#### MS 150 Statistics 4.4 linear regression review

Malware 2005 - 2006
MonthMonth num (x)Threats in 100,000s (y)
Dec110.0
Jan27.5
Feb39.0
Mar410.0
Apr517.5
May612.5
Jun717.0
Jul815.1
Aug917.0
Sep1016.0
Oct1115.1
Nov1216.9

2006 showed a dramatic return to malware threats according to Trend Micro. The number of new malware threats (computer viruses, worms, exploits, and rootkits) appearing per month climbed steadily throughout 2006. Use the third column, the y data, to answer the following questions.

1. __________ Find the mode of the threats column.
2. __________ Find the median of the threats column.
3. __________ Find the mean of the threats column.
4. __________ Find the standard deviation of the threats column.

Use the second and third columns in the table on the right to find the linear regression (best fit) line through the data and to answer the questions below.

1. ______________ Use the computer to plot the data. Does the relationship appear to be linear (roughly a straight line) or non-linear (curved)?
2. ______________ Determine the slope of the linear regression for the data.
3. ______________ Determine the y-intercept of the linear regression for the data.
4. ______________ Determine the correlation coefficient r.
5. ______________ Is the correlation positive or negative?
6. ______________ Is the correlation none, weak, moderate, strong, or perfect?
7. ______________ Determine the coefficient of determination.
8. ______________ What percent in the variation in month number "explains" the variation in the grayware threats?
9. ______________ Given that the trend has held to date, use the slope and intercept above to calculate the predicted grayware threat in September 2007 (for the month number use 22).
10. ______________ Presume that the trend will continue. Use the slope and intercept to calculate the the month number in which the threats will be 20.
11. ______________ Toughie: What month name and year does the above month number correspond?

Data based on the white paper The trend of threats today: 2006 Annual Threat Roundup and 2007 Forecast ©2007 by Trend Micro Incorporated.