Question

Suppose for families who live in apartments the scatterplot of the family’s income and the amount of rent they pay is approximately linear with a correlation of r = 0.60. Consider the following statements:
I. In general, families with higher incomes pay more rent.
II. On average, families spend 60% of their income on rent.
III. The regression line passes through 60% of the (income, rent) data points.

Answer 1

Answer:

Option I

Step-by-step explanation:

Given that for  families who live in apartments the scatterplot of the family’s income and the amount of rent they pay is approximately linear with a correlation of r = 0.60.

This implies that there is a positive association between income and rent paid.

Also since r is greater than 0.5, we can say that there is a moderately strong correlation.

All these can be interpreted as if income goes high, rent also would be higher.  

The rise in rent due to income would be 0.6^2 =36% only

The regression line need not pass through 60% of income rent data points but it passes through average of the data points.

Hence only option I is right.