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 1996, 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 1410.

What is the regression equation?
And what is the final answer?

Answer 1

The regression equation which models the data given is : y = 38.8x + 1058.3 ; The year in which 1410 ew cases will be recorded is 2005.

Using Technology or a linear regression calculator, the regression equation produced in the form ; y = bx + c is y = 38.8x + 1053.3

2.)

The year in which 1410 new cases would be reach is :

• y = 1410 ; substituting into the equation

1410 = 38.8x + 1053.3

1410 - 1053.3 = 38.8x

356.7 = 38.8x

x = 356.7 / 38.8

x = 9.19

This is approximately after 9 years

1996 + 9 years = 2005

Hence, 1410 new cases would be recorded in 2005.