11C Line of Best Fit By Eye, 11D Linear Regression Unit 3: Statistical Applications 11C, 11D 2/28/2019 5:58 PM

Line of Best Fit vs. Linear Regression Model residual: vertical difference between a data point and the possible line of best fit a line of best fit is the result of minimizing the sum of the squares of the residuals use GDC (STAT > CALC > LinReg) on external assessments use formulas for internal assessment (project) 11C, 11D 2/28/2019 5:58 PM

Least Squares Formula Copy only mathematically appropriate if the two sets of data have a linear relationship least squares line: mean point: gradient: Example Start by finding: x y 1 3 5 6 11C, 11D 2/28/2019 5:58 PM

Estimating Copy two ways to use a linear regression equation to predict values: interpolating: using a value between the minimum and maximum independent variable data values extrapolating: using a value outside the minimum and maximum independent variable data values Which prediction method is more prone to error? 11C, 11D 2/28/2019 5:58 PM

Estimating how well the equation represents the association depends on factors including: correlation’s strength correlation coefficient r correlation’s shape linear or non-linear quantity and quality of data number of data pairings n collection process and instrument Copy 11C, 11D 2/28/2019 5:58 PM

Example Using technology, calculate the correlation coefficient and coefficient of determination. Find the equation of the linear regression model. You may have to round values, but make sure to round to three significant figures. Construct a scatter plot for the data set. Graph the linear regression model using the “mean point” (labelled with a capital M) and the y-intercept. Should you use the linear regression model to estimate values of y for given values of x? If not, what would you do to determine a more appropriate model? HT (in) 63 62 75 61 66 67 64 WT (lb) 117 107 170 91 118 130 135 120 125 88 11C, 11D 2/28/2019 5:58 PM

Anscombe’s Quartet The four sets of data demonstrate the importance of the following ideas. Obtaining the “line of best fit” does not mean that the line should be used to represent the data. Always start by graphing the data in a scatter plot to determine if the shape of the scatter is linear. If it is linear, a “further” mathematical process can be done by finding an equation of a line of best fit by hand along with the correlation coefficient and coefficient of determination. If it is not linear, you can use technology to determine other regression models. This would be a “simple” mathematical process. 11C, 11D 2/28/2019 5:58 PM

Guided Practice p. 330: 2 (line of best fit by EYE) p. 332: 1, 5 (Calculate r and find regression equation, both by hand) Read and follow all instructions. List the page and problem numbers alongside your work and answers in your notes. Use the back of the book to check your answers. Copy 11C, 11D 2/28/2019 5:58 PM