Question

Data Table The scatterplot to the right and the data table below show, for 2008 cars, the carbon footprint (tons of CO2 per year) vs. highway mileage for 20 family sedans. a) The correlation is - 0.740. Describe the association. b) Are the assumptions and conditions met for finding a correlation? c) Using technology, find the correlation of the data when the car with the lowest carbon footprint and highest highway mpg is not included with the others. Explain why it changes in that way. B Click the icon to view the data table. Carbon Footprint 25 35 45 Highway Carbon mpg Footprint 45 Full data set Highway Carbon mpg Footprint 30 7.5 7.5 Highway mpg 5.9 5.8 20 7.8 a) Choose the correct answer below. 8.1 7.2 6.6 6.6 6.3 6.8 7.2 7.8 7.8 8.1 8.5 O A. There is a weak positive linear association. O B. There is a strong positive linear association. O C. There is a weak negative linear association. O D. There is a no evidence of a linear association. O E. There is a strong negative linear association. 6.6 7.2 8.2. Print Done b) Are the assumptions and conditions met for finding a correlation? O A. Yes, because the quantitative variables. linearity. and outlier conditions have all been met.

Answer 1

a) Correlation = -0.740

Answer: Answer E. There is a strong negative linear association.

b) Answer B. No, because the quantitative variables and linearity conditions have been met but the outlier condition has not been met.

c)

Ʃx =	569
Ʃy =	139.4
Ʃxy =	4150.9
Ʃx² =	17135
Ʃy² =	1032.34
Sample size, n =	19
SSxx = Ʃx² - (Ʃx)²/n = 17135 - (569)²/19 =	94.9473684
SSyy = Ʃy² - (Ʃy)²/n = 1032.34 - (139.4)²/19 =	9.58421053
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 4150.9 - (569)(139.4)/19 =	-23.7631579

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = -23.76316/√(94.94737*9.58421) = -0.788

Answer B. Data values far from the main body of the data and not in line with the linear trend tend to decrease the strength of the correlation, so removing this point has the opposite effect.