Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 10–2 Regression 553Formulas for the Regression Line y a bxa yx2 xxynx 2 x 2nxy xyb nx 2 x 2where a is the y intercept and b is the slope of the line.Rounding Rule for the Intercept and Slopethree decimal places.Round the values of a and b toExample 10–9Car Rental CompaniesFind the equation of the regression line for the data in Example 10–4, and graph the lineon the scatter plot of the data.SolutionThe values needed for the equation are n 6, x 153.8, y 18.7, xy 682.77,and x 2 5859.26. Substituting in the formulas, you getHence, the equation of the regression line ya bx isy0.396 0.106xTo graph the line, select any two points for x and find the corresponding values fory. Use any x values between 10 and 60. For example, let x 15. Substitute in the equationand find the corresponding y value.Let x 40; thena yx2 xxynx 2 x 2b nxy xynx 2 x 2y0.396 0.396 0.106(15) 1.986y0.396 0.106x 0.396 0.106(40) 4.63618.75859.26 153.8682.7765859.26 153.8 2 0.3966682.77 153.818.765859.26 153.8 2 0.106Then plot the two points (15, 1.986) and (40, 4.636) and draw a line connecting the twopoints. See Figure 10–14.Note: When you draw the regression line, it is sometimes necessary to truncate thegraph (see Chapter 2). This is done when the distance between the origin and the firstlabeled coordinate on the x axis is not the same as the distance between the rest of the10–21