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STAT 200 Week 7 Homework Problems Please type your answers to these questions in this document using FULL SENTENCES. Show your work and/or include your reasoning for all problems. Save your work as a...

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STAT 200 Week 7 Homework Problems
Please type your answers to these questions in this document using FULL SENTENCES. Show your work and/or include your reasoning for all problems. Save your work as a Word or .rtf file (NO “.pages”, please!) with file name “YourLastName_HW7”. Attach your file to the Assignment link and submit your work before 11:59 pm on Tuesday of Week 7.
    Question/Solution
    Score
    1. The table below contains the value of the house and the amount of rental income in a year that the house
ings in ("Capital and rental," 2013).
Create a scatter plot and find a regression equation between house value and rental income. Then use the regression equation to find the rental income a house worth $227,000 and for a house worth $402,000. Which rental income that you calculated do you think is closer to the true rental income? Why?
Table 1: House Value versus Rental Income
    Value
    Rental
    Value
    Rental
    Value
    Rental
    Value
    Rental
    81000
    6656
    77000
    4576
    75000
    7280
    67500
    6864
    95000
    7904
    94000
    8736
    90000
    6240
    85000
    7072
    121000
    12064
    115000
    7904
    110000
    7072
    104000
    7904
    135000
    8320
    130000
    9776
    126000
    6240
    125000
    7904
    145000
    8320
    140000
    9568
    140000
    9152
    135000
    7488
    165000
    13312
    165000
    8528
    155000
    7488
    148000
    8320
    178000
    11856
    174000
    10400
    170000
    9568
    170000
    12688
    200000
    12272
    200000
    10608
    194000
    11232
    190000
    8320
    214000
    8528
    208000
    10400
    200000
    10400
    200000
    8320
    240000
    10192
    240000
    12064
    240000
    11648
    225000
    12480
    289000
    11648
    270000
    12896
    262000
    10192
    244500
    11232
    325000
    12480
    310000
    12480
    303000
    12272
    300000
    12480
    
    2. The table in problem 1 contains the value of the house and the amount of rental income in a year that the house
ings in ("Capital and rental," XXXXXXXXXXFind the co
elation coefficient and coefficient of determination and then interpret both.
    
    3. The table in problem 1 contains the value of the house and the amount of rental income in a year that the house
ings in ("Capital and rental," XXXXXXXXXXTest at the 5% level for a positive co
elation between house value and rental amount. Use the 4 steps of the Problem-Solving Process.
    
    4. The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of women receiving prenatal care ("Pregnant woman receiving," XXXXXXXXXXThe data for the countries where this information is available for the year 2011 are in the table below:
Table 4. Health Expenditure versus Prenatal Care
    Health Expenditure (% of GDP)
    Prenatal Care (%)
    9.6
    47.9
    3.7
    54.6
    5.2
    93.7
    5.2
    84.7
    10.0
    100.0
    4.7
    42.5
    4.8
    96.4
    6.0
    77.1
    5.4
    58.3
    4.8
    95.4
    4.1
    78.0
    6.0
    93.3
    9.5
    93.3
    6.8
    93.7
    6.1
    89.8
Test at the 5% level for a co
elation between percentage spent on health expenditure and the percentage of women receiving prenatal care. Use the 4 steps of the Problem-Solving Process.
    
    5. A person’s educational attainment and age group was collected by the U.S. Census Bureau in 1984 to see if age group and educational attainment are related. The counts in thousands are in the table below ("Education by age," XXXXXXXXXXDo the data show that educational attainment and age are independent? Test at the 5% level, including these steps
1. State the null and alternative hypotheses and level of significance.
2. State and check assumptions.
3. Find the test statistic and p value
4. State your conclusion about whether or not to reject the null hypothesis
5. Interpret your findings
Table 5: Educational Attainment and Age Group
    
Education
    Age Group
    Row Total
    
    25-34
    35-44
    45-54
    55-64
    >64
    
    Did not complete HS
    5416
    5030
    5777
    7606
    13746
    37575
    Competed HS
    16431
    1855
    9435
    8795
    7558
    44074
    College 1-3 years
    8555
    5576
    3124
    2524
    2503
    22282
    College 4 or more years
    9771
    7596
    3904
    3109
    2483
    26863
    Column Total
    40173
    20057
    22240
    22034
    26290
    130794
    
    6. A project conducted by the Australian Federal Office of Road Safety asked people many questions about their cars. One question was the reason that a person chooses a given car, and that data is in the table below ("Car preferences," 2013).
Table 6: Reason for Choosing a Ca
    Safety
    Reliability
    Cost
    Performance
    Comfort
    Looks
    84
    62
    46
    34
    47
    27
Do the data show that the frequencies observed substantiate the claim that the reasons for choosing a car are equally likely? Test at the 5% level, including these steps.
1. State the null and alternative hypotheses and level of significance.
2. State and check assumptions.
3. Find the test statistic and p value
4. State your conclusion about whether or not to reject the null hypothesis
5. Interpret your findings
Answered Same Day Aug 02, 2021

Solution

Sudharsan.J answered on Aug 04 2021
137 Votes
Question-1:
    SUMMARY OUTPUT
     
     
     
     
     
     
     
    
    
    
    
    
    
     
    Regression Statistics
     
    
    
    
    
    
     
    Multiple R
    0.76
    
    
    
    
    
     
    R Square
    0.58
    
    
    
    
    
     
    Adjusted R Square
    0.58
    
    
    
    
    
     
    Standard E
o
    1441.62
    
    
    
    
    
     
    Observations
    48
    
    
    
    
    
     
     
    
    
    
    
    
    
     
    ANOVA
    
    
    
    
    
    
     
     
    df
    SS
    MS
    F
    Significance F
    
     
    Regression
    1
    134646420.39
    134646420.39
    64.79
    0.0000
    
     
    Residual
    46
    95600982.28
    2078282.22
     
     
    
     
    Total
    47
    230247402.67
     
     
     
    
     
     
    
    
    
    
    
    
     
     
    Coefficients
    Standard E
o
    t Stat
    P-value
    Lower 95%
    Upper 95%
     
    Intercept
    5363.86
    567.24
    9.46
    0.0000
    4222.07
    6505.66
     
    House Value
    0.02
    0.00
    8.05
    0.0000
    0.02
    0.03
     
Inference:
The model is run with an explanatory variable (House value), the above table says that there is a positive relationship between house value and rental income. There was a statistically significance difference noted between house value and rental income I. Based on the test of significance and adjusted R-squared value it is found model is Less fits the data with adj-R square (0.58).
The fitted equation of the best model is:
 Rental Income= 5363.865+(0.0244*HouseWorth)
When a house worth is $227,000, the predicted rental income of the house is found to be $10902.7 and When a house worth is $40200, the predicted rental income of the house is found to be $15172.7
Question-2:
     
    House Value
    Rental Income
    House Value
    1.00
    
    Rental Income
    0.76
    1.00
    Regression Statistics
     
    Multiple R
    0.76
    R Square
    0.58
    Adjusted R Square
    0.58
Co
elation is used to find the relation between the two variables, Here the given data follows normal distribution, so we used pearson co
elation to find the relationship between house value and rental income. It is found that house value is positive relation with 0.76% of co
elation with Rental income.
The co
elation coefficient is r= 0.764 and coefficient of determination is r2 = 0.584.
Because r is close to 0.8, it tells us that the linear relationship is strong, but not very strong. The r2 value tells us...
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