House Value vs Rental Value: Which is More Important? Free Essay Example

10.1.2

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

Scatter Plot

Regression Equation

ŷ = 0.02X + 5363.86

Calculating rental income for a house worth of:

$230,000

ŷ = 0.02 (230,000) + 5363.86

ŷ = 9,963.86

$400,000

ŷ = 0.02 (400,000) + 5363.86

ŷ = 13,363.86

Note : The calculated rental income for $230,000 value appears to be closer than that of $400,000 to the true rental income. This is because the higher the x value in a regression equation, the lower the chances of accuracy.

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10.1.4

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

Scatter Plot

Regression Equation

ŷ = 1.6606 X + 69.7394

Calculating the percent of women receiving prenatal care for:

5.0% of GDP

ŷ = 1.6606 (5) + 69.7394

ŷ = 78.0424

12.0% of GDP

ŷ = 1.6606 (12) + 69.7394

ŷ = 89.6666

Note : The percent of women receiving prenatal care for 5.0% GDP appears to be closer than that of 12.0% of GDP to the true percentage. This is because the higher the x value in a regression equation, the lower the chances of accuracy.

10.2.2

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

Calculations

X Values

∑ = 8370000

Mean = 174375

∑ (X - Mx)2 = SSx = 226935750000

Y Values

∑ = 461344

Mean = 9611.333

∑ (Y - My)2 = SSy = 230247402.667

X and Y Combined

N = 48

∑ (X - Mx) (Y - My) = 5527756000

Correlation coefficient (R) Calculation:

R = ∑ ((X - My) (Y - Mx)) / √((SSx)(SSy))

R = 5527756000 / √ ((226935750000) (230247402.667)) = 0.7647

R = 0.7647

This is a strong positive correlation implying that high X variable scores (values) go with high Y variable scores (rental income).

Coefficient of determination (R 2 ) Calculation:

R 2 = (0.7647)2

R 2 = 0.5848

10.2.4

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

X Values ∑ = 91.9 Mean = 6.127 ∑(X - M x ) 2 = SS x = 56.729 Y Values ∑ = 1198.7 Mean = 79.913 ∑(Y - M y ) 2 = SS y = 5318.417 X and Y Combined N = 15 ∑(X - M x )(Y - M y ) = 94.205 R Calculation R = ∑((X - M y )(Y - M x )) / √((SS x )(SS y )) R = 94.205 / √((56.729)(5318.417)) = 0.1715 R = 0.1715

Although technically a positive correlation, the relationship between the variables is weak

Coefficient of determination (R 2 ) Calculation:

R 2 = 0.0294

10.3.2

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

R = 0.7647

N = 48

The P-Value is < .00001. The result is significant at p < .05

10.3.4

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

R = 0.1715

N = 15

The P-Value is .541101. The result is not significant at p < .05.

House Value vs Rental Value: Which is More Important?

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