Simple Linear Regression The following table presents data on tar, nicotine, weight (in grams) and carbon monoxide contents (in milligrams) for a sample of 25 (filter) brands of cigarettes tested in a recent year. Tar (x1) 14.1 . . 12.0 Nicotine (x2) 0.86 . . 0.82 Weight (x3) 0.9853 . . 1.1184 Carbon Monoxide (y) 13.6 . . 14.9 1. Answer the following for the variables Carbon Monoxide (response variable) and Tar (predictor variable). a. Make a scatterplot of this data. Fit the regression line. Report the parameter estimates (the estimates of the intercept and slope). b. Is Tar useful (use = 0.05) in predicating Carbon Monoxide? Why? c. What percentage of the variation in Carbon Monoxide is explained by Tar? Is that high or low? d. Are there any outliers (i.e. values with a studentized residual with an absolute value greater than 2.5)? If so, identify the observation numbers and delete the observation and repeat parts a-c. e. Make a residual plot. Comment on the fit of the model. f. What is the predicted value for Carbon Monoxide when Tar is 10? Give a 95% prediction interval for this estimate. 2. Answer the following for the variables Carbon Monoxide (response variable) and Nicotine (predictor variable). a. Make a scatterplot of this data. Fit the regression line. Report the parameter estimates (the estimates of the intercept and slope). b. Is Nicotine useful (use = 0.05) in predicating Carbon Monoxide? Why? c. What percentage of the variation in Carbon Monoxide is explained by Nicotine? Is that high or low? d. Are there any outliers (i.e. values with a studentized residual with an absolute value greater than 2.5)? If so, identify the observation numbers and delete the observation and repeat parts a-c. e. Make a residual plot. Comment on the fit of the model. f. Perform a log transformation on the variable Carbon Monoxide and repeat parts a-d using Log(Carbon Monoxide) as the dependent variable. g. What is the predicted value for Carbon Monoxide when Nicotine is 1.00? Give a 95% prediction interval for this estimate. 3. Answer the following for the variables Carbon Monoxide (response variable) and Weight (predictor variable). a. Make a scatterplot of this data. Fit the regression line. Report the parameter estimates (the estimates of the intercept and slope). b. Is Weight useful (use = 0.05) in predicating Carbon Monoxide? Why? c. What percentage of the variation in Carbon Monoxide is explained by Weight? Is that high or low? d. Are there any outliers (i.e. values with a studentized residual with an absolute value greater than 2.5)? If so, identify the observation numbers and delete the observation and repeat parts a-c. e. Make a residual plot. Comment on the fit of the model. f. What is the predicted value for Carbon Monoxide when Weight is 1.0g? Give a 95% prediction interval for this estimate. 4. Summarize your conclusions of the three analyses done above. Which of the above models do you think is the best? Tar Nicotine Weight Carbon 14.1 0.86 0.9853 13.6 16 1.06 1.0938 16.6 29.8 2.03 1.165 23.5 8 0.67 0.928 10.2 4.1 0.4 0.9462 5.4 15 1.04 0.8885 15 8.8 0.76 1.0267 9 12.4 0.95 0.9225 12.3 16.6 1.12 0.9372 16.3 14.9 1.02 0.8858 15.4 13.7 1.01 0.9643 13 15.1 0.9 0.9316 14.4 7.8 0.57 0.9705 10 11.4 0.78 1.124 10.2 9 0.74 0.8517 9.5 1 0.13 0.7851 1.5 17 1.26 0.9186 18.5 12.8 1.08 1.0395 12.6 15.8 0.96 0.9573 17.5 4.5 0.42 0.9106 4.9 14.5 1.01 1.007 15.9 7.3 0.61 0.9806 8.5 8.6 0.69 0.9693 10.6 15.2 1.02 0.9496 13.9 12 0.82 1.1184 14.9