# Estimate the following multiple regression models | Complete Solution

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).