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 cant tell which data set displays a stronger linear pattern without seeing the scatterplots. (e) a mistake has been made—r cannot be negative.

Explanation:

Question 2:

Correlation does not imply causation. Just because there is a high - positive correlation between liquor consumption per capita and cigarette consumption per capita in Canadian provinces does not mean one causes the other. There could be a common - cause factor.

Question 3:

A correlation coefficient of \(r = + 1\) indicates a perfect positive linear association. It does not imply causation (poverty causes low SAT scores or wealth causes high SAT scores), but it does imply a very strong association.

Question 4:

A positive correlation coefficient (\(r=0.7\)) means that when one variable (corn prices) is above average, the other variable (soybean prices) also tends to be above average.

Question 5:

The magnitude of the correlation coefficient (ignoring the sign) measures the strength of the linear relationship. Since \(|0.65|=|- 0.65|\), A and B are similar in the extent to which they display a linear pattern.

Answer:

Question 2: D

Question 3: C

Question 4: A

Question 5: C