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Calculating the Least Squares Regression Line

Calculating the Least Squares Regression Line. Lecture 49 Secs. 13.3.2 Fri, Apr 28, 2006. The Least Squares Regression Line. The equation of the regression line is y ^ = a + bx . Thus, we need to find the coefficients a and b . The formulas are. or. Example.

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Calculating the Least Squares Regression Line

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  1. Calculating the Least Squares Regression Line Lecture 49 Secs. 13.3.2 Fri, Apr 28, 2006

  2. The Least Squares Regression Line • The equation of the regression line is y^ = a + bx. • Thus, we need to find the coefficients a and b. • The formulas are or

  3. Example • Consider again the data set

  4. Method 1 • Compute the means and deviations for x and y. x = 5 y = 9

  5. Method 1 • Compute the squared deviations, etc.

  6. Method 1 • Find the sums of the last three columns. 30 110 57

  7. Method 1 • Compute b: • Then compute a:

  8. Method 2 • Consider again the data

  9. Method 2 • Compute x2, y2, and xy for each row.

  10. Method 2 • Then find the sums of x, y, x2, y2, and xy. 25 45 155 515 282

  11. Method 2 • Then find the sums of x, y, x2, y2, and xy. x = 25 y = 45 x2 = 155 y2 = 515 xy = 282 25 45 155 515 282

  12. Method 2 • Compute b: • Then compute a:

  13. Example • The second method is usually easier. • By either method, we get the equation y^ = -0.5 + 1.9x.

  14. TI-83 – Regression Line • On the TI-83, we could use 2-Var Stats to get the basic summations. Then use the formulas for a and b. • For our example, 2-Var Stats L1, L2 reports that • n = 5 • x = 25 • x2 = 155 • y = 45 • y2 = 515 • xy = 282

  15. TI-83 – Regression Line • Or we can use the LinReg function. • Put the x values in L1 and the y values in L2. • Select STAT > CALC > LinReg(a+bx). • Press Enter. LinReg(a+bx) appears in the display. • Enter L1, L2. • Press Enter.

  16. TI-83 – Regression Line • The following appear in the display. • The title LinReg. • The equation y = a + bx. • The value of a. • The value of b. • The value of r2 (to be discussed later). • The value of r (to be discussed later).

  17. TI-83 – Regression Line • To graph the regression line along with the scatterplot, • Put the x values in L1 and the y values in L2. • Select STAT > CALC > LinReg(a+bx). • Press Enter. LinReg(a+bx) appears in the display. • Enter L1, L2, Y1 • Press Enter. • Press Y= to see the equation. • Press ZOOM > ZoomStat to see the graph.

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