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    Interpretation of Regression Analysis Output

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    First Simple Regression Equation
    Cost1 = $13,123 - $0.30 Output

    Predictor Coefficient Standard Deviation t Ratio p
    Constant 13,123 2,635 4.98 0.000
    Output -0.297 2.285 -0.13 0.899

    SEE = $4,871; R² = 0.2%; R-bar² = 0.0%; F statistic = 0.02 (p = 0.899)

    Second Simple Regression Equation
    Cost2 = $8,455 + $7.40 Output

    Predictor Coefficient Standard Deviation t Ratio p
    Constant 8,455 1,550 5.45 0.000
    Output 7.397 1.345 5.50 0.000

    SEE = $2,866; R² = 75.2%; R-bar² = 72.7%; F statistic = 30.26 (p = 0.000)

    Third Simple Regression Equation
    Cost3 = $662 + $12.7 Output

    Predictor Coefficient Standard Deviation t Ratio p
    Constant -$661.5 488.4 -1.35 0.205
    Output 12.7298 0.4236 30.05 0.000

    SEE = $902.8; R² = 98.9%; R-bar² = 98.8%; F statistic = 903.1 (p = 0.000)

    Interpret the three simple cost regressions. Interpret the regression results. Examine each equation.

    What is the quantitative relation between changes in output and costs?

    How much of the relationship does the equation explain (R square)?

    Is the coefficient statistically significant enough to base a forecast on (t statistic)?

    Is the entire regression statistically significant (F statistic)?

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    Solution Preview

    HW # 1
    General Explanation:
    The t value of a regression coefficient provides idea about the statistical significance of the regression coefficients.
    The F value of a regression equation provides idea about the overall significance of the regression model.
    The p value of test statistics (in the present case t & F) can be explained as the probability of wrongly rejecting the statistical significance of the calculated values. This means lower p values for a statistic (less than 0.05 in the case of 5% level test) indicate high statistical significance.
    R2 is known as the coefficient of determination of the model and R-bar 2 (or Adjusted R2) is the coefficient of determination adjusted for the degrees of freedom of the model. Both these values provide the explanatory power of the model. For example if for a model R2 = 0.90 it means 90% of the variations in the model can be explained by the explanatory variables.
    Based on the explanations given above the given regression equations are interpreted as follows
    Regression Equation 1
    1. The regression equation, cost 1 = $13,123 -$0.30 output, indicate that the cost per unit is negatively related to ...

    Solution Summary

    Several statistical packages provide tools for Regression Analysis. This solution provides detailed explanations of the concepts and meanings of the various characteristics provided in a Regression Output of statistical packages such as Data Analysis Tool of MS Excel, SPSS etc. Meaning and idea of the various characteristics such as regression coefficients, t values, F values and their interpretations using p values are provided as general explanation. The meaning of R square and adjusted R square and their relationship are also provided. The examples provided in the solution will really be helpful to understand the concepts and interpret the regression results properly.