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The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2008, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the number of new cases would reach 543

The number of newly reported crime cases in a county in New York State is shown in the accompanying table where x represents the number of years since 2008 and class=

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tatiklisek

Answer:

Step-by-step explanation:

I use  84+ CE

stat edit, then fill in the #s

then

vars 5

then

2'nd stat plot, on

then, click stat

Click arrow 1 time to the left to get to Calc

then click (4)(LinReg(ax+b))

then click enter 5 times

(y=-25.31428571x+1000.285714

y=-25.3x+1000.3

now, lets use computer:

y=-25.31(543)+1000.3

y=-12743.03

round to the biggest whole number )

this doesn't really work, so I will put 1999, 2000, 2001, 2002, 2003, 2004 instead of 0, 1, 2, 3, 4, 5 and do the same thing

now I get

y=-25.31428571x+51603.54286

y=-25.3x+51603.5

now, lets use computer:

y=-25.3(543)+51603.5

y=37865.6

round to the biggest whole number:

y=37866

so, year 37866

Using the line of best-fit, it is found that:

  • The linear regression model is [tex]y = -25.31x + 1000[/tex]
  • The estimate is that the number of cases would reach 543 in the year of 2026.

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The line of best-fit is given by:

[tex]y = bx + a[/tex]

  • The slope is:

[tex]b = \frac{\sum (x - \overline{x})(y - \overline{y})}{\sum (x - \overline{x})^2}[/tex]

  • After the slope is found, using the means for x and y, the coefficient a is found.

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The means are given by:

[tex]\overline{x} = \frac{0 + 1 + 2 + 3 + 4 + 5}{6} = 2.5[/tex]

[tex]\overline{y} = \frac{1015 + 960 + 950 + 902 + 929 + 866}{6} = 937[/tex]

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The sums are:

[tex]\sum (x - \overline{x}) = (0 - 2.5) + (1 - 2.5) + ... + (5 - 2.5)[/tex]

[tex]\sum (y - \overline{y}) = (1015 - 937) + ... + (866 - 937)[/tex]

Using a calculator:

[tex]\sum (x - \overline{x})(y - \overline{y}) = -443[/tex]

[tex]\sum (x - \overline{x})^2 = 17.5[/tex]

Thus, the slope is:

[tex]b = -\frac{443}{17.5} = -25.31[/tex]

And

[tex]y = -25.31x + a[/tex]

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Using the means to find a:

[tex]y = -25.31x + a[/tex]

[tex]937 = -25.31(2.5) + a[/tex]

[tex]a = 1000[/tex]

Thus, the linear regression model is:

[tex]y = -25.31x + 1000[/tex]

---------------------

The number of cases would reach 543 in x years after 2008, and x is found when y = 543. Thus:

[tex]y = -25.31x + 1000[/tex]

[tex]543 = -25.31x + 1000[/tex]

[tex]25.31x = 1000 - 543[/tex]

[tex]x = \frac{1000 - 543}{25.31}[/tex]

[tex]x = 18.1[/tex]

2008 + 18 = 2026

The estimate is that the number of cases would reach 543 in the year of 2026.

A similar problem is given at https://brainly.com/question/21826199

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