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    Regression Analysis

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    The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed "weight-in-motion" scale. To see if the new device was accurate, they conducted a calibration test. They weighed several trucks when stopped (static weight) assuming that this weight was correct. They the weighed the trucks while they were moving to see how well the new scale could estimate the actual weight.

    Simple Linear Regression
    Simple linear regression results:
    Dependent Variable: Weight-in-Motion
    Independent Variable: Static-Weight
    Weight-in-Motion = -13.668853 + 1.460641 Static-Weight
    Sample size: 10
    R (correlation coefficient) = 0.9653
    R-sq = 0.931764
    Estimate of error standard deviation: 1.5751272

    Parameter estimates:
    Parameter Estimate
    Intercept -13.668853
    Slope 1.460641

    a.Looking at the scatter plot of the data, what does it tell you about the relationship between the static weight and the "weight-in-motion"?

    b.Find the equation of the least squares line of regression for this data.

    c.What does the correlation coefficient tell you about the relationship between the static weight and the "weight-in-motion"?

    d.Predict the "weight-in-motion" for a static weight of 32.

    e.Are you confident that predictions based on the equation of this least squares line of regression will be quite accurate? Why or why not?

    f.What percent of the variation in the "weight-in-motion" can be explained by the regression on (relationship with) the static weight?

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    Solution Summary

    Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.