Homework SourseThe city council of Pine Bluffs is considering increasing th
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.
Determine the regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.)
Estimate the number of crimes for a city with 23 police officers. (Round your answer to 4 decimal places.)
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 19 16 Holgate 21 6 Starksville 21 12 Carey 15 18 Danville 27 6 Whistler 13 21 Athens 29 7 Woodville 25 8 Picture Click here for the Excel Data File (a) Determine the regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.) formula304.mml = + X (b) Estimate the number of crimes for a city with 23 police officers. (Round your answer to 4 decimal places.) Number of crimes (c) Interpret the regression equation. For each policeman added, the number of crimes goes by one.
| 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. |
Solution
Mean of X = X / n = 21.25
Mean of Y = Y / n = 11.75
(Xi - Mean)^2 = 219.5
(Yi - Mean)^2 = 245.5
(Xi-Mean)*(Yi-Mean) = -207.48
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = -207.48 / 219.5 = -0.9452
bo = Y / n - b1 * X / n
bo = 11.75 - -0.9452*21.25 = 31.8363
Y = bo + b1 X
Y\'=31.8363-0.9452*X
[ANSWERS]
1. Y\'=31.8363-0.9452*X
2. 31.8363-0.9452*(23) = 10.0967
3. decrease atmost by 0.9452 ~ 1
| Line of Regression Y on X i.e Y = bo + b1 X | ||||
| Xi | Yi | (Xi - Mean)^2 | (Yi - Mean)^2 | (Xi-Mean)*(Yi-Mean) |
| 19 | 16 | 5.063 | 18.063 | -9.56 |
| 21 | 12 | 0.063 | 0.063 | -0.06 |
| 27 | 6 | 33.063 | 33.063 | -33.06 |
| 29 | 7 | 60.063 | 22.563 | -36.81 |
| 21 | 6 | 0.063 | 33.063 | 1.44 |
| 15 | 18 | 39.063 | 39.063 | -39.06 |
| 13 | 21 | 68.063 | 85.563 | -76.31 |
| 25 | 8 | 14.063 | 14.063 | -14.06 |
