The table below contains on 48 houses: the value of the house and the amount of

Question

The table below contains on 48 houses: the value of the house and the amount of rental income in a year that the house brings in.

1. Determine the correlation between variables (if it exists) in this relation. Which variable is the dependent (output) variable?

A. Value of house

B. Annual rental income generated

2. Using technology, determine coefficient of correlation r

3. What type of linear correlation does the calculated r value indicate?

A. Strong positive correlation

B. Moderate positive correlation

C. Weak negative correlation

D. No linear correlation

E. None of the above are correct

4. Use the correlation coefficient r to find the coefficient of determination r2

5. What percentage of the variability in the annual rental income is accounted for by the value of the house?

Value Renta ReValueRenta Value Rental 4576 75 8736 9 7904 11 81 728 675 6240 85 7072 104 624? 125 9152 135 7488 148 9568 17 6656 77 686 95 79 94 707 121 12064 115 79 135 8320 13 79 9776 126 9568 14 8528 155 145 8320 14 748 165 13312 165 832 178 11856 174 1040? 17 1268 832 832 1248 20 12272 2 10608 194 11232 19 8528 208 10192 24 11648 27 1248? 31 214 10400 20 10400 20 12064 24 12896 262 1248? 303 11648 225 10192 244500 11232 12272 3 24 2890 325 1248

Explanation / Answer

Using correl function in excel, correlation is found to be 0.764716.

Dependent variable is annual rental income generated.

Type of correlation is moderate because it is less than 0.85.

Since coefficient of determination is equal to square of correlation coefficient, therefore coefficient of determination is equal to 0.5848.

58.48 percentage of variability in annuaal rental income is accounted for by the value of house.

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