Question

The Victorian Government is considering increasing the number of police employed in a region in Victoria in an effort to reduce crime. Before making the final decision on number of police to be employed, the Ministry of Police asked that various regions of similar size throughout Victoria to be surveyed to determine the relationship between the number of police employed and the number of crimes reported per day. The data collected is shown in the table below.

region	no. of police	no. of crimes per day
1	34	28
2	44	14
3	36	12
4	48	9
5	49	15
6	24	36
7	32	28
8	20	42
9	25	30
10	32	31

∑?? = 344 ∑?? = 245 ∑?? 2 = 12742 ∑?? 2 = 7135 ∑?? ?? = 7509

a) State the dependent and independent variables. Briefly explain your selection of the dependent and independent variables.

b) Calculate Sx 2 , Sy 2 and Sxy using the information given above. Display working.

c) Calculate the sample correlation coefficient. Display working.

d) Provide an interpretation of the calculated value of the sample correlation coefficient in terms of the relation between number of police and number of crimes.

Answer 1

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Answer:

a)

The dependent and independent variables in this study are respectively Number of Crimes per day and Number of Police. The explanation for this choice is-- the number of crimes in an area will obviously depend upon the system of law in that place, i.e., the number of police provided in that specific area. Thus, in that way, number of police briefly explains the number of crimes occurring. Let x=independent variable and y=independent variable

b)

SSxx =    Σx² - (Σx)²/n =  12742 - (344)^2/10 = 908.400          
SSxy=   Σxy - (Σx*Σy)/n = 7509 - (344*245)/10 -919.000          
SSyy =    Σy²-(Σy)²/n = 7135 - (245)^2/10 = 1132.500  

c)

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.9061

there is STRONG, LINEAR, AND NEGATIVE relation between two variables

d)

An interpretation of the calculated value of the sample correlation coefficient in terms of the relation between number of police and number of crimes is stated as--

There is a strong negative correlation between the number of police and number of crimes, which means, as the number of police increases, no. of crimes will decrease.