Question

The scanorpiot to the night and the dola tabie below show, for 2006 cars, the cation tootpent (tons of c0, per yoar) is highwir miesge for 20 taenly sedans a) The correlation is −0739. Descree the assocation b) Are the assumptons and condtions met for finding a correation? c) Using tochnologs find the coreinton of the data when the cat ith the bowett carbon footerm and highest highuad meg is not notaded wen the chers Explain why z chonges in that way Click the icon to vew the data table a) Choose the correct anwer beion. A. There is a sbong postive linear akcciaton B. Thore e a stong negative linear astociation c. There is a weak regative incar asscciation 0. There s a weak postive inear astociation E. Thore s a no bivence of a hear associaton b) Aee the assumptions and condtons met bor tnding a ceneiaten? A. No, becase the quantative varaties md outior condsons hrre been met but the lnearty condton has not been met B. No, beciuse the quantiative vansbles and linearity condtrons have been met but lewe outler condton has not been mel c. Yes because the quartative variabies. Ineariy, and outier conatoss have al been mut. c) The correlation with fise pont (44 5 9) removed is

Answer 1

a) No, the assumptions and conditions for finding a correlation are not met.

b) The correlation with the data point (44.5, 9) removed is -0.739.

c) The correct option is C. There is a weak negative linear association.

Explanation:

The negative correlation coefficient of -0.739 in part (a) indicates a weak negative linear association between carbon footprint and highway mileage for 2006 cars. This implies that, on average, as the carbon footprint increases, the highway mileage tends to decrease, but the relationship is not strongly linear. In part (b), the lack of meeting assumptions and conditions for finding a correlation suggests potential issues.

While quantitative variables are present, the negative correlation implies a weak linearity, and the likelihood of outliers challenges the validity of the correlation. Outliers can disproportionately influence the correlation, affecting its accuracy.

Part (c) involves the removal of a specific data point (44.5, 9), and the resulting correlation of -0.739 quantifies the impact of this particular data point. If the correlation significantly changes, it implies that the removed data point had a substantial influence on the overall correlation. This underscores the importance of scrutinizing individual data points for their impact on statistical relationships, particularly in instances where their presence can disproportionately affect the outcome.