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    Correlation and Simple Linear Regression

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    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 December 24, 2021, 4:54 pm ad1c9bdddf
    https://brainmass.com/statistics/regression-analysis/correlation-simple-linear-regression-15219

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    SOLUTION This solution is FREE courtesy of BrainMass!

    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 0.79659 7.30883 0.00075

    Answer: -3.88811

    4.) What is the value of the slope 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 0.79659 7.30883 0.00075

    Answer: 5.81993

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

    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

    Y=-3.88811 + 5.81993 X

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

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

    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

    p value=0.00075

    a.) at p < .05? p = .05 >0.00075 hence significant
    b.) at p < .01? p = .01 >0.00075 hence significant
    c.) at p < .001? p = .001 >0.00075 hence significant

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

    For a unit change in the dependent variable X the dependent variable Y changes by 5.81993 (slope of regression line)

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

    Y=-3.88811 + 5.81993 X

    X= 10

    Therefore Y= -3.88811 + 5.81993 X = -3.88811 + 5.81993 * 10= -3.88811 + 58.1993 = 54.31119

    Answer : 54.31119

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

    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

    percent of the variation in y (dependent variable) is explain by x (independent) variable= 91.44% ( R square value expressed as a percentage)

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

    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

    F value and Significance F
    F value is very high=53.4189
    Corresponding to this value of F, Significance F =0.00075 Which means that the relationship is significant at level=0.00075 or 0.075%
    This means that the strength of the relationship between the independent and dependent variable is very high ( the lower the level of significance the higher the strength of relationship)

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

    Any number

    How many dependent variables may be used?
    One

    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

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:54 pm ad1c9bdddf>
    https://brainmass.com/statistics/regression-analysis/correlation-simple-linear-regression-15219

    Attachments

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