A nutritionist wants to understand the influence of income and healthy food on the incidence of smoking. He collects 2009 data on the percentage of smokers in each state in the U.S. and the corresponding median income and the percentage of the population that regularly eats fruits and vegetables. A portion of the data is shown in the accompanying table. Use Table 2 and Table 4.
State Smoke Fruits/
Vegetables Income State Smoke Fruits/
Vegetables Income
AK 14.6 23.3 61,604 MT 12.2 25.7 40,437
AL 16.4 20.3 39,980 NC 14.4 20.6 41,906
AR 15.5 20.4 36,538 ND 13.3 22.5 50,075
AZ 11.0 24.1 45,739 NE 12.9 20.9 49,595
CA 8.1 27.7 56,134 NH 11.3 27.9 64,131
CO 12.0 24.7 55,930 NJ 10.0 26.3 64,777
CT 10.7 28.3 64,851 NM 11.2 23.1 43,542
DC 9.0 31.4 53,141 NV 15.7 23.7 51,434
DE 13.2 25.0 52,114 NY 12.0 26.7 50,216
FL 13.9 24.5 45,631 OH 15.6 21.0 45,879
GA 12.6 24.5 43,340 OK 18.8 14.5 45,878
HI 10.3 23.5 55,649 OR 13.1 26.3 49,098
IA 13.4 18.4 50,721 PA 15.1 24.1 48,172
ID 12.2 24.6 46,778 RI 10.2 26.1 51,634
IL 12.0 22.4 52,870 SC 14.6 17.4 41,101
IN 17.1 20.6 44,305 SD 12.4 15.7 45,826
KS 13.2 18.6 44,717 TN 17.6 23.3 40,517
KY 20.5 21.0 42,664 TX 11.7 23.8 47,475
LA 16.4 16.9 45,433 UT 6.9 23.3 58,491
MA 10.9 26.2 59,373 VA 13.8 27.3 52,318
MD 10.3 27.6 47,502 VT 12.5 29.3 60,501
ME 12.5 27.9 64,186 WA 10.7 25.0 60,392
MI 13.6 22.5 45,994 WI 12.6 22.7 51,237
MN 11.2 21.8 56,090 WV 20.6 16.1 40,490
MO 18.2 19.8 48,769 WY 15.2 23.3 52,470
MS 17.0 16.8 35,078
SOURCE: Centers for Disease Control and Prevention and U.S. Census Bureau.
picture Click here for the Excel Data File
a.
Estimate: Smoke = ?0 + ?1Fruits/Vegetables + ?2Median Income + ?. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
1formula431.mml =
27.41
+
-0.3484
Fruits/Vegetables +
-0.0001
Median Inc
b. At the 5% level of significance, are the explanatory variables individually and jointly significant?
Yes since the t-tests as well as the F-test are significant.
Yes, since the F-test is significant.
Yes since the t-tests are significant.
c-1.
Find the sample correlation coefficients between Fruits/Vegetables and Income. (Round your answer to 4 decimal places.)
Sample correlation coefficient
c-2. Is multicollinearity a potentially serious problem?
Yes since the residuals are not randomly dispersed.
No since the sample correlation is less than 0.8.
No since the residuals are randomly dispersed.
Yes since the sample correlation is more than 0.8.