Cigarette Consumption Data: A national insurance organization wanted to study the consumption pattern of cigarettes in all 50 states and the District of Columbia. The variables chosen for the study are given in Table 3.16. The data from 1970 are given in Table 3.17. The states are given in alphabetical order. The data can be found in the book’s Web site. In (a)-(b) below, specify the null and alternative hypotheses, the test used, and your conclusion using a 5% level of significance (a) Test the hypothesis that the variable Female is not needed in the regression equation relating Sales to the six predictor variables. (b) Test the hypothesis that the variables Female and HS are not needed in the above regression equation. (c) Compute the 95% confidence interval for the true regression coefficient of the variable Income. (d) What percentage of the variation in Sales can be accounted for when Income is removed from the above regression equation? Explain. (e) What percentage of the variation in Sales can be accounted for by the three variables: Price, Age, and Income? Explain. (f) What percentage of the variation in Sales that can be accounted for by the variable Income, when Sales is regressed on only Income? Explain. State Age HS Income Black Female Price Sales AL 27 41.3 2948 26.2 51.7 42.7 89.8 AK 22.9 66.7 4644 3 45.7 41.8 121.3 AZ 26.3 58.1 3665 3 50.8 38.5 115.2 AR 29.1 39.9 2878 18.3 51.5 38.8 100.3 CA 28.1 62.6 4493 7 50.8 39.7 123 CO 26.2 63.9 3855 3 50.7 31.1 124.8 CT 29.1 56 4917 6 51.5 45.5 120 DE 26.8 54.6 4524 14.3 51.3 41.3 155 DC 28.4 55.2 5079 71.1 53.5 32.6 200.4 FL 32.3 52.6 3738 15.3 51.8 43.8 123.6 GA 25.9 40.6 3354 25.9 51.4 35.8 109.9 HI 25 61.9 4623 1 48 36.7 82.1 ID 26.4 59.5 3290 0.3 50.1 33.6 102.4 IL 28.6 52.6 4507 12.8 51.5 41.4 124.8 IN 27.2 52.9 3772 6.9 51.3 32.2 134.6 IO 28.8 59 3751 1.2 51.4 38.5 108.5 KA 28.7 59.9 3853 4.8 51 38.9 114 KY 27.5 38.5 3112 7.2 50.9 30.1 155.8 LA 24.8 42.2 3090 29.8 51.4 39.3 115.9 ME 28 54.7 3302 0.3 51.3 38.8 128.5 MD 27.1 52.3 4309 17.8 51.1 34.2 123.5 MA 29 58.5 4340 3.1 52.2 41 124.3 MI 26.3 52.8 4180 11.2 51 39.2 128.6 MN 26.8 57.6 3859 0.9 51 40.1 104.3 MS 25.1 41 2626 36.8 51.6 37.5 93.4 MO 29.4 48.8 3781 10.3 51.8 36.8 121.3 MT 27.1 59.2 3500 0.3 50 34.7 111.2 NB 28.6 59.3 3789 2.7 51.2 34.7 108.1 NV 27.8 65.2 4563 5.7 49.3 44 189.5 NH 28 57.6 3737 0.3 51.1 34.1 265.7 NJ 30.1 52.5 4701 10.8 51.6 41.7 120.7 NM 23.9 55.2 3077 1.9 50.7 41.7 90 NY 30.3 52.7 4712 11.9 52.2 41.7 119 NC 26.5 38.5 3252 22.2 51 29.4 172.4 ND 26.4 50.3 3086 0.4 49.5 38.9 93.8 OH 27.7 53.2 4020 9.1 51.5 38.1 121.6 OK 29.4 51.6 3387 6.7 51.3 39.8 108.4 OR 29 60 3719 1.3 51 29 157 PA 30.7 50.2 3971 8 52 44.7 107.3 RI 29.2 46.4 3959 2.7 50.9 40.2 123.9 SC 24.8 37.8 2990 30.5 50.9 34.3 103.6 SD 27.4 53.3 3123 0.3 50.3 38.5 92.7 TN 28.1 41.8 3119 15.8 51.6 41.6 99.8 TX 26.4 47.4 3606 12.5 51 42 106.4 UT 23.1 67.3 3227 0.6 50.6 36.6 65.5 VT 26.8 57.1 3468 0.2 51.1 39.5 122.6 VA 26.8 47.8 3712 18.5 50.6 30.2 124.3 WA 27.5 63.5 4053 2.1 50.3 40.3 96.7 WV 30 41.6 3061 3.9 51.6 41.6 114.5 WI 27.2 54.5 3812 2.9 50.9 40.2 106.4 WY 27.2 62.9 3815 0.8 50 34.4 132.2

Cigarette Consumption Data: A national insurance organization wanted to study the consumption pattern of cigarettes in all 50 states and the District of Columbia. The variables chosen for the study are given in Table 3.16. The data from 1970 are given in Table 3.17. The states are given in alphabetical order. The data can be found in the book’s Web site. In (a)-(b) below, specify the null and alternative hypotheses, the test used, and your conclusion using a 5% level of significance (a) Test the hypothesis that the variable Female is not needed in the regression equation relating Sales to the six predictor variables. (b) Test the hypothesis that the variables Female and HS are not needed in the above regression equation. (c) Compute the 95% confidence interval for the true regression coefficient of the variable Income. (d) What percentage of the variation in Sales can be accounted for when Income is removed from the above regression equation? Explain. (e) What percentage of the variation in Sales can be accounted for by the three variables: Price, Age, and Income? Explain. (f) What percentage of the variation in Sales that can be accounted for by the variable Income, when Sales is regressed on only Income? Explain. State Age HS Income Black Female Price Sales AL 27 41.3 2948 26.2 51.7 42.7 89.8 AK 22.9 66.7 4644 3 45.7 41.8 121.3 AZ 26.3 58.1 3665 3 50.8 38.5 115.2 AR 29.1 39.9 2878 18.3 51.5 38.8 100.3 CA 28.1 62.6 4493 7 50.8 39.7 123 CO 26.2 63.9 3855 3 50.7 31.1 124.8 CT 29.1 56 4917 6 51.5 45.5 120 DE 26.8 54.6 4524 14.3 51.3 41.3 155 DC 28.4 55.2 5079 71.1 53.5 32.6 200.4 FL 32.3 52.6 3738 15.3 51.8 43.8 123.6 GA 25.9 40.6 3354 25.9 51.4 35.8 109.9 HI 25 61.9 4623 1 48 36.7 82.1 ID 26.4 59.5 3290 0.3 50.1 33.6 102.4 IL 28.6 52.6 4507 12.8 51.5 41.4 124.8 IN 27.2 52.9 3772 6.9 51.3 32.2 134.6 IO 28.8 59 3751 1.2 51.4 38.5 108.5 KA 28.7 59.9 3853 4.8 51 38.9 114 KY 27.5 38.5 3112 7.2 50.9 30.1 155.8 LA 24.8 42.2 3090 29.8 51.4 39.3 115.9 ME 28 54.7 3302 0.3 51.3 38.8 128.5 MD 27.1 52.3 4309 17.8 51.1 34.2 123.5 MA 29 58.5 4340 3.1 52.2 41 124.3 MI 26.3 52.8 4180 11.2 51 39.2 128.6 MN 26.8 57.6 3859 0.9 51 40.1 104.3 MS 25.1 41 2626 36.8 51.6 37.5 93.4 MO 29.4 48.8 3781 10.3 51.8 36.8 121.3 MT 27.1 59.2 3500 0.3 50 34.7 111.2 NB 28.6 59.3 3789 2.7 51.2 34.7 108.1 NV 27.8 65.2 4563 5.7 49.3 44 189.5 NH 28 57.6 3737 0.3 51.1 34.1 265.7 NJ 30.1 52.5 4701 10.8 51.6 41.7 120.7 NM 23.9 55.2 3077 1.9 50.7 41.7 90 NY 30.3 52.7 4712 11.9 52.2 41.7 119 NC 26.5 38.5 3252 22.2 51 29.4 172.4 ND 26.4 50.3 3086 0.4 49.5 38.9 93.8 OH 27.7 53.2 4020 9.1 51.5 38.1 121.6 OK 29.4 51.6 3387 6.7 51.3 39.8 108.4 OR 29 60 3719 1.3 51 29 157 PA 30.7 50.2 3971 8 52 44.7 107.3 RI 29.2 46.4 3959 2.7 50.9 40.2 123.9 SC 24.8 37.8 2990 30.5 50.9 34.3 103.6 SD 27.4 53.3 3123 0.3 50.3 38.5 92.7 TN 28.1 41.8 3119 15.8 51.6 41.6 99.8 TX 26.4 47.4 3606 12.5 51 42 106.4 UT 23.1 67.3 3227 0.6 50.6 36.6 65.5 VT 26.8 57.1 3468 0.2 51.1 39.5 122.6 VA 26.8 47.8 3712 18.5 50.6 30.2 124.3 WA 27.5 63.5 4053 2.1 50.3 40.3 96.7 WV 30 41.6 3061 3.9 51.6 41.6 114.5 WI 27.2 54.5 3812 2.9 50.9 40.2 106.4 WY 27.2 62.9 3815 0.8 50 34.4 132.2

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

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Cigarette Consumption Data: A national insurance organization wanted to study the consumption pattern of cigarettes in all 50 states and the District of

Columbia. The variables chosen for the study are given in Table 3.16. The data from 1970 are given in Table 3.17. The states are given in alphabetical order. The data can be found in the book’s Web site. In (a)-(b) below, specify the null and alternative hypotheses, the test used, and your conclusion using a 5% level of significance

(a) Test the hypothesis that the variable Female is not needed in the regression equation relating Sales to the six predictor variables.

(b) Test the hypothesis that the variables Female and HS are not needed in the above regression equation.

(d) What percentage of the variation in Sales can be accounted for when Income is removed from the above regression equation? Explain.

(e) What percentage of the variation in Sales can be accounted for by the three variables: Price, Age, and Income? Explain.

(f) What percentage of the variation in Sales that can be accounted for by the variable Income, when Sales is regressed on only Income? Explain.

State	Age	HS	Income	Black	Female	Price	Sales
AL	27	41.3	2948	26.2	51.7	42.7	89.8
AK	22.9	66.7	4644	3	45.7	41.8	121.3
AZ	26.3	58.1	3665	3	50.8	38.5	115.2
AR	29.1	39.9	2878	18.3	51.5	38.8	100.3
CA	28.1	62.6	4493	7	50.8	39.7	123
CO	26.2	63.9	3855	3	50.7	31.1	124.8
CT	29.1	56	4917	6	51.5	45.5	120
DE	26.8	54.6	4524	14.3	51.3	41.3	155
DC	28.4	55.2	5079	71.1	53.5	32.6	200.4
FL	32.3	52.6	3738	15.3	51.8	43.8	123.6
GA	25.9	40.6	3354	25.9	51.4	35.8	109.9
HI	25	61.9	4623	1	48	36.7	82.1
ID	26.4	59.5	3290	0.3	50.1	33.6	102.4
IL	28.6	52.6	4507	12.8	51.5	41.4	124.8
IN	27.2	52.9	3772	6.9	51.3	32.2	134.6
IO	28.8	59	3751	1.2	51.4	38.5	108.5
KA	28.7	59.9	3853	4.8	51	38.9	114
KY	27.5	38.5	3112	7.2	50.9	30.1	155.8
LA	24.8	42.2	3090	29.8	51.4	39.3	115.9
ME	28	54.7	3302	0.3	51.3	38.8	128.5
MD	27.1	52.3	4309	17.8	51.1	34.2	123.5
MA	29	58.5	4340	3.1	52.2	41	124.3
MI	26.3	52.8	4180	11.2	51	39.2	128.6
MN	26.8	57.6	3859	0.9	51	40.1	104.3
MS	25.1	41	2626	36.8	51.6	37.5	93.4
MO	29.4	48.8	3781	10.3	51.8	36.8	121.3
MT	27.1	59.2	3500	0.3	50	34.7	111.2
NB	28.6	59.3	3789	2.7	51.2	34.7	108.1
NV	27.8	65.2	4563	5.7	49.3	44	189.5
NH	28	57.6	3737	0.3	51.1	34.1	265.7
NJ	30.1	52.5	4701	10.8	51.6	41.7	120.7
NM	23.9	55.2	3077	1.9	50.7	41.7	90
NY	30.3	52.7	4712	11.9	52.2	41.7	119
NC	26.5	38.5	3252	22.2	51	29.4	172.4
ND	26.4	50.3	3086	0.4	49.5	38.9	93.8
OH	27.7	53.2	4020	9.1	51.5	38.1	121.6
OK	29.4	51.6	3387	6.7	51.3	39.8	108.4
OR	29	60	3719	1.3	51	29	157
PA	30.7	50.2	3971	8	52	44.7	107.3
RI	29.2	46.4	3959	2.7	50.9	40.2	123.9
SC	24.8	37.8	2990	30.5	50.9	34.3	103.6
SD	27.4	53.3	3123	0.3	50.3	38.5	92.7
TN	28.1	41.8	3119	15.8	51.6	41.6	99.8
TX	26.4	47.4	3606	12.5	51	42	106.4
UT	23.1	67.3	3227	0.6	50.6	36.6	65.5
VT	26.8	57.1	3468	0.2	51.1	39.5	122.6
VA	26.8	47.8	3712	18.5	50.6	30.2	124.3
WA	27.5	63.5	4053	2.1	50.3	40.3	96.7
WV	30	41.6	3061	3.9	51.6	41.6	114.5
WI	27.2	54.5	3812	2.9	50.9	40.2	106.4
WY	27.2	62.9	3815	0.8	50	34.4	132.2

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