth. Interpret the correlation coefficient. c) Use the equation to predict the average speed of an adult man for a stride length of 2.8 meters. d) Use the equation to predict the average speed of an adult man for a stride length of 4.8 meters.

Example 2: Stride Lengths of Camels Stride Length (m) 2.5 3.0 3.2 3.4 3.5 3.8 4.0 4.2 Speed (m/s) 2.3 3.9 4.1 5.0 5.5 6.2 7.1 7.6 a) Equation of the least-squares regression line (round to the nearest thousandths): ___________________________________________________ b) Find the linear correlation coefficient. Round to the nearest hundredth. Interpret the correlation coefficient. c) Use the equation to predict the average speed of a camel with a stride length of 3.6 meters. d) Use the equation to predict the average speed of a camel with a stride length of 4.3 meters. Example 3: Which of the following scatter diagrams suggests: a) a positive linear correlation between the x and y variables? b) a negative linear correlation between the x and y variables? Examples for You to Try J

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Example 4: The following table gives retail values of a 2017 Corvette for various odometer readings. Odometer Reading Retail Value ($) 13,000 52,275 18,000 51,525 20,000 51,200 25,000 50,275 29,000 49,625 32,000 49,075 a) Find the equation of the least-squares regression line for the data (round to the nearest thousandths). b) Use the equation to predict the retail price of a 2017 Corvette with an odometer reading of 30,000. Round to the nearest $100. c) Find the linear correlation for these data and interpret it. How to Make a Scatter Plot in the Calculator (if desired): 1. After typing everything in L 1 and L 2 click on 𝑦 = ¿ 2. Highlight Plot 1 and hit ENTER 3. Click on Zoom 9 Example 5: A psychologist collected data on a person’s age and the number of hours per week that person spent on the Internet.

Age (years) Time (hours) 73 0 67 2 63 4 56 6 49 8 46 10 39 12 32 14 25 16 21 18 15 20 a) Find the equation of the least-squares regression line for the data (round to four decimal places): b) Use the equation to predict the number of hours a 30-year-old spends on the Internet. c) Find the linear correlation for these data and interpret it.

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