1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
JulijaS [17]
3 years ago
7

The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a fin

al 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 15 19 Holgate 17 10
Starksville 17 16 Carey 11 23
Danville 25 8 Whistler 9 27
Athens 28 10 Woodville 21 10

A. Determine the regression equation. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.)
B. Estimate the number of crimes for a city with 20 police officers. (Round your answer to 4 decimal places.)
C. Interpret the regression equation.

Mathematics
1 answer:
bulgar [2K]3 years ago
3 0

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y: Number of crimes committed for a city.

X: Number of police officers in a city.

a) You have to estimate the linear regression of the number of crimes in the function of the number of police officers per city.

The population model is

E(Yi)= α + βXi

Where α is the intercept and β is the slope of the population model.

To estimate the linear equation you have to estimate both of these values

The estimate of the intercept is "a" (some Authors call it b₀ and you might find the intercept in the model symbolized as β₀)

a= Y[bar] - b*X[bar]

And the estimate of the slope is "b"

b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }

n=8; ∑X=143; ∑X²= 2855; ∑Y= 123; ∑Y²= 2239; ∑XY= 1913

X[bar]= ∑X/n= 143/8= 17.88

Y[bar]= ∑Y/n= 123/8= 15.38

b= \frac{1913-\frac{143*123}{8} }{2855-\frac{(143)^2}{8} }= -0.96

a= 15.38-(-0.96)*17.88= 32.46

The estimated regression equation is ^Y= 32.46 - 0.96Xi

B) To estimate the number of crimes given a determined number of police officers, you have to replace the value of X in the regression equation:

^Y_{X=20}=32.46-0.96*20= 13.26

The estimated number of crimes for a city with 20 police officers is 13.26.

C) See attachment for graph.

The slope of the estimated regression equation is negative this means that the linear regression is also negative. A negative linear regression means that when the variable X: number of police officers, increases, the variable Y: number of crimes committed, decreases.

I hope this helps!

You might be interested in
A circle has a radius of five ft.
Flura [38]
A. for the circumference it is C=pi(d)=pi(2r)=pi(10)=  31.4 ft
b. for the area it is A=pi(r)^2=pi(5)^2=pi(25)= 78.5 ft squared
c. since the are is 78.5 ft squared multiply by $4.50= $353.25 to floor the circle.
6 0
3 years ago
Use properties to find the sum or product<br>8 x 51
Lostsunrise [7]

8(51)

=8(50+1)

=8*50+8*1

=8*5*10+8*1

=400+8

=408

5 0
3 years ago
Find the length indicated
Contact [7]

Answer:

the answer is b, 12

Step-by-step explanation:

16-4=12

8 0
3 years ago
Hope someone help.me​
zvonat [6]

x = r sin θ cos Ф

x² = r² sin² θ cos² Ф

y = r sin θ sin Ф

y² = r² sin² θ sin² Ф

z = r cos θ

z² = r² cos²  θ

x² + y² + z²

= r² sin² θ cos² Ф  +  r² sin² θ sin² Ф +  r² cos²  θ

= r² sin² θ (cos² Ф + sin² Ф) +  r² cos²  θ

= r² sin² θ + r² cos²  θ

= r² (sin² θ + cos²  θ)

= r²       √

7 0
3 years ago
Ng Order of Operations George has $15. He would like to know if he has enough money to see a movie ($9.00) and buy a pretzel ($2
UNO [17]

Answer:

No, George does not have enough money to buy everything.

The correct expression is:

15 - 9 - 2.65 - 1.35 - 2(1.74)

Step-by-step explanation:

Given that:

Money present with George initially = $15

Money required to see the movie = $9

Money required to buy a pretzel = $2.65

Money required to buy a drink = $1.35

Money required to buy 2 veggie cups = $2(1.74)

To find:

Whether there is enough money with George to complete all the tasks.

Solution:

First of all, let us calculate all the money required and then we can subtract all the money from the initial amount to find whether there is enough money present with George.

If the result is in positive, there is enough money with George.

Total money required for all the activities = $9 + $2.65 + $1.35 + $2(1.74) = $16.48

Expression = $15 - $16.48 = -$1.48

The result is negative, therefore there is not enough money.

The correct expression is:

15 - 9 - 2.65 - 1.35 - 2(1.74)

5 0
3 years ago
Other questions:
  • Simplify the polynomial (-8×)+×+(-2×)
    6·1 answer
  • If x=9 and y=−2, evaluate the following expression : 6x−8y
    9·2 answers
  • 50 POINTS AND BRAINLIEST!!! QUICK
    14·2 answers
  • Which fraction is equivalent to -4/6
    5·1 answer
  • An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many face
    5·1 answer
  • A student knows the height of a pyramid and the area of its base. What should the student do to find the volume of the pyramid
    5·2 answers
  • Consider the following pair of equations:
    7·2 answers
  • If a puzzle measures 14 in x 16 in, how many inches of frame for the puzzle?
    5·1 answer
  • Use the graph of f to describe the transformation that results in the graph of g.
    8·1 answer
  • -. A medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probabili
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!