11.4 CHAPTER 11. STATISTICS
(d) Calculate the correlation coefficient r.
(e) What conclusion can you reach, regardingthe relationship between the length
of the right foot and height of the students in thedata set?
- A class wrote two tests, and the marks for each were recorded in the table below. Full
marks in the first test was 50 , and the second test was out of 30.
(a) Is there a strong association between the marks for the first and second test?
Show why or why not.
(b) One of the learners(in Row 18) did not write the second test. Given her mark
for the first test, calculate an expected mark forthe second test.
Learner Test 1 Test 2
(Full marks: 50 ) (Full marks: 30 )
1 42 25
2 32 19
3 31 20
4 42 26
5 35 23
6 23 14
7 43 24
8 23 12
9 24 14
10 15 10
11 19 11
12 13 10
13 36 22
14 29 17
15 29 17
16 25 16
17 29 18
18 17
19 30 19
20 28 17
- A fast food companyproduces hamburgers. The number of hamburgers made, and
the costs are recorded over a week.
Hamburgers made Costs
495 R2 382
550 R2 442
515 R2 484
500 R2 400
480 R2 370
530 R2 448
585 R2 805
(a) Find the linear regression function that bestfits the data.
(b) If the total cost in a day is R2 500, estimate the number ofhamburgers produced.
(c) What is the cost of 490 hamburgers?
- The profits of a newshop are recorded overthe first 6 months. Theowner wants
to predict his future sales. The profits so far have been R90 000; R93 000; R99 500;
R102 000; R101 300; R109 000.
(a) For the profit data, calculate the linear regression function.
(b) Give an estimate ofthe profits for the next two months.
(c) The owner wants a profit of R130 000. Estimate how many months this will take.
- A company produces sweets using a machine which runs for a fewhours per day.
The number of hours running the machine andthe number of sweets produced are
recorded.
