Question

1. from tax records, it is relative easy to determine the amount of liquor consumed per capita and the number of cigarettes consumed per capita for each of the 10 provinces of canada. these are plotted on a scatterplot and a high positive correlation is found. which of the following is correct? (a) this implies that heavy smoking causes people to drink more. (b) this implies that heavy drinking causes people to smoke more. (c) we cannot conclude cause and effect, but this also implies that there is a high positive correlation between cigarette smoking and alcohol consumption for individuals. (d) this could be an example of a correlation caused by a common cause because both activities are highly correlated with average family income and average income varies widely among the provinces. (e) we cannot conclude cause and effect, but this also implies that the same individuals both smoke and consume liquor. 3) suppose a study finds that the correlation coefficient relating family income to sat scores is r = +1. which of the following are proper conclusions? i. poverty causes low sat scores. ii. wealth causes high sat scores. iii. there is very strong association between family income and sat scores. (a) i only (b) ii only (c) iii only (d) i and ii (e) i, ii and iii 4) an agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. this means that (a) when corn prices are above average, soybean prices also tend to be above average. (b) there is almost no relation between corn prices and soybean prices. (c) when corn prices are above average, soybean prices tend to be below average. (d) when soybean prices go up by 1 dollar, corn prices go up by 70 cents. (e) the economist is confused, because correlation makes no sense in this situation. 5) if data set a of (x, y) data has correlation r = 0.65, and a second data set b has correlation r = -0.65, then (a) the points in a fall closer to a linear pattern than the points in b. (b) the points in b fall closer to a linear pattern than the points in a. (c) a and b are similar in the extent to which they display a linear pattern. (d) you can’t tell which data set displays a stronger linear pattern without seeing the scatterplots. (e) a mistake has been made—r cannot be negative.

Explanation:

1. Question 2: A high positive correlation between liquor and cigarette consumption per - capita in provinces of Canada does not imply causation. It could be due to a common - cause factor. Just because there is a correlation at the provincial level does not mean it holds for individuals. Option D is correct as it mentions the possibility of a common - cause factor.
2. Question 3: A correlation coefficient of \(r = + 1\) indicates a perfect positive linear association between family income and SAT scores. However, correlation does not imply causation. We can only conclude that there is a very strong association. So, only conclusion III is correct.
3. Question 4: A correlation coefficient \(r=0.7\) (a positive value) means that when one variable (corn prices) is above average, the other variable (soybean prices) also tends to be above average.
4. Question 5: The magnitude of the correlation coefficient (ignoring the sign for the purpose of measuring the strength of the linear relationship) indicates how closely the points follow a linear pattern. A correlation coefficient of \(|r| = 0.65\) for both data sets A and B means they are similar in the extent to which they display a linear pattern.

Answer:

1. D. This could be an example of a correlation caused by a common cause because both activities are highly correlated with average family income and average income varies widely among the provinces.
2. C. III only
3. A. when corn prices are above average, soybean prices also tend to be above average.
4. C. A and B are similar in the extent to which they display a linear pattern.