Question

he city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information. City Police Number of Crimes City Police Number of Crimes Oxford 18 17 Holgate 19 7 Starksville 19 13 Carey 14 21 Danville 28 4 Whistler 13 25 Athens 31 7 Woodville 24 5 %media:excel.png%Click here for the Excel Data File Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.) Estimate the number of crimes for a city with 26 police officers. (Round your answer to the nearest whole number.) Interpret the regression equation.

Answer 1

Let the no of police be X and no of crime be Y .

To calculate regression line we need to draw a table of X , Y , XY , X^2 and find each sum as in below figure.

In the equation of regression curve N denotes the number of observation which are 8.

In the regression equation Y=a+bX ,

a is the intercept of cure on X axis and b is the slope of the curve.

These are calculated in the figure

For calculating no of crime in case of 26 police officers we substitute 26 in place of X .

After placing 26 in the equation we get the no of crimes be 12.