1. What is the equation for a residual, e_i?

e_i = Y_i - Y-hat_i

2. What do we know about the sum of residuals when we use a least-squares regression line?

The sum of residuals is zero

3. What do we know about the sum of squared residuals from a least-squares regression line?

The sum of squared residuals is the minimum possible for the data points.

4. In words, what are a, b, and r?

a is the intercept of the least-squares regression line, b is the slope, and r is the correlation coefficient.

5. In words, what are S_x, S_y and S_xy?

S_x is the sample standard deviation of the X variable, S_yis the sample standard deviation of the Y variable, and S_xy is the sample covariance of X and Y.

6. If we know S_x = 10, S_y = 20 and S_xy = 6, then what is b? What is r?

b = S_xy/S²_x = 6/100 = .06
r = S_xy/S_xS_y = .03

7. (new problem) If we know S_x = 8, S_y = 4 and r =.6, then what is b?

b = r S_y/ S_x = .3