# Regression

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A). Create a scatter plot (using excel) of the data.

b). Find the equation of the linear regression line.

c). Plot the regression line on the same plot as the data.

d). How well do you think the line fits the data?

e). Use the regression equation to predict the number of officers hired for each city.

f). Calculate the residuals and the standard error of the estimate.

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##### Solution Summary

Ex. 15.5

As part of the anti-crime bill passed in 1995, the U.S. government granted money to different cities to hire new beat-patrol officers. Nine cities in New Jersey were give grants and hired officers. In trying to assess the program, government analysts wanted to look at the relationship between the number of officers hired and the amount of the grant. The data are:

Grant ($) Number of Officers

150,000 2

375,000 5

471,125 6

70,967 1

450,000 6

525,000 7

375,370 7

750,000 10

1,000,000 12

a). Create a scatter plot (using excel) of the data.

b). Find the equation of the linear regression line.

c). Plot the regression line on the same plot as the data.

d). How well do you think the line fits the data?

e). Use the regression equation to predict the number of officers hired for each city.

f). Calculate the residuals and the standard error of the estimate.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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