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    Regression Line, RMSE and Interpretation of Slope

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    A regression (trend) line model is fit to examine the relationship between daily high temperatures (T), measured in degrees, and power consumption (P), and measured in thousands of kilowatt hours in a small Kansas town. The data are collected in the months of July and August.
    A straight line is found to fit the data relatively well, and the regression line that was computed resulted in the equation P=-500 + 25T. The root MSE of the model was found to be 15.0.

    a. What is a quantitative interpretation of the slope here? (Use appropriate units in your explanation.)

    b. Although some might be concerned about the intercept being negative (you can't, after all, have a negative power use), that is not a problem. Explain why not. (This has to do with the time of year in which the data are collected.)

    c. What does the root MSE tell you about the variability in power usage (in particular for the predicted value of a day with a given high temperature)?

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    Solution Preview

    a. The slope is 25. This tells us that for every one degree change in temperature, the power consumption will change 25 units.
    For example, if there is a 2-degree increase in T, there will be an increase of ...

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