HW 7.1-7.4 Correlation and Causality

What is the​ correlation?

There is positive correlation between the number of hours spent studying and their test scores.

Drinking greater amounts of alcohol slows a​ person's reaction time.

The causal connection is valid. Alcohol is a depressant to the central nervous​ system, which leads to slower reaction time.

Is the correlation most likely due to​ coincidence, a common underlying​ cause, or a direct​ cause?

The correlation is most likely due to a direct cause. As students study​ more, they gain a better understanding of the subject and their test scores are likely to be higher.

I found a strong negative correlation for data relating the percentage of people in various countries who are literate and the percentage who are undernourished. I concluded that an increase in literacy causes a decrease in undernourishment.

The statement does not make sense. Correlation is not necessarily causation.

The scatterplot showed all the data points following a nearly straight diagonal​ line, but only a weak correlation between the two variables being plotted.

The statement does not make sense. The data points following a nearly straight diagonal line would indicate a very strong correlation between the two variables.

The two variables I studied showed such a strong correlation that they had a correlation coefficient of r=1.50.

The statement does not make sense. The value of the correlation coefficient ranges from −1 to​ 1, so having a value of r=1.50 is not possible

Researchers conducted animal experiments to study smoking and lung cancer because it would have been unethical to conduct these experiments on humans.

The statement makes sense. Researchers cannot randomly assign people to treatment and control groups and ask subjects in the treatment group to smoke.

Suppose that people living near a particular​ high-voltage power line have a higher incidence of cancer than people living farther from the power line. Can you conclude that the​ high-voltage power line is the cause of the elevated cancer​ rate? If​ not, what other explanations might there be for​ it? What other types of research would you like to see before you conclude that​ high-voltage power lines cause​ cancer?

You cannot conclude that the power line is the cause of the elevated cancer rate because cause cannot be established until a mechanism is confirmed. A study that determines the effect of electricity on a​ cell's growth mechanism.

The weights of aircrafts and their fuel consumption rates measured in miles per gallon.

negative correlation because aircrafts that weigh more tend to have worse gas mileage

Consider the following scatterplot that shows one​ year's total sales​ (revenue) and profits for eight large retailers in a country. Estimate the correlation coefficient and determine whether there appears to be a correlation between sales and profits.

there is strong positive correlation between sales and profits, and the