Question

Linear Regressions

The number of newly reported crime cases in a county in New York State is shown in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest thousandth. Using this equation, find the projected number of new cases for 2002, rounded to the nearest whole number.

Year (x)	New Cases (y)
1993	911
1994	909
1995	974
1996	953

Regression Equation:  
Final Answer:  

Answer 1

Using R software we observe the linear regression equation to be :-

y=-37158.2+19.1*x ; where y denotes number of new cases and x denotes the year. Here -371558.2 denotes the intercept term for the regression, y is the dependant variable and x the explanatory variable.

The R code is:-

y=c(911,909,974,953)
x=c(1993,1994,1995,1996)
lm(y~x) # command to perform regression

Putting x=2002 in the linear regression equation we get y, that is the number of predicted new cases to be 1080.