46. Drug abuse. In the exercises of the last chapter yöu ex amined results of a
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46. Drug abuse. In the exercises of the last chapter yöu ex amined results of a survey conducted in the United States and 10 countries of Western Europe to determine the per- centage of teenagers who had used marijuana and other drugs. Below is the scatterplot. Summary statistics showed that the mean percent that had used marijuana was 23.9%, with a standard deviation of 15.6%. An aver- age of 11.6% of teens had used other drugs, with a standard deviation of 10.2%. 30.0 22.5 7.5 12.5 25.0 37.5 50.0 Marijuana (96) a) Do you think a linear model is appropriate? Explain. b) For this regression, R2 is 87.3%. Interpret this statistic in this context. c) Write the equation you would use to estimate the percentage of teens who use other drugs from the percentage who have used marijuana. d) Explain in context what the slope of this line means e) Do these results confirm that marijuana is a "gateway drug," that is, that marijuana use leads to the use of other drugs? T 47. More used cars 2007. Use the advertised prices forExplanation / Answer
a) Yes as from graph we can see that marijuan and other drug is approximately linearly related
b) this represent that 87.3% variability in other Drugs values explained by the linear model.
c) here sloe b1 =r*Sy/Sx =(0.873)1/2*(10.2/15.6)=0.6109
and intercept : bo =Ybar -b1*Xbar =11.6-0.6109*23.9=-3
hence least square line: Y hat (other drug) =-3+0.6109*X(Marijuana)
d)slope represent that for every one percent increase in Marijuana uses predicts 0.6109% increase in other drugs uses
e) the result confirm that there is a asscociation or coorelation ; but that does not lead to the conclusion that Marijuana uses leads to use other drugs as there may some other factors included
correlation does not guarantee causation,
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