Question

In a government study of the relationship between the number of passengers on an aircraft and the total weight in kg of luggage stored in the aircraft's baggage compartment, the coefficient of correlation is computed to be 0.8. We can therefore, conclude that:________

a. 80% of the variation in the weight of luggage is explained by the number of passengers
b. 20% of the variation in the weight of luggage is explained by the number of passengers
c. 64% of the variation in the weight of luggage is explained by the number of passengers
d. 36% of the variation in the weight of luggage is explained by the number of passengers

Answer 1

c. 64% of the variation in the weight of luggage is explained by the number of passengers

Explanation:

The explained variance is a measure given by the coefficient of determination, R².

The value Given above is the correlation Coefficient, R, which is 0.8

The Coefficient of determination, R² = 0.8² = 0.64, expressing as a percentage ; 0.64 * 100% = 64%

This means that 64% of the variation in the dependent variable is can be explained by the regression line. (independent variable)