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Estimate the following multiple regression models | Complete Solution
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Estimate the following multiple regression models (remember that all of your independent variables will have to be in adjacent columns in Excel). Look at each set of results critically and consider how you would interpret the strengths and weaknesses of each model. Save your results from each model for use when completing the end-of-module assessment. C, the dependent variable, will always be “Consumption of Soft Drinks per Capita;” for independent variables, use the following specifications. (The notation f(X, Y, Z) means “a function of X, Y, Z; i.e., X, Y, and Z are your independent variables. Even though it isn’t listed, each model will include an intercept.) NOTE: when Excel reports a value like 2.4E-06, this is scientific notation for 2.4 * (10^-6), or 0.0000024.

 

Model A: C = f(% obese, dentists, physicians)

 

Model B: C = f(food services, % smokers total)

Model C: C = f(food services, % male smokers, % female smokers)

Model D: C = f(food services, % smokers total, % male smokers)

 

Model E: C = f(per capita income, mean annual temp)

Model F: C = f(mean annual temp, % obese, dentists, food services, % male smokers)

Model G: C = f(mean annual temp, % obese, dentists, food services, % smokers total)

 

State Consumption of Soft Drinks per Capita population, 2008 Per Capita Income ($1000) Mean Annual Temperature, F % obese adults dentists per 1000 people physicians per 100,000 number of food service businesses, 2006 % smokers, total % male smokers % female smokers
Alabama 200 4,661,900 13 66 28.9 0.540552135 215.1105777 3905 23.3 26.3 20.6
Arizona 150 6,500,180 17 62 21.2 0.71736475 207.5306528 5463 18.1 21.7 14.7
Arkansas 237 2,855,390 11 63 26.1 0.491351444 202.8907755 2526 23.7 25.9 21.7
California 135 36,756,666 25 56 22.2 0.954221474 262.4312457 36424 14.9 18.5 11.4
Colorado 121 4,939,456 19 52 16.8 0.842198007 258.6792506 5914 17.9 19.3 16.4
Connecticut 118 3,501,252 27 50 19.7 0.944233663 368.0942385 3851 17 18.9 15.3
Delaware 217 873,092 28 52 21.1 0.546334178 249.9191541 874 21.7 23.3 20.2
Florida 242 18,328,340 18 72 22.9 0.74709439 242.5885666 16838 21 23.6 18.7
Georgia 295 9,685,744 14 64 24.7 0.539555867 217.3230267 8877 20 22.4 17.7
Idaho 85 1,523,816 16 46 20.8 0.779621687 169.0459711 1658 16.8 18.7 15
Illinois 114 12,901,563 24 52 23 0.764481017 275.1798827 12939 20.5 24.2 17
Indiana 184 6,376,792 20 52 25.5 0.628529204 214.8880498 6281 24.1 26.3 21.9
Iowa 104 3,002,555 16 50 23.5 0.715390726 186.6814662 3453 21.5 23.2 19.9
Kansas 143 2,802,134 17 56 23.2 0.632018312 220.833371 2872 20 22.2 18
Kentucky 230 4,269,245 13 56 25.8 0.764303759 229.9293831 3539 28.6 29.1 28.1
Louisiana 269 4,410,796 15 69 27 0.610320677 266.5489364 3800 23.4 28.6 20.5
Maine 111 1,316,456 16 41 23.4 0.622124856 270.0567656 1946 20.9 21.8 20
Maryland 217 5,633,597 21 54 23.9 0.942914447 415.4582301 5214 17.8 19.1 16.7
Massachusetts 114 6,497,967 22 47 18.4 1.139894986 462.2511707 7750 17.8 19.4 16.4
Michigan 108 10,003,422 21 47 25.4 0.801025889 245.0760194 9599 22.4 24.8 20.1
Minnesota 108 5,220,393 18 41 22.6 0.793618411 286.6791263 5456 18.3 18.5 18.2
Mississippi 248 2,938,618 10 65 29.5 0.490706856 176.9087523 2304 25.1 27.9 22.5
Missouri 203 5,911,605 19 57 24.9 0.616414662 241.634323 5984 23.3 24.7 22.1
Montana 77 967,440 19 44 19.7 0.787645745 220.8267346 1687 19 18.5 19.6
Nebraska 97 1,783,432 16 49 23.2 1.030036469 241.6402811 2079 18.6 19.6 17.7
Nevada 166 2,600,167 24 48 21.1 0.719569166 184.7704435 2632 22.2 22.9 21.4
New Hampshire 177 1,315,809 18 35 21.6 0.767588609 263.3670369 1703 18.7 19.3 18.2
New Jersey 143 8,682,661 24 54 21.9 0.95466125 310.5142265 9440 18.1 20.8 15.6
New Mexico 157 1,984,356 15 56 21.5 0.558367551 239.4864624 1981 20.2 22.6 17.8
New York 111 19,490,297 25 48 22.1 0.909632111 392.3250909 21246 18.3 19 17.6
North Carolina 330 9,222,414 13 59 24.2 0.592578039 252.989187 8745 22.1 25.3 19
North Dakota 63 641,481 14 39 24.6 0.636028191 242.8180736 892 19.6 21 18.1
Ohio 165 11,485,910 22 51 25.3 0.689888742 264.166093 11705 22.5 24.9 20.2
Oklahoma 184 3,642,361 16 82 24.9 0.606749304 172.2166779 3349 25.1 27.9 22.5
Oregon 68 3,790,060 19 51 21.2 0.699197374 270.3229987 4878 18.5 19.7 17.2
Pennsylvania 121 12,448,279 20 50 24.3 0.81585575 297.0591259 13109 21.5 22.3 20.8
Rhode Island 138 1,050,788 20 50 19 0.653795057 366.3322749 1449 19.3 19.7 18.9
South Carolina 237 4,479,800 12 65 25.1 0.612527345 228.7995901 4536 22.3 25.7 19.2
South Dakota 95 804,194 13 45 23.8 0.589410018 219.8437434 1166 20.4 21.6 19.2
Tennessee 236 6,214,888 13 60 27.2 0.675152955 263.7112024 5572 22.6 23.8 21.5
Texas 222 24,326,974 17 69 25.8 0.533646314 211.5894978 20621 18.1 20.6 15.6
Utah 100 2,736,424 16 50 20.4 0.814566748 211.7986889 2231 9.8 10.4 9.2
Vermont 64 621,270 16 44 18.7 0.775830154 362.7137334 974 18 19.4 16.7
Virginia 270 7,769,089 16 58 23.1 0.752597891 269.9373692 7563 19.3 20.1 18.5
Washington 77 6,549,224 20 49 22.2 0.883310756 265.2522797 7684 17.1 18.9 15.3
West Virginia 144 1,814,468 15 55 27.6 0.632141212 229.0936887 1729 25.7 25.4 26
Wisconsin 97 5,627,967 19 46 23.2 0.738632618 256.5821039 7060 20.8 23.4 18.3
Wyoming 102 532,668 19 46 20.8 0.643928301 184.4645867 858 21.6 23.8

19.4

 

 

Questions

 

 

1.) How would you interpret the coefficient for dentists?

a. As the number of dentists increases by 1 per 1000 people, annual soft drink consumption increases by about 2.85% per year.

b. As the number of dentists increases by 1 per 1000 people, annual soft drink consumption decreases by about 175 per year.

c. When the number of dentists per 1000 people decreases by about 175, then soft drink consumption per capita is expected to increase by 1 unit annually.

d. As the number of dentists increases by 1 per 1000 people, annual soft drink consumption decreases by about 2.265% per year.

 

2.) What seems to be the relationship between soft drink consumption and the percent who smoke?

a. It is difficult to draw any conclusions because the smoker variables were all insignificant (at the 10% level) in all models.

b. For the smoker variables that are statistically significant, the relationship between % smokers and soft drink consumption appears to be negative.

c. % smokers in total seems important (in model B), but once you separate male vs. female smokers it appears that it is only % male smokers that is significantly related to soft drink consumption.

d. As the % smokers rise, soft drink consumption increases, since all of the smoking coefficients in models B-D were positive.

 

3.) A state that currently has 11,000 food service businesses also currently has 20% of its population who smoke (total, both male and female). The state is considering a major initiative to reduce its smoking population to 15%. If it is successful, this will also cause soft drink consumption to fall from about 165 drinks annually to about ___???_____ Answer drinks annually (round to nearest whole number, no decimals).

 

4.) The relationship between number of food service businesses and soft drink consumption per capita

a. is unimportant since, even though it was statistically significant, its coefficient estimate was always small.

b. is negative since, because all of the estimated coefficients were positive, the fact that they were insignificant (at the 10% level) means that you switch the signs.

c. is difficult to summarize because it was insignificant (at the 10% level) in models B-D.

d. is negatively or inversely related since the intercept was always negative in models B-D.

 

5.) Of all the variables in models E through G, mean annual temperature is the only one that is statistically significant (at the 10% level).

True

False

 

6.) In models B-D, it was seen that male smokers was significant. With additional variables added in models E-G, % male smokers

a. is significant but negatively related to soft drink consumption.

b. is insignificant (at the 10% level) while total smokers is now significant.

c. has about the same effect on soft drink consumption as does mean annual temperature.

d. still has a positive coefficient but is insignificant (at the 10% level).

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