Quiz 4
Question 1
1. Rockhampton City Council wished to investigate the effect of household income and household size on water consumption. From a survey of 315 households, the following relationship between weekly water consumption in litres, weekly household income measured in dollars and the number of members of the household was estimated:
WATER = 86.64 + 0.3685*INCOME + 358.5*SIZE
Holding weekly income constant, by how much does water consumption (measured in litres) increase if a household gains an extra member? Give your answer correct to one decimal place.
Question 2
1. The Financial Review wished to estimate the amount of annual government spending using tax revenue and level of nationwide debt. Data from 1958-2008 (inclusive) was used. All variables were measured in billions of dollars. It was found that the mean square error for the regression was 14 and the total sum of squares was 3600. Hence, what percentage of the variation in annual government spending is explained by the regression equation? Give your answer correct to two decimal places.
Question 3
1. A recent study by the World Bank wished to determine whether there was a relationship between the abundance of natural resources in a country and its long term rate of economic growth. Their study used 65 (n) countries over a long period to 1995. Letting Y be the rate of growth measured as a percentage and X be a measure of natural resource abundance, the following relationship between the two variables was estimated. Standard errors of bo and b1 are reported in parentheses under the coefficients bo and b1.
Y = 5.358 - 0.0052 X (1.380) (0.0030)
To test the significance of the relationship, a 5% level of significance was adopted.
1. State the direction of the alternative hypothesis used to test the statistical significance of the relationship. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.
2. Use the
1. Rockhampton City Council wished to investigate the effect of household income and household size on water consumption. From a survey of 315 households, the following relationship between weekly water consumption in litres, weekly household income measured in dollars and the number of members of the household was estimated:
WATER = 86.64 + 0.3685*INCOME + 358.5*SIZE
Holding weekly income constant, by how much does water consumption (measured in litres) increase if a household gains an extra member? Give your answer correct to one decimal place.
Question 2
1. The Financial Review wished to estimate the amount of annual government spending using tax revenue and level of nationwide debt. Data from 1958-2008 (inclusive) was used. All variables were measured in billions of dollars. It was found that the mean square error for the regression was 14 and the total sum of squares was 3600. Hence, what percentage of the variation in annual government spending is explained by the regression equation? Give your answer correct to two decimal places.
Question 3
1. A recent study by the World Bank wished to determine whether there was a relationship between the abundance of natural resources in a country and its long term rate of economic growth. Their study used 65 (n) countries over a long period to 1995. Letting Y be the rate of growth measured as a percentage and X be a measure of natural resource abundance, the following relationship between the two variables was estimated. Standard errors of bo and b1 are reported in parentheses under the coefficients bo and b1.
Y = 5.358 - 0.0052 X (1.380) (0.0030)
To test the significance of the relationship, a 5% level of significance was adopted.
1. State the direction of the alternative hypothesis used to test the statistical significance of the relationship. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.
2. Use the