Answer to Question #161349 in Statistics and Probability for FE4

Question

A study has been conducted on the management of 100 homestay operators nationwide.

The study focuses on the factors influencing homestay operators’ income. The

regression results from the multiple regression estimate is as follows.

Model Summary

b

R Square Adjusted R Square Std. Error of the Estimate

- 0.4952 5.512

ANOVA

a

Sum of Squares df Mean Square F

Regression 3132.80 6 522.13 17.19

Residual 2825.60 93 30.38

Total 5958.40 99

Coefficients

a

Unstandardized Coefficients

t Sig.

B Std. Error

Constant 38.14 6.99 5.46 0.000

X1 -0.0076 0.0013 -5.85 0.000

X2 1.65 0.63 2.62 0.011

X3 0.020 0.003 6.67 0.000

X4 0.21 0.13 1.62 0.116

X5 0.41 0.14 2.93 0.004

X6 -0.23 0.18 -1.28 0.211

Predictors: Constant, X1: number of homestay within 1 km, X2: proximity to other

homestay, X3: homestay size area, X4: number of residents around homestay, X5:

median income of residents close to the homestay, X6: distance between the homestay

and the city.

Dependent Variable: monthly income , Y

Multiple linear regression is as follows:

          0 1 1 2 2 3 3 4 4 5 5 6 6 Y X X X X X X

EPPD2023

Student No.

7

Based on the above information,

(i) Write the estimated regression equation.

(2 marks)

(ii) Test for goodness of fit of the regression model at 5% significant level.

(4 marks)

(iii) Calculate R2 and explain the meaning.

(3 marks)

EPPD2023

Student No.

8

(iv) Using  = 0.01, do factors affecting the income of the homestay operators are statistically significant? Explain.

(6 marks)

GOOD

Answer 1

Based on the above information,

The estimated regression equation is given by,

$y=38.14-0.0076x_1+1.65x_2+0.020x_3+0.21x_4+0.41x_5+0.23x_6$

Test for goodness of fit of the regression model at 5% level of significance.

H$_o:$ Null Hypothesis is not applicable here., regression model is not significant.

At $\alpha=0.01,$ Since Null hypothesis is not applicable here so The value of $R_2$ is less than the standard value of Regression constant of y on x,

Thus These factor does not affect the income of the homestay operator are not statistically significant.