Question 1

b) When food expenditure (Y) was regressed on gender, the following equation was obtained.

Y_i=3176.833-503.166 D_i

SE=(233.0446) (3295749)

t= (13.6318) P value=0.15 r²=0.189.

Where D_i-=1 if female; 0 if male.

i) At =0.05, do you think that gender significantly influences the annual food expenditure for a household?

ii) What are the annual food expenditure for males and females respectively.

c) Besides D_i in the above model another independent variable which is the after tax income was incorporated in the model. The following results were obtained using SPSS:

Y_i=1506.244-228.9868D_i+0.058gX_i

S.E =(188.0096)(107.0582) (0.006)

t = (8.0115)(_______) (____)

V_alue (0.001) (0.0611)(0.000)

R²=0.9312; n=5

i) Compute the missing values above.

ii) Why is r² in (b) above smaller than R² in this expanded model?

iii) From your results here, test the research hypothesis that "after tax income significantly improves the annual food expenditure per household? Take=0.0?

iv) At=0.05, do you think the gender and after tax income of a sponsor of household food expenditure significantly influence/determined the annual food expenditure? How do you explain the high R²?

v) State the annual food expenditure for a female Kenyan whose annual income after KRA tax reduction is Ksh 100,000

vi) how would one go about confirming the presence or absence of heteroscedasticity in a multiple linear regression model. What are the consequences of heteroscedasticity?

Question 2

Let Y_i denote quantity demanded, X₂ be the price of the quantity demanded, X₃. X₄ being the earnings per week and income per week respectively. Based on a sampled set of data, the following estimating regression were obtained.

1. Y_i=49.667-2.1576 x_2i

S.E=(0.746) (-0.1203)

t=(66.535) (-17.935)

r²=0.9757

2. Y_i=145.37-2.7775X₂-0.3191X_4i

SE=(120.06) (0.822) (0.400)

t=(1.2107) (-3.44) (-0.7971)

R²=0.9778

1. Comment on the sign of price coefficient on both equation i.e (1) and (2)
2. Use both results in equation (1) and (2) to outline some of the consequences of multicollinearity.
3. Explain the meaning of subsidiary (quantity) regression, variance Inflation factor (VIF). How would you use subsidiary regression and VIF to check for multicolinearity?