Question

In: Math

Table #10.1.6 contains the value of the house and the amount of rental income in a...

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.

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

Solutions

Expert Solution

The table as

House 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
225000 12480
244500 11232
300000 12480

The Corelaton coefficeient calculated as


∑ 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

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

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

and Coefficient of determination calculated as by formulae.

Hence Coeeficient if determination calculated as

0.5848 or 58.48%.

Interpretation :

R -squared is statistical measure which shows that how close is our values to the best fitted line or we can say that how the values is coreleated to each other.here value of house is 58.48 % somewhat releated to Rental.

milcah answered 10 months ago
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