Question

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Answer 1

The projected number of newly reported crime cases in the New York county in 2011, found using linear regression is 703 newly reported crime cases

What is a linear regression?

A linear regression models the relationship between a scalar quantity and other explanatory variables, using a linear approach.

The linear regression equation is presented as follows;

y = a + b•x

Where;

$\displaystyle{ b = \frac{ \sum (x - \bar x) \times (y - \bar y)}{ (x - \bar x)^{2} } }$

$\displaystyle{ a = \frac{ \sum (y ) + b \times \sum (x)}{ n } }$

$\displaystyle{ \bar x}$ =(0+1+2+3)/4 = 1.5

$\displaystyle{ \bar y}$ =(994+946+928+880)/4 = 937

$\displaystyle{ \sum x}$ =(0+1+2+3) = 6

$\displaystyle{ \sum y}$ =(994+946+928+880) = 3748

n = 4

Using the statistics function of a graphing calculator, under Scatter plot, plot type, we have;

y = 991 - 36•x

Which gives;

b = -36

a = 991

From the given parameters, we have;

x = The number of years since 2003

y = The number of newly reported crime cases

Required;

The number of projected new cases in 2011

Solution;

In 2011, x = 2011 - 2003 = 8

Which gives;

y = 991 - 36×8 = 703

The number of newly reported crime cases in 2011 is 703

Learn more about linear regression equation here:

brainly.com/question/19712770

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