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    Statistics: Confidence Interval Problem

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    A study was carried out by JT Co. Regarding the stopping distance of a 1300 kilogram car under perfect
    weather conditions at various driving speeds. The results are shown in the following table:
    Speed of the Car
    (in kilometres per hour)
    Stopping Distance (in metres)
    30 11
    50 19
    60 34
    80 52
    100 85
    110 95

    To save calculation time, you can use the following sums and sums of squares and cross-products for
    subsequent calculations:

    a. Construct a scatter diagram for these data.
    b. Calculate the least squares regression line with stopping distance (y) as the dependent variable and
    speed of the car (x) as the independent variable.
    c. Plot the regression line on your scatter diagram. Show your calculations for x = 40 and x = 100.
    d. Interpret the value "b" in the sample regression line.
    e. Construct a 99% confidence interval for B. [Note: Assume Sb = 0.0976].
    f. Construct a 95% prediction interval for the stopping distance of a car when its speed is 70 kph. Assume
    Se = 6.68.
    g. What percent of stopping distance is explained by its linear relationship with the speed of the car?

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    Solution Summary

    This solution provides a detailed, step by step calculation of the given statistics problem.