1) In a certain section of a city, muggings have been a problem. The number of police officers patrolling that section of the city has varied. The
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4.png3.png1) In a

certain section of a city, muggings have been a problem. The number of police officers patrolling that section of the city has varied. The following chart shows the number of police officers and the number of muggings for 8 successive days.

2.png2) Does the weight of a car affect miles per gallon? We would like to determine if there is a linear relationship between weight of a car and miles per gallon of the car. Using the Minitab printout below answer the following questions: 1.png

1.png

1) In a certain section of a city, muggings have been a problem. The number of police officers patrolling that
section of the city has varied. The following chart shows the number of police officers and the number of
muggings for 8 successive days.
Police Officers
20
12
18
15
22
10
20
12
Muggings
5
9
10
8
6
13
7
15
a) What is the explanatory variable?
What is the response variable?
b) What is the least squares regression equation?
c) What is the correlation coefficient, r?
Interpret this result.
d) What is the coefficient of determination, r??
Interpret this result.

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c) What is the correlation coefficient, r?
Interpret this result.
d) What is the coefficient of determination, r??
Interpret this result.
e) Use the equation in part (b) to estimate the average number of muggings when 16 police officers are
patrolling that section of the city.

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2] Does the weight of a car affect miles per gallon? We would like to determine if there is a linear relationship
between weight of a car and miles per gallon ofthe car. Using the Minitab printout below answer the
following questions:
a} What is the explanatory variable?
What is the response variable? b} What is the least squares regression equation? 5] What is the ooefficient of determination, r2? Interpret this result. d} What is the correlation coefficient, r? Interpret this result. e} Are there any:r outliers? If so, which observations are outliers? Are there any influential observations? If so, which observations are influential? f] Suppose the weight of the cars in this sample ranged from 1.95 to 4.35 thousand pounds
What would be the predicted miles per gallon of a car weighing 2.5 thousand pounds? What would be the predicted miles per gallon of a car weighting ?.5 thousand pounds?

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Are there any influential observations?
It so, which observations are influential?
f) Suppose the weight of the cars in this sample ranged from 1.95 to 4.36 thousand pounds
What would be the predicted miles per gallon of a car weighing 2.5 thousand pounds?
What would be the predicted miles per gallon of a car weighting 7.5 thousand pounds?
Regression Analysis: MPG versus Weight
Analysis of Variance
Source
DE
Ass
ATMS
F-Value
P-Value
Regression
1293.52
1293.52
0.000
Weight
1293.52
159.16
159.16
0.0DO
Error
36
8.13
Lack-of-Fit
34
290 27
854
7.41
0.126
Pure Error
2.31
1.15
Totel
37
1586.09
Model Summary
S
R-5q R-sqladj)
R-sq(pred)
2.85080 81.55%
81.04%
79.57%
+ Coefficients
Term
Cool SE Coel
T-Value
P-Value
VIF
Constant
48.71
1.95
24.93
0.000
Weight
-8.365
0.563
-12.62
D.OOO
1.00
Regression Equation
MPG = 48.71 -8.365 Weight
Fits and Diagnostics for Unusual Observations
Obs
MPG
Fit
Resid
Std Resid
5 16.200 29.299
-13.099
-3.86 R
19 33.500 27.328
6.172
2.20 RX
25 37.300
30.891
6.409
2.31 R
32 25.500
23.521
1.979
0.28 X
R Large residual

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