A multiple regression analysis between yearly income Y in 10

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 10 people, and the following results were obtained.

Coefficients

Standard Error

Intercept

  4.0928

1.4400

X₁

10.0230

1.6512

X₂

  0.1020

0.1225

X₃

-4.4811

1.4400

ANOVA

DF

SS

Regression

360.59

Residual (Error)

  23.91

(a)

Write the regression equation for the above [2]

(b)

Interpret the meaning of the coefficient of X₃ [3]

(c)

Compute the R² [4]

(d)Compute the test statistic to test the following hypothesis: [2]

Ho: b₁=0

Ha: b₁0

(e)Compute the p value [3]

(f) If =0.05, do you reject or accept Ho [1]. Explain why [1]

(g) Compute a 95% confidence interval for b₂ [4]

(h) do you reject or accept Ho:b2=0 [1] Explain why [1]

Solution