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example 3 Earnings and Gender Chapter 2.2 The table shows the earnings of year- round full-time workers by gender and educational attainment. a.Let x represent earnings for males, let y represent earnings for females, and create a scatter plot of the data. b.Create a linear model that expresses females’ annual earnings as a function of males’ earnings. c.Graph the linear function and the data points on the same graph, and discuss how well the function models the data. 2009 PBLPathways Educational Attainment Average Annual Earning for Males ($ thousand) Less than ninth grade 21.65917.659 Some high school26.27719.162 High school graduate 35.72526.029 Some college41.87530.816 Associate’s degree44.40433.481 Bachelor’s degree57.22041.681 Master’s degree71.53051.316 Doctorate degree82.40168.875 Professional degree 100.00075.036

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. a.Let x represent earnings for males, let y represent earnings for females, and create a scatter plot of the data. b.Create a linear model that expresses females’ annual earnings as a function of males’ earnings. c.Graph the linear function and the data points on the same graph, and discuss how well the function models the data. Educational Attainment Average Annual Earning for Males ($ thousand) Less than ninth grade 21.65917.659 Some high school26.27719.162 High school graduate 35.72526.029 Some college41.87530.816 Associate’s degree44.40433.481 Bachelor’s degree57.22041.681 Master’s degree71.53051.316 Doctorate degree82.40168.875 Professional degree 100.00075.036

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. a.Let x represent earnings for males, let y represent earnings for females, and create a scatter plot of the data. Educational Attainment Average Annual Earning for Males ($ thousand) Less than ninth grade 21.65917.659 Some high school26.27719.162 High school graduate 35.72526.029 Some college41.87530.816 Associate’s degree44.40433.481 Bachelor’s degree57.22041.681 Master’s degree71.53051.316 Doctorate degree82.40168.875 Professional degree 100.00075.036

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. a.Let x represent earnings for males, let y represent earnings for females, and create a scatter plot of the data. Educational Attainment xy Less than ninth grade 21.65917.659 Some high school26.27719.162 High school graduate 35.72526.029 Some college41.87530.816 Associate’s degree44.40433.481 Bachelor’s degree57.22041.681 Master’s degree71.53051.316 Doctorate degree82.40168.875 Professional degree 100.00075.036

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. a.Let x represent earnings for males, let y represent earnings for females, and create a scatter plot of the data. Educational Attainment xy Less than ninth grade 21.65917.659 Some high school26.27719.162 High school graduate 35.72526.029 Some college41.87530.816 Associate’s degree44.40433.481 Bachelor’s degree57.22041.681 Master’s degree71.53051.316 Doctorate degree82.40168.875 Professional degree 100.00075.036 Xmin = 0 Xmax = 120 Xscl = 20 Ymin = 0 Ymax = 80 Yscl = 20

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. a.Let x represent earnings for males, let y represent earnings for females, and create a scatter plot of the data. Educational Attainment xy Less than ninth grade 21.65917.659 Some high school26.27719.162 High school graduate 35.72526.029 Some college41.87530.816 Associate’s degree44.40433.481 Bachelor’s degree57.22041.681 Master’s degree71.53051.316 Doctorate degree82.40168.875 Professional degree 100.00075.036 Xmin = 0 Xmax = 120 Xscl = 20 Ymin = 0 Ymax = 80 Yscl = 20

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. a.Let x represent earnings for males, let y represent earnings for females, and create a scatter plot of the data. Xmin = 0 Xmax = 120 Xscl = 20 Ymin = 0 Ymax = 80 Yscl = 20 y x

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. b.Create a linear model that expresses females’ annual earnings as a function of males’ earnings. y x

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. b.Create a linear model that expresses females’ annual earnings as a function of males’ earnings. y x

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. b.Create a linear model that expresses females’ annual earnings as a function of males’ earnings. y x Male earnings in thousands of dollars Female earnings in thousands of dollars

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. b.Create a linear model that expresses females’ annual earnings as a function of males’ earnings. y x Male earnings in thousands of dollars Female earnings in thousands of dollars

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. c.Graph the linear function and the data points on the same graph, and discuss how well the function models the data. y x Male earnings in thousands of dollars Female earnings in thousands of dollars

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2009 PBLPathways The table shows the earnings of year- round full-time workers by gender and educational attainment. c.Graph the linear function and the data points on the same graph, and discuss how well the function models the data. y x Male earnings in thousands of dollars Female earnings in thousands of dollars

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2009 PBLPathways Enter the data 1.To enter the data, press . 2.Press to select 1: Edit... 3.If there is already data in the L1 and L2 lists, move you cursor to the name of the list and press . This should remove the contents of the list. Enter the male earning in the L1 list and female earnings in the L2 list. 4.Press to format Plot 1. Select 1: Plot 1 and press .

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2009 PBLPathways 5.Make sure the plot is turned on and that the data is coming from L1 and L2. Make any changes so that the screen looks like the one to the right. 6.Press and adjust the window to the values shown to the right. 7.Press to see the scatter plot.

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2009 PBLPathways Find the linear model 8.The command to find the least squares line is located under the CALC menu when you press . 9.Press or highlight 4: LinReg(ax+b). This will paste the linear regression command to the home screen. 10.The linear regression command needs to be followed by the source of the data. Press . This indicates that linear regression will be carried out with the x values from L1 and the y values from L2.

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2009 PBLPathways 11.To paste the resulting model into Y 1, we need to paste it after the sources of the data. Press . 12.Use to move to the Y-Vars menu. 13.Press or highlight 1: Function... and press . 14.To paste Y 1 to the home screen, press or highlight 1: Y 1 and press . 15.The complete linear regression command should look like what you see to the right. Press to carry out the linear regression.

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2009 PBLPathways 16.You’ll see the equation of the line. In this case, the equation is shown. Below the model is the value of the correlation coefficient r. If you do not see the correlation coefficient, follow step 18 to force your calculator to display the correlation coefficient. 17.Press to see the scatter plot with the corresponding linear model.

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2009 PBLPathways 18.To insure your calculator displays the correlation coefficient, press to access the calculator’s catalog of commands. Scroll down to the entry DiagnosticOn. Press to paste the command to the home screen. Press again to execute the DiagnosticOn command. The next time you carry out the LinReg(ax+b) command, the correlation coefficient will be displayed.

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