9. (17 pts) Based on data from L. Brown, Vital Sens 2003: The Environmenial Trem
ID: 3169243 • Letter: 9
Question
9. (17 pts) Based on data from L. Brown, Vital Sens 2003: The Environmenial Tremds that are Shaping our Fature the following chant of cigaretle smoking data has been pepard Average Number of Cigarettes Smoked Per Person, world-wide 1040 1020 1000 980 960 940 920 900 -86893x+ 18303 R·0.8978 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 Year The line of best fit, the regression line, is y- 86893 18,303, where r - year and y- average number of cigarettes smoked per person, world-wide. The value of r is 0.8978 (a) Use the regression line to estimate the average number of cigarcttes smoked per person in 1990,to the nearest integer. Show some work. (b) Use the regression line to estimate the average number of cigarcties smoked per penon in 2000, to the nearest integer. Show some work (c) In what year (to the nearest year) does the regression line estimate an average number of cigarcttes smoked per person of 830 cigarettes per person? Show work, solving an appropiate equation. (d) What is the slope of the regression line and what are the units of measurement? In a sentience interpret what the slope is telling us, in the context of this real-world application. (e) What is the value of the correlation coefficient, r (rounded to 2 decimal places)? Also, interpret ie value: Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak?Explanation / Answer
(a)
y = -8.6893*x + 18303
y(1990) = -8.6893*1990 + 18303 = 1011.29 ~ 1011
(b)
y = -8.6893*x + 18303
y(2000) = -8.6893*2000 + 18303 = 924.4 ~ 924
(c)
880 = -8.6893*x + 18303
x = (18303 - 880)/8.6893 = 2005
(d)
slope = coefficient of x in slope-intercept form of the equation
slope = -8.6893
Slope is telling that every year 8.6893 less cigrettes are smoked per person compared to last year
(e)
Give r-squared = 0.8979
so r = - (0.8979)0.5 = -0.95
since the year and smoked cigrettes have negative relation (notice that with year increase, cigretters smoked is decreasing)
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