Question

Statistics

EXERCISE 2. Anna Sheehan is the manager of the Spendwise supermarket chain. She would like to be able to predict paperback book sales (books per week) based on the amount of shelf display space (in feet) provided. Anna gathers data for a sample of 11 weeks.

Week	Number of books sold, Y	Feet of shelf space, X
1	275	6,8
2	142	3,3
3	168	4,1
4	197	4,2
5	215	4,8
6	188	3,9
7	241	4,9
8	295	7,7
9	125	3,1
10	266	5,9
11	200	5,0

a) Plot a scatter diagram b) What kind of relationship exists between these two variables? c) Compute the correlation coefficient. d) Determine the sample regression equation e) Estimate paperback book sales for a week in which 4 feet of shelf space are provided. Answer. b) positive c) 0,95 d) Y = 36,4053X + 32,4576 e) 178,0779.

EXERCISE 3. A random sample of 5 families shows the following information concerning annual family income and annual expenditure on durable goods (refrigerators, washing machines, stereos and so on):

Family	Annual Income (thousand of euros)	Expenditure on Durable Goods (hundreds of euros)
Addison	5	1
Baum	8	2
Clearly	7	1
Dunn	10	2
Evans	15	4

a) Determine the estimated regression equation Y = aX + b; b) Estimate the annual expenditure on durable goods of a family earning 12000 euros per year. Answer. a) Y = 0,31X – 0,79; b) 293 euros.

Please show your workings, I have provided you with the possible answers but they might be wrong as well due our book. Thank you in advance!

Answer 1

Solution:

EXERCISE 2:

a) Plot a scatter diagram

Answer:

b) What kind of relationship exists between these two variables?

Answer: Since the scatterplot shows an uphill pattern from the left to the right of the scatterplot, therefore, there exists a positive linear relationship between these two variables.

c) Compute the correlation coefficient

d) Determine the sample regression equation

Answer:

Where:

e) Estimate paperback book sales for a week in which 4 feet of shelf space are provided.

EXERCISE 3:

a) Determine the estimated regression equation Y = aX + b

b) Estimate the annual expenditure on durable goods of a family earning 12000 euros per year.

Answer:

Since expenditure is in 100's, therefore, the predicted value is 2.93 x 100 = 293 euros