Table A contains the value of the house and the amount of rental income in a year that the house brings in. Find the correlation coefficient and coefficient of determination and then interpret both.
Table #A: Data of House Value versus Rental
Value |
Rental |
Value |
Rental |
Value |
Rental |
81000 |
6656 |
77000 |
4576 |
75000 |
7280 |
95000 |
7904 |
94000 |
8736 |
90000 |
6240 |
121000 |
12064 |
115000 |
7904 |
110000 |
7072 |
135000 |
8320 |
130000 |
9776 |
126000 |
6240 |
145000 |
8320 |
140000 |
9568 |
140000 |
9152 |
165000 |
13312 |
165000 |
8528 |
155000 |
7488 |
178000 |
11856 |
174000 |
10400 |
170000 |
9568 |
200000 |
12272 |
200000 |
10608 |
194000 |
11232 |
214000 |
8528 |
208000 |
10400 |
200000 |
10400 |
240000 |
10192 |
240000 |
12064 |
240000 |
11648 |
289000 |
11648 |
270000 |
12896 |
262000 |
10192 |
325000 |
12480 |
310000 |
12480 |
303000 |
12272 |
The Correlation coefficient calculated as
Let X to be the House value and Y to be the rental income
Hence Coefficient if determination calculated as
0.5697 or 56.97%
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 correlated to each other. Here value of house is 56.97% somewhat related to Rental.
The correlation coefficient is used to show how strong or weak the explanatory variable is related to the response variable. It is also used to show whether their relationship is direct or inversely relation by indicating a positive value of r for direct relation and negative value of r for inverse relation of the variables. In this case, r = 0.7548 shows a fairly strong positive linear relationship between house value and rental income.
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