In: Statistics and Probability
The table below shows the murder rate per 100,000 residents for a large American city over a twelve-year period.
Year | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Rate | 8.8 | 7.1 | 7.2 | 6.8 | 6.4 | 7.1 | 5.8 | 6.1 | 5.4 | 6.2 | 6.1 | 4.9 |
Enter the coefficients of the regression line for this data, rounding each to two decimal places: | ||||
Slope: | Intercept: | |||
Use your regression line (with rounded coefficients) to estimate this city’s murder rate in 2012. Round your answer to the nearest tenth. | ||||
Estimate: |
The necessary calculation are done below.
year(x) | rate (y) | s1=(x-xbar)^2 | s2=(x-xbar)*(y-ybar) |
2000 | 8.8 | 30.25 | -12.6958 |
2001 | 7.1 | 20.25 | -2.7375 |
2002 | 7.2 | 12.25 | -2.4792 |
2003 | 6.8 | 6.25 | -0.7708 |
2004 | 6.4 | 2.25 | 0.1375 |
2005 | 7.1 | 0.25 | -0.3042 |
2006 | 5.8 | 0.25 | -0.3458 |
2007 | 6.1 | 2.25 | -0.5875 |
2008 | 5.4 | 6.25 | -2.7292 |
2009 | 6.2 | 12.25 | -1.0208 |
2010 | 6.1 | 20.25 | -1.7625 |
2011 | 4.9 | 30.25 | -8.7542 |
xbar=sum(x)/n | ybar=sum(y)/n | sxx=sum(s1) | sxy=sum(s2) |
2005.5 | 6.4917 | 143 | -34.05 |
b1=sxy/sxx | b0=ybar-b1*xbar | ||
-0.23811 | 484.0251 | ||
The calculation are done in above table i stope bia intercept = be 0.24 484.0.3 The estimated city murder rate in 2012 is given by Rate bot bi * Year 484.0.3 0.24 * 2012 1:15 a The estimated city murder nate in 2012 is 71:15.