Is the nicotine content of a cigarette related to the “tar”? A collection of dat

Question

Is the nicotine content of a cigarette related to the “tar”? A collection of data (in milligrams) on 29 cigarettes is shown in “Question 2” table. Run the simple linear regression analysis in excel and use the content of “Tar” to predict the content of “Nicotine”

(a) Run the simple linear regression analysis

(b) Report the correlation coefficient and the coefficient of determination. Explain what the latter means.

(c) Find and report the regression line.

(d) Find the predicted content of Nicotine with 4mg of Tar.

Brand Tar (mg) (X) Nicotine (mg)(Y) American Filter 16 1.2 Benson & Hedges 16 1.2 Camel 16 1 Capri 9 0.8 Carlton 1 0.1 Cartier Vendome 8 0.8 Chelsea 10 0.8 GPC Approved 16 1 Hi-Lite 14 1 Kent 13 1 Lucky Strike 13 1.1 Malibu 15 1.2 Marlboro 16 1.2 Merit 9 0.7 Newport Stripe 11 0.9 Now 2 0.2 Old Gold 18 1.4 Pall Mall 15 1.2 Players 13 1.1 Raleigh 15 1 Richland 17 1.3 Rite 9 0.8 Silva Thins 12 1 Tareyton 14 1 Triumph 5 0.5 TRUE 6 0.6 Vantage 8 0.7 Viceroy 18 1.4 Winston 16 1.1

Explanation / Answer

from data-- data analysis: --regression : below is output:

b)

correlation coefficient =0.9614

coefficient of determination =0.9242

whcih tells that 92.42% of variation in nicotine level can be explained by variation in level of Tar

c)regression line : Nicotine =0.1540+0.0651*Tar

d) estimated Nicotine content =0.1540+0.0651*4=0.4144

Regression Statistics Multiple R 0.9614 R Square 0.9242 Adjusted R Square 0.9214 Standard Error 0.0879 Observations 29 ANOVA df SS MS F Significance F Regression 1 2.5419 2.5419 329.3393 0.0000 Residual 27 0.2084 0.0077 Total 28 2.7503 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.1540 0.0464 3.3231 0.0026 0.0589 0.2491 0.0589 0.2491 Tar (mg) (X) 0.0651 0.0036 18.1477 0.0000 0.0577 0.0724 0.0577 0.0724

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