**Economics**

**ECONOMETRICS**

An econometrician wanted to investigate the effects of family size () and income () on household consumption expenditure (). Using a sample size of 89 households he obtained the following results in deviation form.

50.5 -66.2 36.8

-66.2 967.1 39.1

0.0218 0.0015

0.0015 0.0011

, , ,

(i). Specify a model to estimate the relationship between consumption expenditure, income and family size. (2 Marks)

(ii) Estimate the model and interpret your results. (8 Marks)

(iii) Calculate the variance covariance matrix for the estimate. (2 Marks)

(iv) Calculate the coefficient of determination and comment on your result (4 Marks)

(v) Conduct joint test hypothesis test on the slope coefficients at 5% level of significance

(4 Marks)

The following estimated regression equation based on 10 observations was presented.

TSS= 6724.125, RSS = 6216. 375 , ,

Interpret the results of the model. (3 marks)

Calculate the coefficient of determination and comment on your results. (3 Marks)

Are the independent variables related to the dependent variable at 5% level of significance (2 Marks)

Test the overall significance of the regression model at 5% level of significance.

(2 Marks)

management proposed the following regression model to predict sales at a fast-food outlet.

Where

Number of competitors within one mile

=Population within one mile (1000s)

1 if drive-up window present

= 0 otherwise

= sales ($1000s)

The following estimated regression equation was obtained after 20 observations were surveyed.

Determine the expected amount of sales attributable to the drive-up window. (3 Marks)

Predict sales for a store with two competitors, a population of 8000 within one mile and no drive-up window. (4 marks)

Predict sales for a store with one competitor, a population of 3000 within one mile and drive-up window. (3 Marks)

Assume for the model that

, ,, 26.7 4.5 -8

= 4.5 1 -1.5

-8 -1.5 2.5

Determine the following

Variance-covariance matrix for (7 marks)

Conduct hypotheses test on the slope coefficients at 5% levels of significance

given that =2.5 and (6 marks)

iii. The value of and interpret your results. (4 marks)

Assume for the model that

,

,

Calculate the following:

The estimates of the model and interpret your results (8 Marks)

Variance-covariance matrix for (5 Marks)

Conduct hypotheses test on the slope coefficients at 5% levels of significance

(6 Marks)

Calculate the coefficient of determination,and adjusted .

Interpret your results in (iv) above (2 Marks)