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A multiple regression analysis between yearly income (y in thousands of dollars), college grade point average...

A multiple regression analysis between yearly income (y in thousands of dollars), college grade point average (X1), age of the individuals (X2 in years), and the gender of the individual (X3: 0 representing female and 1 representing male) was performed on a sample of 10 people, and the following results were obtained.

Coefficients Standard of Error

Intercept 4.0928 1.4400

x1 10.0230 1.6512

x2 0.1020 0.1225

x3 -4.4811 1.4400

ANOVA

Source of Variation DF Sum of Squares Mean Square F

Regression (A)   360.59 (E) (G)

Residual (Error) (B) 23.91 (F)

Total (C) (D)

(1) What are the missing values (A, B, C, D, E, F, and G) in the blank cells in the ANOVA table? (No calculation procedure needed)  

NEED TO ANSWER EACH OF THE FOLLOWING QUESTIONS WITH MANUAL CALCULATION PROCEDURE OR APPROPRIATE JUSTIFICATION.

(2) Compute the adjusted multiple coefficient of determination

(3) At a = 0.05, perform an F test and determine whether or not yearly income (y) is significantly related to college grade point average (x1), age of individuals (x2), and the gender of the individual (x3)

(4) Perform a t test and determine whether or not the coefficient of the variable "age" (i.e. x2) is significantly different from zero. Let a = 0.05.

Solutions

Expert Solution

(1) The missing values are filled in the table. The forst table shows the calculated numers and the second tables presents the formula view of the calculations.

Steps: Since number of observations = 10, total DF = 10 - 1 = 9. There are 3 explanatory variables and hence DF for regression = 3. Therefore DF for residual = 9 - 3 = 6.

Total sum of squares = regression sum of squares + residual sum of squares

Mean square = sum of square / df

F = regression mean sum of square / residual mean sum of squares

(3) As calculated above in the ANOVA table, the F-statistic = 30.1622752. Further, the critical value at 5% level of significance and degree of freedom (3, 6) = 4.757063.

Since, the calculated F (30.1622752) > critical F (4.757063), we may reject the null hypothesis and conclude that at least one of the three explanatory variables has significant effect on yearly income.

Rahul Sunny answered 2 years ago
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