Question

Suppose we are interested in the moons of Saturn and how moon diameter relates to moon mass. Furthermore, suppose we selected 12 moons and looked at a regression output for the independent variable: diameter of moon, in kilometers versus the dependent variable: mass of moon, in × 10^15 kg. Below is the regression output from MS Excel that represents the data of concern: SUMMARY OUTPUT Regression Statistics Multiple R 0.933834593 R Square 0.872047048 Adjusted R Squa 0.859251752 Standard Error 14512700.61 Observations 12 ANOVA df SS MS F Significance F Regression 1 1.43544E+16 1.43544E+16 68.1537261 8.93102E-06 Residual 10 2.10618E+15 2.10618E+14 Total 11 1.64606E+16 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept -14162653.92 5231878.263 -2.706992251 0.022047146 -25820005.14 -2505302.688 -23645229.87 -4680077.964 Diameter (km) 25668.66517 3109.27033 8.255527003 8.93102E-06 18740.77914 32596.55119 20033.23357 31304.09676 From the table, extract and interpret the p-value for the hypothesis test for ?, the slope coefficient of the population regression line. Assume H?: ? = 0, H?: ? ? 0, and a level of significance of ? = .05.

          Suppose we are interested in the moons of Saturn and how moon diameter relates to moon mass. Furthermore, suppose we selected 12 moons and looked at a regression output for the independent variable: diameter of moon, in kilometers versus the dependent variable: mass of moon, in × 10^15 kg. Below is the regression output from MS Excel that represents the data of concern:

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.933834593
R Square 0.872047048
Adjusted R Squa 0.859251752
Standard Error 14512700.61
Observations 12

ANOVA
df SS MS F Significance F
Regression 1 1.43544E+16 1.43544E+16 68.1537261 8.93102E-06
Residual 10 2.10618E+15 2.10618E+14
Total 11 1.64606E+16

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0%
Intercept -14162653.92 5231878.263 -2.706992251 0.022047146 -25820005.14 -2505302.688 -23645229.87 -4680077.964
Diameter (km) 25668.66517 3109.27033 8.255527003 8.93102E-06 18740.77914 32596.55119 20033.23357 31304.09676

From the table, extract and interpret the p-value for the hypothesis test for ?, the slope coefficient of the population regression line. Assume H?: ? = 0, H?: ? ? 0, and a level of significance of ? = .05.

Suppose we are interested in the moons of Saturn and how moon diameter relates to moon mass. Furthermore, suppose we selected 12 moons and looked at a regression output for the independent variable: diameter of moon, in kilometers versus the dependent variable: mass of moon, in × 10^15 kg. Below is the regression output from MS Excel that represents the data of concern:

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.933834593
R Square 0.872047048
Adjusted R Squa 0.859251752
Standard Error 14512700.61
Observations 12

ANOVA
df SS MS F Significance F
Regression 1 1.43544E+16 1.43544E+16 68.1537261 8.93102E-06
Residual 10 2.10618E+15 2.10618E+14
Total 11 1.64606E+16

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0%
Intercept -14162653.92 5231878.263 -2.706992251 0.022047146 -25820005.14 -2505302.688 -23645229.87 -4680077.964
Diameter (km) 25668.66517 3109.27033 8.255527003 8.93102E-06 18740.77914 32596.55119 20033.23357 31304.09676

From the table, extract and interpret the p-value for the hypothesis test for ?, the slope coefficient of the population regression line. Assume H?: ? = 0, H?: ? ? 0, and a level of significance of ? = .05.

Added by Rita T.

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