Example: Cigarettes and Carbon Monoxide (CO) The Federal Trade Commission annual
ID: 3311158 • Letter: E
Question
Example: Cigarettes and Carbon Monoxide (CO)
The Federal Trade Commission annually rates varieties of domestic cigarettes according to their tar, nicotine, and carbon monoxide content. The United States Surgeon General considers each of these substances hazardous to a smoker's health. Past studies have shown that increases in the tar and nicotine content of a cigarette are accompanied by an increase in the carbon monoxide emitted from the cigarette smoke. The data presented here are taken from Mendenhall and Sincich (1992) and are a subset of the data produced by the Federal Trade Commission.
A simple linear regression relating the response variable (CO) to each of the explanatory variables (Tar, Nicotine, and Weight) and the results are shown below. Use the computer output to answer the questions.
a. What is the R-squared value for the model relating carbon monoxide (CO) to tar (Tar)? Round your answer to four decimal places.
b.What is the R-squared value for the model relating carbon monoxide (CO) to nicotine (Nicotine)? Round your answer to four decimal places.
c.What is the R-squared value for the model relating carbon monoxide (CO) to weight (Weight)? Round your answer to four decimal places.
Explanation / Answer
(a) R 2 = 0.9168
(b) R2 = 0.8574
(c) R2 = 0.2153
R square is a statistical measure of how close the data is fitted to the regression line
First two r square values tell us the model is good fit but the third one says it is poor fit
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