Question

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Maximum daily temperature and cooling costs b. Interest rate and number of loan applications c. Incomes of husbands and wives when both have fulltime jobs d. Height and IQ e. Height and shoe size f. Score on the math section of the SAT exam and score on the verbal section of the same test g. Time spent on homework and time spent watching television during the same day by elementary school children h. Amount of fertilizer used per acre and crop yield (Hint: As the amount of fertilizer is increased, yield tends to increase for a while but then tends to start decreasing.)

Short answer

a. Positive correlation; b. Negative correlation; c. Positive correlation; d. Correlation close to 0; e. Positive correlation; f. Positive correlation; g. Negative correlation; h. Initially positive then negative correlation.

Step-by-step solution

Analyzing the Relationship between Maximum Daily Temperature and Cooling Costs

As the maximum daily temperature increases, the need for cooling also increases, thus raising the cooling costs, indicating a positive correlation.

Analyzing the Relationship between Interest Rate and Number of Loan Applications

When interest rates are high, loans become expensive and hence the number of loan applications may decrease. This suggests a negative correlation.

Analyzing the Relationship between Incomes of Husbands and Wives

If both husbands and wives have full-time jobs, their incomes might be similar or depend on the similar economical conditions, indicating a likely positive correlation.

Analyzing the Relationship between Height and IQ

Height and IQ are two different variables that don't seem to affect each other significantly. Hence, a correlation close to 0 would be expected.

Analyzing the Relationship between Height and Shoe Size

Usually, taller people tend to have larger shoe sizes. Thus, it is likely to expect a positive correlation between height and shoe size.

Analyzing the Relationship between Scores on Different Sections of the SAT Exam

Performing well on one section of the SAT may likely indicate good performance on other sections too, indicating a potential positive correlation.

Analyzing the Relationship between Time Spent on Homework and Time Spent Watching Television

If more time is spent on watching television, it might mean less time for homework, suggesting a negative correlation.

Analyzing the Relationship between Amount of Fertilizer Used and Crop Yield

While initially an increase in the amount of fertilizer might boost the crop yield, excessive use of fertilizer may have an adverse effect, indicating a positive correlation initially followed by a negative correlation.