The Federal Trade Commission rates different brands of domestic cigarettes. In t

Question

The Federal Trade Commission rates different brands of domestic cigarettes. In the study they measured the amount of carbon monoxide (co) in mg. and the amount of nicotine (mg) produced by a burning cigarette of each brand. A simple linear regression model was run co as the dependent variable and nicotine as the independent (predictor) variable. The output is shown below, use this output to answer the questions below.

           Sum of        Mean

Source        DF    Squares        Square        F Value    Pr > F

Model        1    462.25591    462.25591    138.27    <.0001

Error        23    76.89449    3.34324

Total        24    539.15040

Root MSE   1.82845        R-Square    0.8574

Dependent Mean    12.52800   

Parameter    Estimates

           Parameter    Standard

Variable    DF   Estimate    Error        t Value        Pr > |t|

Intercept    1   1.66467        0.99360        1.68        0.1074

nicotine       1    12.39541    1.05415        11.76        <.0001

How many samples did the Federal Trade Commission evaluate?

What percentage of variation in carbon monoxide is explained by the amount of nicotine?

Write down the equation for least-squares regression.

Does the amount of carbon monoxide produced by a cigarette depend on how much nicotine is in the cigarette? Perform an appropriate hypothesis test to answer this question using the above output. Define any parameters you use. Base the conclusion on the p-value of the test.

Give an estimate as to how much carbon monoxide increases on average for each additional milligram of nicotine in the cigarette.

Explanation / Answer

How many samples did the Federal Trade Commission evaluate?

Number of samples = dF(error ) +2 = 25

What percentage of variation in carbon monoxide is explained by the amount of nicotine?

Here as R2 = 0.8574 so 85.74% of variation in carbon monoxide is explained by the amount of nicotine.

Write down the equation for least-squares regression.

y^ = 1.66467 + 12.39541 x (nicotine)

Does the amount of carbon monoxide produced by a cigarette depend on how much nicotine is in the cigarette? Perform an appropriate hypothesis test to answer this question using the above output. Define any parameters you use. Base the conclusion on the p-value of the test.

Here, test statistic

t = B1 / se(B1) = 12.39541/ 1.05415 = 11.76

p - value = < 0.001

so we can reject the null hypothesis and can conclude that the amount of carbon monoxide produced by a cigarette depend on how much nicotine is in the cigarette.

Give an estimate as to how much carbon monoxide increases on average for each additional milligram of nicotine in the cigarette.

Here as the slope of the regression line is 12.3954 that means by an increase of each additional miligram there will be 12.3954 gm increase in CO increase.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.