Question

The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it​ best? Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not?

TAR	NICOTINE	CO
6	0.4	5
15	1.0	18
16	1.3	16
13	0.7	18
13	0.8	18
13	0.9	14
16	1.0	17
16	1.2	15
16	1.1	15
9	0.8	12
14	0.7	18
14	0.8	17
13	0.8	18
15	1.0	16
2	0.3	3
16	1.2	18
15	1.1	15
13	0.8	17
15	0.9	15
16	0.9	18
16	1.1	14
14	1.2	15
6	0.5	7
17	1.3	16
15	1.2	13

1. Find the best regression equation for predicting the amount of nicotine in a cigarette. Use predictor variables of tar​ and/or carbon monoxide​ (CO). Select the correct choice and fill in the answer boxes to complete your choice. ​(Round to three decimal places as​ needed.)

A. Nicotine = ____ + (____) CO

B. Nicotine = ____ + (____) Tar

C. Nicotine = ____ + (____) Tar + (____) CO

2. Why is this equation best?

A. It is the best equation of the three because it has the lowest adjusted R2​, the highest​ P-value, and only a single predictor variable.

B. It is the best equation of the three because it has the highest adjusted R2 the lowest​ P-value, and only a single predictor variable.

C. It is the best equation of the three because it has the lowest adjusted R2​, the highest​ P-value, and removing either predictor noticeably decreases the quality of the model.

D. It is the best equation of the three because it has the highest adjusted R2​, the lowest​ P-value, and removing either predictor noticeably decreases the quality of the model.

3. Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not?

A. ​No, the large​ P-value indicates that the model is not a good fitting model and predictions using the regression equation are unlikely to be accurate.

B. Yes, the small​ P-value indicates that the model is a good fitting model and predictions using the regression equation are likely to be accurate.

C. No, the small​ P-value indicates that the model is not a good fitting model and predictions using the regression equation are unlikely to be accurate.

D. ​Yes, the large​ P-value indicates that the model is a good fitting model and predictions using the regression equation are likely to be accurate.

Answer 1

1. A. NICOTINE = 0.362 + 0.0379 CO

         adjusted R² =30.5    P- value = 0.002

    B. NICOTINE = 0.095 + 0.0618 TAR

          adjusted R² =72.9     P- value = 0.0001

    C. NICOTINE = 0.177 + 0.0948 TAR - 0.0356 CO

         adjusted R² =80.7     P- value = 0.0001

2.   Out of above three, the equation in C) is the best regression equation since it has highest adjusted R² =80.7

       and lowest P- value=0.0001 .

3. the best regression equation a good regression equation for predicting the nicotine content, because the small P-value

     indicates that the model is a good fitting model and predictions using the regression equation are likely to be

    accurate.