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Activity 2 - 9

Activity 2 - 9. College Tuition. Response. Explanatory. 5-Minute Check on Activity 2-7. Describe the scatter plot to the right What is the linear correlation coefficient, r, in the graph above? What is another name for the “residual”?

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Activity 2 - 9

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  1. Activity 2 - 9 College Tuition

  2. Response Explanatory 5-Minute Check on Activity 2-7 • Describe the scatter plot to the right • What is the linear correlation coefficient, r, in the graph above? • What is another name for the “residual”? • From LINREG on our calculator:What value do we find the slope?What value is the y-intercept? Direction: Negative Form: Linear Strength: Moderate Outliers: None Clusters None Since the slope is negative, then the r value is negative also Error = observed – predicted y = ax + b the “a” value the “b” value Click the mouse button or press the Space Bar to display the answers.

  3. Objectives • Determine the equation of a regression line using a graphing calculator • Use the regression equation to interpolate and extrapolate

  4. Vocabulary • Interpolation – using a regression model to predict an output within the boundaries of the input values • Extrapolation – using a regression model to predict an output outside the boundaries of the input values

  5. Interpolation and Extrapolation Interpolation Extrapolation Extrapolation Minimum input value Maximum input value

  6. Activity The following table contains the average tuition and required fees for all 4-year colleges from 1987 through 2003 • Enter the year data in L1 and the tuition data in L2 • Graph the scatterplot on your calculator • Determine the regression line • Determine the correlation coefficient

  7. y Activity Solutions • Graph the scatterplot on your calculator • Determine the regression line • Determine the correlation coefficient Direction: Positive Form: Linear Strength: Strong Outliers: None Clusters: None 15,000 10,000 5,000 x y = 523.561 x + 5754.428 r = 0.9973

  8. Activity cont The following table contains the average tuition and required fees for all 4-year colleges from 1987 through 2003 • Use the regression equation to predict the average tuition and fees at a private 4-year colleges in 1993 (t=6). Is this an interpolation or extrapolation? • In 2005 (t=18). Is this an interpolation or extrapolation? • Use your graph to estimate what year the tuition will exceed $20,000 y = 523.561 (6) + 5754.428 8,896 Since its in-between min and max  interpolation y = 523.561 (18) + 5754.428 15,179 Since its outside the min and max  extrapolation 20000 = 523.561 x + 5754.428 27.209 = x Exceed $20000 in 2015

  9. Problem Over the past quarter century, the number of bachelor’s degrees conferred by degree-granting institutions has steadily increased. The following table contains data on the number of bachelor’s degrees (in thousands) earned by women in a given year. • Enter the year data in L1 and the tuition data in L2 • Graph the scatterplot on your calculator • Determine the regression line • What is the slope of the line? What is the meaning? • Predict the number of degrees granted in 2010

  10. y Problem Solutions 800 • Scatterplot: • Regression line: • What is the slope of the line? What is the meaning? • Predict the number of degrees granted in 2010 600 x 400 200 y = 13.10 (x) + 405.30 4 8 14182428 13.10 is the slope The number of Bachelor’s degrees earned by women has increased by 13.10 thousand per year y = 13.10 (33) + 405.30 = 837.6 thousand Extrapolation!

  11. Summary and Homework • Summary • The linear regression equation is the linear equation that “best fits” a set of data • The regression line is a mathematical model for the data • Interpolation is a prediction of an output value using the regression line within the extremes of the input values • Extrapolation is a prediction of an output value using the regression line outside the extremes of the input value (always viewed with skepticism) • Homework • Pg 255-6; 1-2

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