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1. A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X1),...

1. A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X1), age of the individuals (X2), and the gender of the individual (X3; zero representing female and one representing male) was performed on a sample of ten students, and the following results were obtained:

  

Coefficients Standard Error p-value
Intercept 4.0928 1.4400
X1 10.0230 1.6512
X2 0.1020 0.1225
X3 ‐4.4811 1.4400

  

ANOVA
DF SS MS
Regression 360.59
Residual error 23.91  

a. Write the regression equation for the above.

b. Interpret the meaning of the coefficient of X3.

c. Compute the coefficient of determination, and state its meaning.

d. Use the built‐in functions in Excel/XLSTAT® to calculate the p‐value associated with the coefficient of X1. Is it significant? Use α = 0.05. Now, use the t‐Table and interpolate the p‐value.

e. Use the built‐in functions in Excel/XLSTAT® to calculate the p‐value associated with the coefficient of X2. Is it significant? Use α = 0.05. Now, use the t‐Table and interpolate the p‐value.

f. Use the built‐in functions in Excel/XLSTAT® to calculate the p‐value associated with the coefficient of X3. Is it significant? Use α = 0.05. Now, use the t‐Table and interpolate the p‐value.

g. Perform an F‐test, what is your conclusion.

math   Statistics-And-Probability   
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