#### Interactive Exercise #1 Regression with a small dataset

a. Correlation, Slope, and Y-intercept

r = .535, b = 2.0, a = 2.0

b. The regression equation is y´ = a +bx . a = y-intercept, b = Slope, y´  = predicted score for x.

 Case X Y Y´ 1 1 2 2.0+2.0(1) = 4 2 1 6 2.0+2.0(1) = 4 3 2 5 2.0+2.0(2) = 6 4 2 7 2.0+2.0(2) = 6 Sum

c. SS Total Calculations

 Case X Y Y´ 1 1 2 4 2-5 = -3 (-3)2 = 9 2 1 6 4 6-5 = 1 (1)2 = 1 3 2 5 6 5-5 = 0 (0)2 = 0 4 2 7 6 7-5 = 2 (2)2 = 4 Sum Σ = 14

d. Largest deviation from mean is –3 for Case 1.

e. Contribution of SS Total for Case 3 is 0 because Y = 5 is equal to the mean.

f. See answer for c above.

g. SS Error Calculations

 Case X Y Y´ (Y - Y´) (Y - Y´)2 1 1 2 4 2-4 = -2 (-2)2 = 4 2 1 6 4 6-4 =  2 (2)2 = 4 3 2 5 6 5-6 = -1 (-1)2 = 1 4 2 7 6 7-6 =  1 (1)2 = 1 Sum Σ = 10

h. The largest deviations are for Cases 1 and 2, and the size of the deviation is 2.The smallest deviations are for Cases 3 and 4, and the size of the deviation is 1.

i. See g above. Both values should be 10

j. SS Predicted Calculations

 Case X Y Y´ 1 1 2 4 4-5 = -1 (-1)2 = 1 2 1 6 4 4-5 = -1 (-1)2 = 1 3 2 5 6 6-5 = 1 (1)2 = 1 4 2 7 6 6-5 = 1 (1)2 = 1 Sum Σ = 4

l. See j above

#### [SS Predicted/ SS Total] = 4 / 14 = .286.

Applet reports r = .535; r squared = .286

Back to Module 4 Exercise 1