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Mitchell likes to study the weather. He is fascinated by the sophistication of the computer models used to make weather predictions. Mitchell wonders if he can make his own model to predict the next day’s high temperature in his area based only on today’s high temperature. He selects days at random and gets the temperatures from the Internet. The results from his computer spreadsheet are shown.

A first quadrant scatter plot and increasing line of best fit with the x axis labeled as Random Day High in degrees Fahrenheit and y axis labeled as Next Day High in degrees Fahrenheit. Most of the scatterplots are close to the line. Your teacher will provide you with a model of the graph.

  1. Write a few sentences that describe the association. Remember to include interpretations of slope and .

    Read Math Note box in section 4.2.4 on correlation coefficients and the meaning of R².
    Also remember to look at the axis labels when working with slope.
    Be sure to discuss outliers as well.

  2. Use the graph to estimate the largest residual. To what point does it belong?

    The largest residual belongs to the day after the degree day with a value of about degrees.

  3. Using the model, estimate tomorrow’s high temperature based on today’s high temperature of in Mitchell’s area. Use appropriate precision.

    Let in the given equation.

    degrees because .

  4. Consider the upper and lower bounds of the prediction Mitchell made in part (c) above. Is Mitchell’s model ready to replace the complex models of the professional meteorologists? Support your answer.

    Draw upper and lower boundary lines on the graph. How far apart are these lines?