A Regression of the Mean Daily High Temperature as a Function

question 13

Multiple Choice

A regression of the mean daily high temperature as a function of mean daily low temperature across cities yielded High = 21 + Low,R² = .98,and RMSE = 1.4.Interpret these results.

• A) The regression says that if a city's average low temperature is 1 degree higher than some other city's, their average high temperatures are also likely to be 1 degree different. The high R² and low RMSE are inconsistent and suggest a serial correlation problem.
• B) The regression says that if a city's average low temperature is 10 degrees higher than some other city's, their average high temperatures are also likely to be 10 degrees different and that the average difference between average daily high temperatures and average daily low temperatures is 21 degrees. The model explains 98% of the variation in average daily high temperatures, and the standard error of the estimate is quite small.
• C) The regression says that if a city's average low temperature is 1 degree higher than some other city's, their average high temperatures are also likely to be 1 degree different. The high R² and low RMSE are inconsistent and suggest a multicollinearity problem.
• D) The regression says that if a city's average low temperature is 10 degrees higher than some other city's, their average high temperatures are also likely to be 10 degrees different and that the average difference between average daily high temperatures and average daily low temperatures is 12 degrees. The regression explains all the variation in average daily high temperatures.
• E) None of the above.

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Definitions:

Alternative Hypothesis

A statement in hypothesis testing that proposes a difference or association, contrasting with the null hypothesis which suggests no effect.

Physicians

Medical professionals who are qualified to diagnose and treat diseases, prescribe medications, and perform medical procedures.

P-value

The probability of observing results at least as extreme as those measured when the null hypothesis is true.

Hypotheses

Statements or predictions that can be tested through scientific research, designed to explain phenomena or the relationship between variables.