Computations You Should be Able to Perform.

 

1.         Draw a scatter plot and sketch the regression line on it.

 

The following data represent pairs of test scores for ten students.

 

Test 1

Test 2

ZT1

ZT2

ZT1*ZT2

30

72

-1.89

-1.18

2.230

34

70

-0.96

-1.60

1.536

35

76

-0.72

-0.32

.230

36

80

-0.49

0.53

-.260

39

73

0.21

-0.96

-.202

39

79

0.21

0.32

.067

40

76

0.44

-0.32

-.141

40

83

0.44

1.18

.519

42

85

0.91

1.60

1.456

46

81

1.85

0.75

1.387

Sum

6.822

r

.682

 

Test 1  Mean = 38.1   Standard deviation = 4.28

Test 2  Mean = 77.5   Standard deviation = 4.67

 

2.         Compute the correlation between the two test scores in item 1 using the z-score method.

 

             r = .682

 

4.         Compute a predicted value of one score given another score using z-scores.

 

What are the predicted Z values for Test 1 given the following z score values for Test 2?

 

            1.00                 1.00 x .682 = .682

 

            -2.00                -2.00 x .682 = -1.364

 

            1.47                 1.00

 

            -.98                  .668

 

5.         What are the predicted values for Test 2 given the following z-score values for Test 1?

 

            1.00                 .682

 

            -2.00                -1.364

 

            +.72                 .491

 

            -3.24                -2.21

 

6.         What are the predicted raw score values in test 2 given the following raw scores for test 1?

 

            30

 

            Step 1.             (30 – 38.1)/4.28 = -1.893

            Step 2.             -1.893 x .682 = -1.291

            Step 3.             (-1.291 x 4.67) + 77.5 = 71.47

 

            46

                        83.38

 

            35

                        75.19

 

7          What are the predicated raw score values for test 1 given the following values for test 2?

 

            70

 

            Step 1.             (70 – 77.5) / 4.67 = -1.606

            Step 2              -1.606 x .682 = -1.095

            Step 3.             (-1.095 x 4.28) + 38.1 = 33.41

 

            79

                        34.35

 

            87

                        44.04

 

            68

                        32.16

 

8.         Compute the coefficient of determination, coefficient of alienation, and standard error of estimate.

 

            What is the coefficient of determination for the above problem?

 

                        .6822 = .465

 

                        What is the coefficient of alienation for the above problem?

 

                        1 - .6822 = .535

 

What is the standard error of estimate in predicting  Y (This should be Test 2) for the above problem?

 

                         = 3.42

 

What is the standard error of estimate for predicting X (This should be Test 1) for the above problem?

 

                        3.13

 

9.         Compute the 90% confidence intervals for the following predictions.

 

 

The predicted value of Test 2 is 80.

 

                        80 + (1.64 x 3.42) = 85.61

                        80 – (1.64 x 3.42) = 74.39

 

                        Note:  90% of the scores fall between a z-score of +1.64 and -1.64

 

            The predicted value of Test 1 is 34.

 

                        34 + (1.64 x 3.13) = 39.13

                        34 – (1.64 x 3.13) =28.87

 

10.       Compute the 95% confidence interval for the following values.

 

            The predicted value of Test 2 is 75.

 

                        75 + (1.96 x 3.42)

                        75 – (1.96 x 3.42)

 

                        Question: Where did I get 1.96?

 

            The predicted value of Test 1 is 41.

 

                        34.87 to 47.13