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.

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