Question

In: Advanced Math

1 Over the past decade, there has been a strong positive correlation between teacher salaries and...

1 Over the past decade, there has been a strong positive correlation between teacher salaries and prescription drug cost.

(a) Do you think paying teachers more causes prescription drugs to cost more? Explain.
(b) What lurking variable might be causing the increase in one or both of the variables? Explain.

2 When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

WRITE IN YOUR OWN! WORDS and dont copy from another question that have been answer plz thank you

Solutions

Expert Solution

(a)

No, paying teachers more does not cause prescription drugs to cost more.

Explanation: Correlation does not imply causation. Just because there is a strong positive correlation between teacher salaries and prescription drugs cost, t does imply that paying teachers more cause prescription drugs to cost more.

(b) The lurking variable which might be causing the increase in both the variables is the rising cost of living.

Explanation: Since the cost of living is going up, the teachers are paid more salary so that they can meet the additional expenditure. Since the cost of living is going up, companies have increased prescription drugs to maintain their profit because of increase in production cost of the medicines.

2.

Answer : Extrapolation.

Concerns of extrapolation:

Extrapolation using linear model assumes the same conditions as in the existing values with which the least square line was fit will hold for the future values also. This assumption though valid for some cases cannot hold in general. For example failure rate is constant during the useful life of a product, but when the product enters the wear out phase, failure rate increases with time. So, the linear model which was sufficient in useful life time becomes inapplicable in wear out phase and hence extrapolation is invalid.

Colby Messinger answered 1 year ago
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