Question

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 2006, 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, find the projected number of new cases for 2014, rounded to the nearest whole number.

Answer 1

y = -18x + 843 is the linear regression equation that represents this set of data and the total number of cases in the year 2014 will be 699.

We have a table showing number of newly reported crime cases in a county in New York State.

We have to write a linear regression equation that represents this set of data (rounding all coefficients to the nearest tenth) and calculate the projected number of new cases for 2014 using this equation.

What is Linear regression?

A regression model that estimates the relationship between one independent variable and one dependent variable using a straight line.

According to the question - we have the following data :

x (Yrs. since 2006)      0          1            2             3

y (New cases)            843      825       855        806

We know that the general equation of line is -

y = mx + c

c = y - coordinate at x = 0.

c = 843

m = slope = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$ = $\frac{825 -843}{1 -0}$ = - 18

Substituting these values in the general equation of the line, we get -

y = -18x + 843

For the year 2014 the value of x = 8, substitute the value of x, we get -

y = -18 x 8 + 843 = 699

Hence, the total number of cases in the year 2014 will be 699.

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