A regression of the average temperature in July as a function of the average temperature in January across cities yielded the following: July temperature = 20 + 2.0 * January temperature,Prob F = .03,R² = .64,and RMSE = 20.If a city has an average temperature of 40 degrees in January,what does this regression say about its likely July temperature? A) The July estimate is 100 degrees, and since the F-statistic has only a 3% chance of being so large if the January temperature did not affect the July temperature, we would be confident in this estimate. B) The July estimate is 100 degrees, and since the R² says that variation in the January temperature explains 64% of the variation in the July temperature, we would be confident in this estimate. C) Since the F-statistic has only a 3% chance of being so large if the January temperature did not affect the July temperature and the R² is so high, there is a serial correlation problem that invalidates any inferences we might draw from the regression. D) The July estimate is 100 degrees, and since the RMSE equals 20, normal statistical confidence intervals would allow for most temperatures from 60 to 140 degrees. Although the point estimate of 100 degrees is our best estimate, we must accept that the actual temperature might be quite different; we would not have confidence in this estimate. E) Since the F-statistic has only a 3% chance of being so large if the January temperature did not affect the July temperature and the R² is so high, there is a multicollinearity problem that invalidates any inferences we might draw from the regression.

Question

A regression of the average temperature in July as a function of the average temperature in January across cities yielded the following: July temperature = 20 + 2.0 * January temperature,Prob > F = .03,R² = .64,and RMSE = 20.If a city has an average temperature of 40 degrees in January,what does this regression say about its likely July temperature? A) The July estimate is 100 degrees, and since the F-statistic has only a 3% chance of being so large if the January temperature did not affect the July temperature, we would be confident in this estimate. B) The July estimate is 100 degrees, and since the R² says that variation in the January temperature explains 64% of the variation in the July temperature, we would be confident in this estimate. C) Since the F-statistic has only a 3% chance of being so large if the January temperature did not affect the July temperature and the R² is so high, there is a serial correlation problem that invalidates any inferences we might draw from the regression. D) The July estimate is 100 degrees, and since the RMSE equals 20, normal statistical confidence intervals would allow for most temperatures from 60 to 140 degrees. Although the point estimate of 100 degrees is our best estimate, we must accept that the actual temperature might be quite different; we would not have confidence in this estimate. E) Since the F-statistic has only a 3% chance of being so large if the January temperature did not affect the July temperature and the R² is so high, there is a multicollinearity problem that invalidates any inferences we might draw from the regression.

Quizplus · Accepted Answer

The July temperature estimate is calculated using the regression equation, resulting in 100 degrees (20 + 2.0 * 40). The F-statistic significance (Prob > F = .03) indicates the model is statistically significant, and the R-squared value (.64) shows a good portion of variance in July temperatures is explained by January temperatures. However, the RMSE of 20 suggests there's a considerable standard deviation around the predicted value, meaning actual July temperatures could vary widely around the estimate, hence the lack of confidence in the exact estimate despite it being the best guess.

A Regression of the Average Temperature in July as a Function