Språkstatistik HT97:06

Exercise class 2

Deadline

These exercises are supposed to be handed in on Monday September 22.

Data

Case 1: We have the following pairs of data: (2,3), (3,5), (4,6), (5,7), (6,4), (7,2), and (8,1).

Case 2: In the course Matematisk Lingvistik VT97 there were 28 students that handed in both homework exercise 1 and 2. We have the following data for the two exercises: average(1)=8.7, SD(1)=1.3, average(2)=9.2, SD(2)=0.7 and r=0.6. You may assume that the marks for the exercises were distributed according to the normal curve.

Exercises

1. Represent the data of case 1 in a scatter diagram

2. Compute the averages and the standard deviations for the x-values and the y-values of the data pairs of case 1.

3. Draw the SD line in the scatter diagram of question 1 and specify the coordinates of two of its points explicitly.

4. Compute the correlation coefficient for the data from case 1.

5. Suppose we multiply the y-values in the pairs of case 1 with 7214. Will the correlation coefficient for the new set of data pairs be larger than, smaller than or equal to the previous answer? Why?

6. Draw the regression line in the scatter diagram of question 1 and specify the coordinates of two of its points explicitly.

7. In case 2: what average exercise 2 mark do you expect for a student that got a 10.0 for exercise 1?

8. What is the standard deviation for the exercise 2 mark of the student of the previous question?

9. What average exercise 1 mark in case 2 do you expect for a student that got a 8.5 for test 2?

10. What is the probability that a student that got a mark of 7.8 for the second exercise had a mark of 8.9 or higher for the first exercise?

Each exercise is worth 1 point.

Related Exercises

If you want to make extra exercises you can try the following optional exercises from the second edition of the book:

Scatter diagrams: 8A2, 8A5, 8B2.
Correlation coefficient: 8B6, 8D1, 8D2, 9A3, 9A8, 9A11, 9C1, 9D2, 9E4.
Regression: 10A2, 10B2, 10C1, 10C4, 10D1, 10D2, 10E2, 11A1, 11A3, 11D1, 11D4, 11E3.

A code like 8A2 points to the second exercise of section A from chapter 8. The answers to the exercises can be found in the final part of the book.