STAT 200 Concordia University Inferential Statistics Analysis and Writeup

Content Type

User Generated

User

boensbhe

Subject

Mathematics

School

Concordia University Wisconsin

Description

Unformatted Attachment Preview

STAT 200 Week 7 Homework Problems 10.1.2 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 81000 6656 77000 4576 75000 95000 7904 94000 8736 90000 121000 12064 115000 7904 110000 135000 8320 130000 9776 126000 145000 8320 140000 9568 140000 165000 13312 165000 8528 155000 178000 11856 174000 10400 170000 200000 12272 200000 10608 194000 214000 8528 208000 10400 200000 240000 10192 240000 12064 240000 289000 11648 270000 12896 262000 325000 12480 310000 12480 303000 Rental 7280 6240 7072 6240 9152 7488 9568 11232 10400 11648 10192 12272 Value 67500 85000 104000 125000 135000 148000 170000 190000 200000 225000 244500 300000 Rental 6864 7072 7904 7904 7488 8320 12688 8320 8320 12480 11232 12480 10.1.4 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 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 Prenatal Expenditure Care (%) (% of GDP) 9.6 47.9 54.6 3.7 93.7 5.2 84.7 5.2 100.0 10.0 4.7 4.8 6.0 5.4 4.8 4.1 6.0 9.5 6.8 6.1 42.5 96.4 77.1 58.3 95.4 78.0 93.3 93.3 93.7 89.8 10.2.2 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 81000 6656 77000 4576 75000 95000 7904 94000 8736 90000 121000 12064 115000 7904 110000 135000 8320 130000 9776 126000 145000 8320 140000 9568 140000 165000 13312 165000 8528 155000 178000 11856 174000 10400 170000 200000 12272 200000 10608 194000 214000 8528 208000 10400 200000 240000 10192 240000 12064 240000 289000 11648 270000 12896 262000 325000 12480 310000 12480 303000 Rental 7280 6240 7072 6240 9152 7488 9568 11232 10400 11648 10192 12272 Value 67500 85000 104000 125000 135000 148000 170000 190000 200000 225000 244500 300000 Rental 6864 7072 7904 7904 7488 8320 12688 8320 8320 12480 11232 12480 10.2.4 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 Prenatal Expenditure Care (%) (% of GDP) 9.6 3.7 5.2 5.2 10.0 4.7 4.8 6.0 5.4 4.8 4.1 6.0 9.5 6.8 6.1 47.9 54.6 93.7 84.7 100.0 42.5 96.4 77.1 58.3 95.4 78.0 93.3 93.3 93.7 89.8 10.3.2 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 81000 6656 77000 4576 75000 95000 7904 94000 8736 90000 121000 12064 115000 7904 110000 135000 8320 130000 9776 126000 145000 8320 140000 9568 140000 165000 13312 165000 8528 155000 178000 11856 174000 10400 170000 200000 12272 200000 10608 194000 214000 8528 208000 10400 200000 240000 10192 240000 12064 240000 289000 11648 270000 12896 262000 325000 12480 310000 12480 303000 Rental 7280 6240 7072 6240 9152 7488 9568 11232 10400 11648 10192 12272 Value 67500 85000 104000 125000 135000 148000 170000 190000 200000 225000 244500 300000 Rental 6864 7072 7904 7904 7488 8320 12688 8320 8320 12480 11232 12480 10.3.4 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. Test at the 5% level for a correlation between percentage spent on health expenditure and the percentage of women receiving prenatal care. Table #10.1.8: Data of Health Expenditure versus Prenatal Care Health Prenatal Expenditure Care (%) (% of GDP) 9.6 47.9 54.6 3.7 93.7 5.2 84.7 5.2 100.0 10.0 42.5 4.7 96.4 4.8 77.1 6.0 58.3 5.4 95.4 4.8 78.0 4.1 93.3 6.0 93.3 9.5 93.7 6.8 89.8 6.1 11.1.2 Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013). The numbers in table #11.1.6 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Is there enough evidence to show that the activity and the time period are independent for dolphins? Test at the 1% level. Table #11.1.6: Dolphin Activity Activity Travel Feed Social Column Total Morning 6 28 38 72 Period Noon Afternoon 6 14 4 0 5 9 15 23 Evening 13 56 10 79 Row Total 39 88 62 189 11.1.4 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 table #11.1.8 ("Education by age," 2013). Do the data show that educational attainment and age are independent? Test at the 5% level. Table #11.1.8: Educational Attainment and Age Group Age Group Education 25-34 35-44 45-54 55-64 Did not 5416 5030 5777 7606 complete HS Competed 16431 1855 9435 8795 HS College 1-3 8555 5576 3124 2524 years College 4 or 9771 7596 3904 3109 more years Column Total 40173 20057 22240 22034 >64 13746 Row Total 37575 7558 44074 2503 22282 2483 26863 26290 130794 11.2.4 In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in table #11.2.6 ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table #11.2.6. Do the data show that the death from cardiovascular disease are in the same proportion as all deaths for the different age groups? Test at the 5% level. Table #11.2.6: Deaths of Females for Different Age Groups Age 5-14 15-29 30-49 50-69 Total Cardiovascular 8 16 56 433 513 Frequency All Cause Proportion 0.10 0.12 0.26 0.52 11.2.6 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 table #11.2.8 ("Car preferences," 2013). Table #11.2.8: Reason for Choosing a Car Safety 84 Reliability 62 Cost 46 Performance 34 Comfort 47 Looks 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.
Purchase answer to see full attachment

User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

I have uploaded the solutions to your task. please feel free to ask questions.

Rental
6656
7904
12064
8320
8320
13312
11856
12272
8528
10192
11648
12480
4576
8736
7904
9776
9568
8528
10400
10608
10400
12064
12896
12480
7280
6240
7072
6240
9152
7488
9568
11232
10400
11648
10192
12272
6864
7072
7904
7904
7488
8320
12688
8320

Rental
14000
12000
10000

Rental

Value
81000
95000
121000
135000
145000
165000
178000
200000
214000
240000
289000
325000
77000
94000
115000
130000
140000
165000
174000
200000
208000
240000
270000
310000
75000
90000
110000
126000
140000
155000
170000
194000
200000
240000
262000
303000
67500
85000
104000
125000
135000
148000
170000
190000

8000
6000

y = 0.0244x + 5363.9
R² = 0.5848

4000
2000
0

0

50000

100000

150000

200000

250000

300000

Value

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.76471575
R Square
0.58479018
Adjusted R Square
0.57576388
Standard Error
1441.62486
Observations
48
ANOVA
df
Regression
Residual
Total

Intercept
Value

SS
MS
F
1 1.35E+08 1.35E+08 64.78736
46 95600982 2078282
47 2.3E+08

CoefficientsStandard Error t Stat
P-value
5363.86482 567.2408 9.456062 2.34E-12
0.02435824 0.003026 8.04906
2.5E-10

Regression equation is

Rental=5363.865+0.024358*Value
use the regression equation to find the rental income a house worth $230,000 and for a ho
House worth $230,000
Rental income =
$ 10,966.20
House worth $400,000
Rental income =
$ 15,107.06

200000
225000
244500
300000

8320
12480
11232
12480

The rental income for the house worth $230,000 is closer to the true rent income because

y = 0.0244x + 5363.9
R² = 0.5848

300000

350000

Significance F
2.5E-10

Lower 95% Upper 95%Lower 95.0%
Upper 95.0%
4222.068 6505.661 4222.068 6505.661
0.018267 0.03045 0.018267 0.03045

se worth $230,000 and for a house worth $400,000

o the true rent income because it is within the regression line

9.6
3.7
5.2
5.2
10
4.7
4.8
6
5.4
4.8
4.1
6
9.5
6.8
6.1

Prenatal
Care (%)
47.9
54.6
93.7
84.7
100
42.5
96.4
77.1
58.3
95.4
78
93.3
93.3
93.7
89.8

Prenatal Care (%)
120
100

Prenatal Care (%)

Health Expenditure (% of GDP)

80
60
40
y = 1.6606x + 69.739
R² = 0.0294

20
0
0

2

4

6

Health Expenditure (% of GDP)

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations

0.17150523
0.02941404
-0.04524641
19.9267527
15

ANOVA
df
Regression
Residual
Total

Intercept
Health Expenditure (% of GDP)

SS
MS
F
Significance F
1 156.4362 156.4362 0.393971 0.541089
13 5161.981 397.0755
14 5318.417

CoefficientsStandard Error t Stat
P-value Lower 95% Upper 95%
69.7393976 17.00601 4.100869 0.001251 33.00015 106.4786
1.66059887 2.645652 0.627671 0.541089 -4.05498 7.376182

Regression equation is
Prenatal Care = (1.6606*Health Expenditure) + 69.739

use the regression equation to find the percent of women receiving prenatal care for a country that spends 5.0% of GDP on h
for 5% of GDP
% of women receiving Healthcare

78.04

for 12% of GDP
% of women receiving Healthcare

89.67

Hence, the predicted value for those that spend 5% of GDP is closer to the true percentage, because it is closer to the regress

Care (%)

y = 1.6606x + 69.739
R² = 0.0294
8

10

12

enditure (% of GDP)

Lower 95.0%
Upper 95.0%
33.00015 106.4786
-4.05498 7.376182

at spends 5.0% of GDP on health expenditure and for a country that spends 12.0% of GDP

Value (X) Rental (Y)
81000
6656
95000
7904
121000
12064
135000
8320
145000
8320
165000
13312
178000
11856
200000
12272
214000
8528
240000
10192
289000
11648
325000
12480
77000
4576
94000
8736
115000
7904
130000
9776
140000
9568
165000
8528
174000
10400
200000
10608
208000
10400
240000
12064
270000
12896
310000
12480
75000
7280
90000
6240
110000
7072
126000
6240
140000
9152
155000
7488
170000
9568
194000
11232
200000
10400
240000
11648
262000
10192
303000
12272
67500
6864
85000
7072
104000
7904
125000
7904
135000
7488
148000
8320
170000
12688
190000
8320
200000
8320
225000
12480

(X-Xbar)^2
8718890625
6300390625
2848890625
1550390625
862890625
87890625
13140625
656640625
1570140625
4306640625
13138890625
22687890625
9481890625
6460140625
3525390625
1969140625
1181640625
87890625
140625
656640625
1130640625
4306640625
9144140625
18394140625
9875390625
7119140625
4144140625
2340140625
1181640625
375390625
19140625
385140625
656640625
4306640625
7678140625
16544390625
11422265625
7987890625
4952640625
2437890625
1550390625
695640625
19140625
244140625
656640625
2562890625

(Y-Ybar)^2
(x-xbar)(y-ybar)
8733995.111
275954250
2914987.111
135519583.3
6015573.778
-130911083.3
1667541.778
50846250
1667541.778
37932916.67
13694933.78
-34693750
5038528.444
8136916.667
7079147.111
68179583.33
1173611.111
-42927083.33
337173.7778
38106250
4148011.111
233452916.7
8229248.444
432092916.7
25354581.78
490315583.3
766208.4444
70354916.67
2914987.111
101372916.7
27115.11111
-7307083.333
1877.777778
1489583.333
1173611.111
10156250
621995.1111
-295750
993344.4444
25539583.33
621995.1111
26518916.67
6015573.778
160956250
10789035.11
314096250
8229248.444
389062916.7
5435115.111
231676250
11365888.44
284456250
6448213.778
163469583.3
11365888.44
163088250
210987.1111
15789583.33
4508544.444
41139583.33
1877.777778
189583.3333
2626560.444
31805583.33
621995.1111
20209583.33
4148011.111
133656250
337173.7778
50880916.67
7079147.111
342228250
7547840.444
293621250
6448213.778
226952916.7
2914987.111
120153583.3
2914987.111
84299583.33
4508544.444
83606250
1667541.778
34058916.67
9465877.778
-13460416.67
1667541.778
-20177083.33
1667541.778
-33090416.67
8229248.444
145226250

244500
300000

11232
12480

4917515625 2626560.444
15781640625 8229248.444

Total
Total
SSX
SSY
8370000 461344 2.26936E+11 230247402.7
Mean
Mean
174375 9611.333

113649250
360376250
SXY
5527756000

Health Expenditure (% of GDP)
9.6
3.7
5.2
5.2
10
4.7
4.8
6
5.4
4.8
4.1
6
9.5
6.8
6.1

Total
mean

Correlation Coefficient =

Prenatal Care (%)
47.9
54.6
93.7
84.7
100
42.5
96.4
77.1
58.3
95.4
78
93.3
93.3
93.7
89.8
X
9.6
3.7
5.2
5.2
10
4.7
4.8
6
5.4
4.8
4.1
6
9.5
6.8
6.1
91.90
6.13

Y
47.9
54.6
93.7
84.7
100
42.5
96.4
77.1
58.3
95.4
78
93.3
93.3
93.7
89.8
1198.70
79.91

Health Expenditure (% of GDP)
Health Expenditure (% of GDP)
Prenatal Care (%)

(x-xbar)^2
12.0640
5.8887
0.8587
0.8587
15.0027
2.0354
1.7600
0.0160
0.5280
1.7600
4.1074
0.0160
11.3794
0.4534
0.0007
56.73
SSX

(y-ybar)^2
1024.8535
640.7648
190.0722
22.9122
403.4742
1399.7575
271.8102
7.9148
467.1362
239.8368
3.6608
179.2028
179.2028
190.0722
97.7462
5318.42
SSY

SXY/(sqrt(SSX*SSY)
0.1715

The correlation coefficient is 0.1715
Based on the computation, the correlation coefficient is positive and very small (close to 0) which suggests that there
is a weak positive relationship between Health Expenditure and Prenatal Care Health Expenditure

Coefficient of Determinantion R^2

0.0294

Based on the calculation above, it appears that there is a 2.94% variation in percentage of women receiving prenatal care can
explained by variation in percentage of GDP that a country spends on health expenditures

Health Expenditure (%Prenatal
of GDP) Care (%)
1
0.171505231
1

(x-xbar)(y-ybar)
-111.1930
61.4270
-12.7756
-4.4356
77.8024
53.3764
-21.8723
0.3564
15.7057
-20.5456
3.8777
-1.6956
45.1577
9.2830
-0.2636
94.20
SXY

o 0) which suggests that there
penditure

of women receiving prenatal care can be
res

Value
Rental
81000
6656
95000
7904
121000
12064
135000
8320
145000
8320
165000
13312
178000
11856
200000
12272
214000
8528
240000
10192
289000
11648
325000
12480
77000
4576
94000
8736
115000
7904
130000
9776
140000
9568
165000
8528
174000
10400
200000
10608
208000
10400
240000
12064
270000
12896
310000
12480
75000
7280
90000
6240
110000
7072
126000
6240
140000
9152
155000
7488
170000
9568
194000
11232
200000
10400
240000
11648
262000
10192
303000
12272
67500
6864
85000
7072
104000
7904
125000
7904
135000
7488
148000
8320
170000
12688
190000
8320
200000
8320

SUMMARY OUTPUT
Regression Statistics
Multiple R
0.764716
R Square
0.58479
Adjusted R Square
0.575764
Standard Error
1441.625
Observations
48
ANOVA
df
Regression
Residual
Total

SS
MS
F
1 1.35E+08 1.35E+08 64.78736
46 95600982 2078282
47 2.3E+08

Coefficients
Standard Error t Stat
P-value
Intercept
5363.865 567.2408 9.456062 2.34E-12
Value
0.024358 0.003026 8.04906
2.5E-10
Test at the 5% level for a positive correlation between house value and rental amount.

Null Hypothesis Ho : p=0
Alternative Hypothesis Ha : p>0
Correlation coefficient value equals 0.765 and the coefficient of determination is 0.5848. A
T statistic value is 8.049 The degrees of freedom = 48-2 = 46. P-value is 0.0000000002504
less than the level of significance, therefore we reject the null hypothesis.
There is evidence to support the claim that there is a positive correlation between house a

225000
244500
300000

12480
11232
12480

Significance F
2.5E-10

Lower 95% Upper 95%Lower 95.0%
Upper 95.0%
4222.068 6505.661 4222.068 6505.661
0.018267 0.03045 0.018267 0.03045
ouse value and rental am...