The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.

City Police Number of Crimes City Police Number of Crimes
Oxford 12 17 Holgate 15 6
Starksville 15 13 Carey 8 18
Danville 20 6 Whistler 6 21
Athens 22 7 Woodville 17 7

Click here for the Excel Data File

a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)

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ogorwyne ogorwyne · Answer 1 · 2022-07-18T21:16:43+02:00

The regression equation is calculated as: ŷ = -0.99299X + 26.39918

We have these data for the x axis

12 15 20 22 15 8 6 17

These are the values for the y axis

17 15 6 7 6 18 21 7

Sum of X = 115

Sum of Y = 97

Mean X = 14.375

Mean Y = 12.125

Sum of squares (SSX) = 213.875

Sum of products (SP) = -212.375

Regression Equation = ŷ = bX + a

b = SP/SSX = -212.38/213.88 = -0.99299

a = MY - bMX = 12.13 - (-0.99*14.38) = 26.39918

ŷ = -0.99299X + 26.39918

These values where inputted into a regression analysis calculator and the output is ŷ = -0.99299X + 26.39918