Question 1:

Question 1:
(i) With the aid of diagrams illustrate the following correlations:
a. A perfect correlation
b. A very strong correlation
c. A null correlation
(ii) The data below represents the sales and advert made by a company in for 5years. Establish if there is a relationship between sales and advert using the product moment coefficient of correlation.
Year Sales (£’000) Advert (£’000)
1995 49 8
1996 54 11
1997 52 12
1998 61 12
1999 70 16
Discuss your results
Question 2:
The data below represents the marks obtained by some students in an examination:
Marks (%) Frequency
0 – 10 15
10 – 20 14
20 – 30 18
30 – 40 18
40 – 50 20
50 – 60 8
60 – 70 11
70 – 80 9
80 – 90 2
90 – 100 5
You are required to calculate the:
(i) Median mark.
(ii) Modal mark.
(iii) Upper and Lower Quartiles;
(iv) Quartile Deviation.

Question 3
A book publishing company wishes to develop a model that it can use to help predict text books sales it is considering for future publications. The marketing department has collected data on a number of variables from a sample of ten books. These data are listed below:
Copies Sold (000) – Y Pages
X1 Advertising Budget (£000) – X2 Number of Competing books-X3 Cost (£)-
X4
16 126 27 5 15
10 204 30 7 19
33 411 33 7 14
15 176 25 3 15
77 600 41 9 14
59 333 19 1 13
75 483 40 8 11
57 400 26 3 12
88 504 51 12 9
26 302 58 15 14

(i) Calculate the product moment correlation between Y and X3 and interpret its meaning.
(ii) Using any statistical package such as SPSS, Excel etc., perform a regression analysis such that the number of copies sold depends Pages (X1), Advertising Budget (X2), Number of Competing books (X3) and the Cost (X4).
(iii) Discuss your regression output obtained above based on the following:
a. The regression model;
b. The fitness of the model- Adjusted R Square; Multiple R etc
c. The significance of the model-Significance F.
d. Interpretation of the model based on size and sign.
(iv) Use your regression model to predict the number of copies sold for a book with 350 pages, having an advertising budget of £35,000, with 6 competing books and costing £16

 
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