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    Correlation and Simple Linear Regression

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    Using the Excel SUMMARY OUTPUT below, complete the following:
    All calculations accurate to four decimal places

    1.) What is the value of the correlation coefficient?

    2.) What is the value of the coefficient of determination?

    3.) What is the value of the y-intercept of the least squares line?

    4.) What is the value of the slope of the least squares line?

    5.) Write the equation of the least squares line for this set of data.

    6.) Is the slope of the line significant (yes or no):

    a.) at p < .05?
    b.) at p < .01?
    c.) at p < .001?

    7.) Based on these results, write a sentence explaining the relationship between the dependent and independent variable.

    8.) Compute predicted y for x = 10 using the equation of the least squares line for this data set.

    9.) What percent of the variation in y (dependent variable) is explained by x (independent) variable?

    10.) What value represents the strength of the relationship between the independent and dependent variable?

    In simple linear regression, how many independent variables may be used?

    How many dependent variables may be used?

    SUMMARY OUTPUT

    Regression Statistics

    Multiple R 0.95624857
    R Square 0.914411327
    Adjusted R Square 0.897293593
    Standard Error 5.089839735
    Observations 7

    ANOVA

    df SS MS F Significance F

    Regression 1 1383.8962 1383.8962 53.4189 0.00075
    Residual 5 129.53234 25.906469
    Total 6

    Coefficients Standard Error t Stat P-value

    Intercept -3.88811 4.23842 -0.91751 0.40096
    X Variable 1 5.81993 0.79659 7.30883 0.00075

    please see the attached file

    © BrainMass Inc. brainmass.com April 3, 2020, 1:53 pm ad1c9bdddf
    https://brainmass.com/statistics/regression-analysis/correlation-simple-linear-regression-15219

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    Solution Preview

    See attached file

    Using the Excel SUMMARY OUTPUT below, complete the following:
    All calculations accurate to four decimal places

    1.) What is the value of the correlation coefficient?

    Regression Statistics

    Multiple R 0.95624857
    R Square 0.914411327
    Adjusted R Square 0.897293593
    Standard Error 5.089839735
    Observations 7

    R Square = 0.914411327

    Therefore r= correlation coefficient=√ R Square= √0.914411327 =0.956248

    Answer: r= correlation coefficient=0.956248

    2.) What is the value of the coefficient of determination?

    Regression Statistics

    Multiple R 0.95624857
    R Square 0.914411327
    Adjusted R Square 0.897293593
    Standard Error 5.089839735
    Observations 7

    coefficient of determination= R Square = 0.914411327

    Answer: 0.914411327

    3.) What is the value of the y-intercept of the least squares line?

    Coefficients Standard Error t Stat P-value

    Intercept -3.88811 4.23842 -0.91751 0.40096
    X Variable 1 5.81993 ...

    Solution Summary

    Using Excel output questions on correlation and regression have been answered. The value of the coefficients of determinations are analyzed.

    $2.19

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