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

e) Calculate the slope coefficient of the sample linear regression equation. Display working.

f) Provide an interpretation of the slope coefficient you calculated in terms of the relation between number of police and number of crimes.

g) Calculate the intercept coefficient of the sample linear regression equation. Display working.

h) Provide an interpretation of the intercept coefficient you calculated in terms of the relation between number of police and number of crimes

Answer 1

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Answer:

e)

SSxx =    Σx² - (Σx)²/n =   908.400          
SSxy=   Σxy - (Σx*Σy)/n =   -919.000

estimated slope , ß1 = SSxy/SSxx =   -919.000   /   908.400   =   -1.0117
                  

f)

An interpretation of the slope coefficient calculated in terms of the relation between number of police and number of crimes is--

For every increase in the number of police, there is a decrease of 1.01 units of crimes per day.

g)

intercept,   ß0 = y̅-ß1* x̄

= 24.5 - (-1.01*34.4)

=   59.3014

h)

An interpretation of the intecept coefficient calculated in terms of the relation between number of police and number of crimes is--

Ŷ =   59.30   +   -1.01   *x

For zero police in the number of police, there is a predicted chance of 59.3 crimes per day.