Question

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

Answer 1

If we run the linear model, based on the above data we have correlation of coeffecient is 0.7647

While the correlation of the determinatin is the 0.5847

As the correlation of coeffecient is 0.7647 so we can say that correlation of both these variable is high and moving in the same direction so it is a healthy correlation between two variable.

Howevere correlation of determination is low 0.5847, which indicates how the independant variable can explain the variability of dependant variable. As independant variable can explain upto 0.5847 of the total variablity so it is a bit lower side in the linear modle.

It indicates that probabiliy, we are missing another independant factor which should also explain the additinal variablity of the dependant variable.