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    Multiple Regression

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    See attachment please!

    Results of multiple regression for Defect

    Summary measures
    Multiple R 0.9383
    R-Square 0.8803
    Adj R-Square 0.8612
    StErr of Est 7.2326

    ANOVA Table
    Source df SS MS F p-value
    Explained 4 9621.5292 2405.3823 45.9828 0.0000
    Unexplained 25 1307.7628 52.3105

    Regression coefficients
    Coefficient Std Err t-value p-value
    Constant 1.0312 73.8985 0.0140 0.9890
    Temperature 17.4189 9.5635 1.8214 0.0805
    Density -1.5741 1.7446 -0.9022 0.3755
    Rate 0.1184 0.1330 0.8904 0.3817
    Morning -0.9186 3.0655 -0.2997 0.7669

    Use the output above to answer parts (h) through (l).
    h) Returning to the p-value for the indicator variable Morning, what conclusion can you draw?

    From the above table, we know that the p-value for the indicator variable Morning is 0.7669 and the corresponding t-value=-0.2997. So, we can roughly know that the indicator variable Morning as a predictor variable has a small impact on the number of defects.

    i) Using non-technical language, state and interpret the standard error of the estimate.

    From the above table, we know that the standard error of the estimate is 7.2326. Also, we know the regression equation is
    Number of defects Y=1.0312+ 17.4189* TemperatureX1 -1.5741* DensityX2
    +0.1184 *RateX3-0.9186*MorningX4
    So, we can use this equation to predict the number of defects Y*. If we use 95% confidence level, then the real value for the number of defects can be away from Y* by , ie., (Y*-1.96*7.2326, Y*+1.96*7.2326)

    j) Is Rate significant? What does Rate's significance or lack thereof imply about ...

    Solution Summary

    The results of multiple regression for Defect are determined. An alternative hypothesis is analyzed.