Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2.
                           Linear    Quadratic       Cubic
Intercept             27.43       24.17             18.59
x                         0.17          1.71             6.61
x2                         NA       −0.13          −1.10
x3                         NA             NA             0.05
R2                         0.008       0.047          0.097
Adjusted R2    −0.018       −0.005       0.022
a. Predict y for x = 2 and 5 with each of the estimated models. (Round your answers to 2 decimal places.)
Linear Quadratic Cubic
x = 2
x = 5
b. Select the most appropriate model.
Cubic model
Quadratic model
Linear model
15.(Round all intermediate calculations to at least 4 decimal places.)
Numerous studies have shown that watching too much television hurts school grades. Others have argued that television is not necessarily a bad thing for children (Mail Online, July 18, 2009). Like books and stories, television not only entertains, it also exposes a child to new information about the world. While watching too much TV is harmful, a little bit may actually help. Researcher Matt Castle gathers information on the grade point average (GPA) of 28 middle school children and the number of hours of TV they watched per week. A portion of the data is shown in the accompanying table.
GPA Hours TV
3.24 19
3.10 21
3.24 18
2.61 30
3.03 23
3.37 10
1.60 36
3.20 10
2.96 13
2.18 31
2.50 33
2.95 04
2.72 25
3.05 21
3.45 08
2.49 27
3.62 11
2.33 29
2.36 30
3.28 10
3.35 15
2.64 18
2.88 24
2.02 29
2.60 22
3.18 21
3.31 04
a. Estimate a quadratic regression model where the GPA of middle school children is regressed on hours and hours squared. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
= + Hours + Hours2
b. Is the quadratic term in this model justified?
Yes, based on the R2.
Yes, based on the significance of Hours2.
No, based on the R2.
No, based on the insignificance of Hours2

c. Find the optimal number of weekly hours of TV for middle school children. (Round your answer to 2 decimal places.)
Optimal number of weekly hours

16.According to the World Health Organization, obesity has reached epidemic proportions globally. While obesity has generally been linked with chronic disease and disability, researchers argue that it may also affect wages. Body Mass Index (BMI) is a widely used weight measure that also adjusts for height. A person is considered normal weight if BMI is between 18.5 to 25, overweight if BMI is between 25 to 30, and obese if BMI is over 30. The accompanying table shows data on the salary of 30 college-educated men with their respective BMI.
Salary(in $1,000s) BMI
34                            33
43                            26
44                            26
34                            35
34                            36
53                            20
42                            20
37                            26
35                            28
46                            22
46                            20
34                            35
45                            26
33                            34
25                            29
32                            30
46                            18
31                            31
54                            19
37                            23
42                            27
38                            30
45                            18
38                            26
41                            28
39                            28
50                            20
41                            26
38                            28
45                            21
a-1. Estimate a linear model with salary as the response variable and BMI as the explanatory variable. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
= + BMI
a-2. What is the estimated salary of a college-educated man with a BMI of 25? (Round your answer to 3 decimal places.)
$(1,000)
a-3. What is the estimated salary of a college-educated man with a BMI of 30? (Round your answer to 3 decimal places.)
$(1,000)
b-1. Estimate an exponential model using natural log of salary as the response variable and BMI as the explanatory variable. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
= + BMI
b-2. What is the estimated salary of a college-educated man with a BMI of 25? (Round your answer to 3 decimal places.)
$(1,000)
b-3. What is the estimated salary of a college-educated man with a BMI of 30? (Round your answer to 3 decimal places.)
$(1,000)
c. Which of the above two models is more appropriate for this application? Use R2 for comparison.
Linear model
Exponential model

17.Chad Dobson has heard about the positive outlook for real estate investment in college towns. He is interested in investing in Davis, California, which houses one of the University of California campuses. He uses zillow.com to access data on 2011 monthly rents for 27 houses, along with three characteristics of the home: number of bedrooms (Beds), number of bathrooms (Baths), and square footage (Sqft). The data are shown in the accompanying table.
Rent Beds Baths Sqft
2950 4    4.0 1453
2400 4    2.0 1476
2375 3    3.0 1132
2375 3    3.0 1132
2350 4    2.5 1589
2000 3    2.5 1459
1935 3    2.0 1200
1825 3    2.0    1248
1810 2    2.0    898
1735 3    2.5    1060
1695 3    2.0    1100
1405 3    1.0    1030
1375 2    1.0    924
1365 2    1.0    974
1325 2    2.0       988
1275 2    2.0       880
1200 1    1.0       712
1180 2    1.5    890
1180 2    2.0    960
1115 2    1.0    1020
1100 2    1.0    903
1060 1    1.0    724
1007 3    2.0    1260
850 2    1.5       890
810 1    1.0       570
785 1    1.0       475
744 2    1.0       930
a-1. Estimate a linear model that uses rent as the response variable. (Round your answers to 4 decimal places.
= + Beds + Baths + Sqft
a-2. Estimate an exponential model that uses natural log of rent as the response variable. (Round your answers to 4 decimal places.)
= + Beds + Baths + Sqft
b. Compute the predicted rent for a 1,500-square-foot house with three bedrooms and two bathrooms for the linear and the exponential models (ignore the significance tests). (Use your rounded regression coefficients from Parts a-1 and a-2. Round your answers to 2 decimal places.)
Linear Exponential
c-1. Compute the value of R2, defined in terms of rent. (Round your answers to 4 decimal places.)
Linear Exponential
R2
c-2. Use R2 to select the appropriate model for prediction.
Linear model
Exponential model

Consider the following sample regressions for the linear, the quadr...