Section 2.2: LINEAR REGRESSION
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1 Section 2.2: LINEAR REGRESSION OBJECTIVES Be able to fit a regression line to a scatterplot. Find and interpret correlation coefficients. Make predictions based on lines of best fit. Key Terms line of best fit linear regression line least squares line domain range interpolation extrapolation correlation coefficient strong correlation weak correlation moderate correlation Section 2.2: Linear Regression 1
2 Line of Best Fit When data is displayed with a scatter plot, it is useful to represent the data with an equation of a line for purposes of predicting values that may not be displayed on the plot. A line of best fit is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. Line of best fit may also be called linear regression lineor least squares line. We will calculate the equation of the line using the calculator! Regression Vocabulary Interpolation Predict corresponding -values, given a -value within the domain Extrapolation Predict corresponding -values, given a -value outside the domain Section 2.2: Linear Regression 2
3 Sandwich Total Fat (g) Total Calories Hamburger Cheeseburger Quarter Pounder Quarter Pounder with Cheese Big Mac Arch Sandwich Special Arch Special with Bacon Crispy Chicken Fish Fillet Grilled Chicken Grilled Chicken Light Example 1 Create a scatter plot, line of best fit, and correlation coefficient for the data to the left. Round all coefficients to nearest thousandths. Step 1: Create scatter plot on calculator. Press the STAT button and choose EDIT. Enter data into L1 and L2 as shown in the list to the left. Type in data and press ENTER after each entry. Step 2: Set-up plot on calculator. Press 2 ND Y= for StatPlot, then press ENTER Step 3:Highlight ON and press ENTER to turn on the plot. Step 4:Press ZOOM and choose 9 for ZOOMSTAT to view scatter plot. This is the scatter plot! Section 2.2: Linear Regression 3
4 Step 5:In order to find the correlation coefficient, we need to turn on a certain feature of the calculator: Press 2 nd 0 for catalog. Press D (below the math button) Arrow down to Diagnostic ON Press ENTER. Step 6:Determine the line of best fit. Press STAT and choose CALC Choose 4 LinReg(ax + b) **linear regression** Step 7:You are on the home screen. Xlist: L1 Ylist: L2 FreqList: Store RegEQ: Y1* *Note: To find Y1 : (1) VARS, Y-VARS, Function, #1 Y1 (2) Alpha, Trace, Enter #1 Y1 Section 2.2: Linear Regression 4
5 Step 8:Press ENTER on CALCULATE. Step 9:You have the line of best fit and the correlation coefficient on this screen! Round coefficients to nearest thousandths. This is the line of best fit! This is the correlation coefficient! Example 2 Find the equation of the linear regression line for Rachel s scatterplot in Example 1 from Section 2:1. Round the slope and y-intercept to the nearest hundredth. The points are given below. (65, 102), (71, 133), (79, 144), (80, 161), (86, 191), (86, 207), (91, 235), (95, 237), (100, 243) Interpret the slope as a rate for Rachael s linear regression line. Determine the value of the correlation coefficient. Section 2.2: Linear Regression 5
6 Example 3 Approximately how many more water bottles will Rachel sell if the temperature increases 2 degrees? Example 4 Rachel is stocking her concession stand for a day in which the temperature is expected to reach 106 degrees Fahrenheit. How many water bottles should she pack? Example 5 How many water bottles should Rachael pack if the temperature forecasted were 83 degrees? Is this an example of interpolation or extrapolation? Round to the nearest integer. Section 2.2: Linear Regression 6
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