- x-bar = *sum*x(i)/n

This is just the mean of the x values. - y-bar = *sum*y(i)/n

This is just the mean of the y values. - SS_xx = *sum*(x(i)-(x-bar))^2

This is sometimes written as SS_x (_ denotes a subscript following). - SS_yy = *sum*(y(i)-(y-bar))^2

This is sometimes written as SS_y. - SS_xy = *sum*(x(i)-(x-bar))(y(i)-(y-bar))

- b_1 = (SS_xy)/(SS_xx) (_ denotes a subscript following)
- b_0 = (y-bar) - (b_1) × (x-bar)
- The least squares regression lilne is:

y-hat (lowercase y with a caret circumflex) = (b_0) + (b_1) × x

What is the least squares regression line for the data set {(1,1), (2,3), (4,6), (5,6)}?

- x-bar = (1+2+4+5)/4 = 3
- y-bar = (1+3+6+6)/4 = 4
- SS_xx = ((1-3)^2+(2-3)^2+(4-3)^2+(5-3)^2) = 10
- SS_yy = ((1-4)^2+(3-4)^2+(6-4)^2+(6-4)^2) = 18
- SS_xy = ((1-3)(1-4)+(2-3)(3-4)+(4-3)(6-4)+(5-3)(6-4)) = 13
- b_1 = 13/10 = 1.3
- b_0 = 4-1.3 × 3 = .1
- y-hat = .1 + 1.3x

**Competencies:** For the paired data set {(2,3), (3,5), (4,2), (3,6), (5,8)},

What are the mean, variance, and standard deviation of the x values?

What are the mean, variance, and standard deviation of the y values?

What is the least squares regression line for y as a function of x?

What is y-hat (3) ? y-hat (6) ?

**Reflection:** How is the equation for y as a function of x related to the equation for x as a function of y?