Språkstatistik HT96:06

Class:   06
Date:    960911
Topic:   Exercise class 2

Exercise class 2

These exercises are supposed to be handed in on Monday September 16. If you are asked to perform a computation then please show your computation steps in the answer.

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

1. Represent this data in a scatter diagram

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

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

4. Compute the correlation coefficient for this data.

5. Add 2 to all the y-values in the pairs. Will the correlation coefficient for the new set of five data pairs be larger than, smaller than or equal to the previous answer? Why?

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

   We are interested in the relation between the marks of students for test A and test B. We collect data for these two tests and find out that average(A)=7.0, SD(A)=1.0, average(B)=6.0, SD(B)=1.0 and r=0.6.

7. What average B-mark do you expect for a student that got a 9 for test A?

8. What average A-mark do you expect for a student that got a 5 for test B?

   In the previous two exercises you have estimated a value with an average. The standard deviation that is related to this average can be computed with the formula SD(y)*sqrt(1-r^2) in which sqrt is the square root function, r is the correlation coefficient and SD(y) is the standard deviation of the variable that you are predicting the value of.

9. In question 7 you have computed the average B-mark for students that got a 9 for test A. Compute the standard deviation for the B-mark of this group.

10. Compute the 90th percentile B-mark for the group of students in question 9.

Each exercise is worth 1 point.