Stats Week 5 Problem Sets
Chapter 13 Problems (2, 9, 11, & 14)
2) Determine the coefficient of correlation and the coefficient of determination. Interpret the association between X and Y.
X Y x^2 xy
5 13 25 65
3 15 9 45
6 7 36 42
3 12 9 36
4 13 16 52
4 11 16 44
6 9 36 54
8 5 64 40
39 85 211 378
r = (378) - (39)(85) / 8 = -36.375 √[211 - (39)^2 / 8] * √[983 - (85)^2 / 8] r= -.8908 r^2= .7935
Since r is negative there would be a negative correlation.
9) Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78. At the .01 significance level, is the correlation in the population greater than zero?
Significance = .01 T= (.78√20- 2)/(√1-(〖.78)〗^2 )
T=5.288
DF = 18
Correlation= .78
CV= 2.552
Reject null
11) The Airline Passenger Association studied the relationship between the number of passengers on a particular flight and the cost of the flight. It seems logical that more passengers on the flight will result in more weight and more luggage, which in turn will result in higher fuel costs. For a sample of 15 flights, the correlation between the number of passengers and total fuel cost was .667. Is it reasonable to conclude that there is positive association in the population between the two variables? Use the .01 significance level.
Significance= .01 t= (0.667√15- 2)/(√1- 〖0.667〗^2 ) t= 3.228
CV = 2.650
Reject null
The problem shows a positive correlation between the two variables passengers, and fuel costs.
14) The following sample observations were randomly selected. Y
A) Determine the regression equation.
B) Determine the value of Ŷ when X is 7.
X Y x^2 xy
5 13 25 65
3 15 9 45
6 7 36
2) Determine the coefficient of correlation and the coefficient of determination. Interpret the association between X and Y.
X Y x^2 xy
5 13 25 65
3 15 9 45
6 7 36 42
3 12 9 36
4 13 16 52
4 11 16 44
6 9 36 54
8 5 64 40
39 85 211 378
r = (378) - (39)(85) / 8 = -36.375 √[211 - (39)^2 / 8] * √[983 - (85)^2 / 8] r= -.8908 r^2= .7935
Since r is negative there would be a negative correlation.
9) Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78. At the .01 significance level, is the correlation in the population greater than zero?
Significance = .01 T= (.78√20- 2)/(√1-(〖.78)〗^2 )
T=5.288
DF = 18
Correlation= .78
CV= 2.552
Reject null
11) The Airline Passenger Association studied the relationship between the number of passengers on a particular flight and the cost of the flight. It seems logical that more passengers on the flight will result in more weight and more luggage, which in turn will result in higher fuel costs. For a sample of 15 flights, the correlation between the number of passengers and total fuel cost was .667. Is it reasonable to conclude that there is positive association in the population between the two variables? Use the .01 significance level.
Significance= .01 t= (0.667√15- 2)/(√1- 〖0.667〗^2 ) t= 3.228
CV = 2.650
Reject null
The problem shows a positive correlation between the two variables passengers, and fuel costs.
14) The following sample observations were randomly selected. Y
A) Determine the regression equation.
B) Determine the value of Ŷ when X is 7.
X Y x^2 xy
5 13 25 65
3 15 9 45
6 7 36