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EPPE 6034

ECONOMETRIC METHODS

SEMESTER 1 SESSION 2022/2023

Assignment 1

Download data – food from Ukmfolio.

Variable food_exp denotes weekly food expenditure in $

Variable income denotes weekly income in $100

1.   Using Eviews

(a)  Get the summary statistics for the variables.

(b) Get the scatter plot for the variables with x-axis (independent variable), y-axis (dependent variable). You may improve the basic graph by adding title and changing axis scale where appropriate.

(c)  Estimate the simple regression model and obtain the estimation output.

(d) Give interpretation of the estimates obtained and coefficient of determination

(e)  State the value of and ∑ L 2

(f)  Get the table for observed Y, estimated Y and the least square residuals

(g)  Get the covariance and correlation values for the variables.

(h)  Obtain the coefficient covariance matrix and state the value of vaT () and cOv (, )

(i)  Calculate the income elasticity

(j)  Obtain the graph of the regression line

2.   Refer to the demand for cell phones regression for 34 countries in 2003. i  = 14.4773 + 0.0022Xi

Se (F̂1 ) = 6. 1523            Se (F̂2 ) = 0.00032         T 2  = 0.6023

Where Y : number of cellular phone subscribers per hundred persons

X : income per capita

(a)  Is the estimated intercept coefficient significant at 5% level of significance?

(b) Is the estimated slope coefficient significant at 5% level of significance?

(c)  Establish a 95 percent confidence interval for the true slope coefficient.

3.   In an estimated simple regression model, based on 24 observations, the estimated slope parameter is 0.310 and the estimated standard error is 0.082.

(a)  Test the hypothesis that the slope is zero against the alternative that it is not, at 1% level of significance.

(b) Test the hypothesis that the slope is zero against the alternative that it is positive at 1% level of significance.

(c)  Test the hypothesis that the slope is zero against the alternative that it is negative at 5% level of significance.

(d) Test the hypothesis that the slope is 0.5 against the alternative that it is not at 5% level of significance.

(e)  Obtain a 99% interval estimate of the slope.

4.   A life insurance company wishes to examine the relationship between the amount of life insurance held by a family (INSURANCE) and family income (INCOME). From a random sample of 20 households, the company collected the data in thousands of dollars. The linear relationship between life insurance and income is estimated as

INSÛRANCEi  = 6.8550 + 3.8802 INC0MEi

se        = (7.3835)    (0. 1121)

(a)  What is the estimated change in the amount of life insurance when income increases by $1000?

(b) One member of the management board claims that for every $1000 increase in income, the amount of life insurance held on average will go up by $5000. Does your estimated relationship support this claim? Use a 5% significance level.

(c)  Test the hypothesis that as income increases the amount of life insurance increases by the same amount. Use a 5% significance level.