1
Table #10.1.6 contains the value of the house and the amount of rental income in a year that the house brings 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 $230,000 and for a house worth $400,000. Which rental income that you calculated do you think is closer to the true rental income? Why?
Table #10.1.6: Data of House Value versus Rental
|
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 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," 2013). The data for the countries where this information are available for the year 2011 is in table #10.1.8. Create a scatter plot of the data and find a regression equation between percentage spent on health expenditure and the percentage of women receiving prenatal care. Then use the regression equation to find the percent of women receiving prenatal care for a country that spends 5.0% of GDP on health expenditure and for a country that spends 12.0% of GDP. Which prenatal care percentage that you calculated do you think is closer to the true percentage? Why?
Table #10.1.8: Data of 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
|
3.
Table #10.1.6 contains the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013). Find the correlation coefficient and coefficient of determination and then interpret both.
Table #10.1.6: Data of House Value versus Rental
|
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
|
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," 2013). The data for the countries where this information is available for the year 2011 are in table #10.1.8. Find the correlation coefficient and coefficient of determination and then interpret both.
Table #10.1.8: Data of 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
|
5.
Table #10.1.6 contains the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013).
Test at the 5% level for a positive correlation between house value and rental amount.
Table #10.1.6: Data of House Value versus Rental
|
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
|