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# Conducting and Econometrics Analysis

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An investigator analysing the relationship between food expenditure, disposable income and prices in the US using annual data over the period 1959-83 computes the following regression

log(FOOD) = 4.7377 + 0.1069TIME + 0.3506log(PDI) - 0.5086log(PRICE)
(0.6805) (0.0033) (0.0899) (0.1010)

FOOD Total household expenditure on food
TIME A time trend
PDI Personal disposable income
PRICE The price of food deflated by a general price index

Figures in parentheses are standard errors

(i) Give an economic interpretation of the coefficients on log(PDI) and log(PRICE)

(ii) Test the hypothesis (using a 5% significance level) that the coefficient of log(PRICE) is equal to zero against the alternative that it is nonzero.

(iii) Test the hypothesis (using a 5% significance level) that the coefficient of log(INCOME) is equal to 1 against the alternative that is significantly different from 1.

You are now given the following extra information

SST = sum(y_t - mean(Y))^2 = 0.53876

SSR = sum(e_t)^2 = 0.0046276

(iv) Compute the SSE and R^2 for the above regression

(v) Test the joint hypothesis (at the 5% level) that the three 'slope' coefficients are all equal to zero against the alternative that at least one 'slope' coefficient is non-zero.

https://brainmass.com/statistics/hypothesis-testing/conducting-econometrics-analysis-511186

#### Solution Preview

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Solution.

(i) The coefficient on log(PDI) was 0.3506. It means that the elasticity was 0.3506. In other words, there is 35.06% change in Food for 1% change in PDI.

The coefficient on log(PRICE) was -0.5086. It means that the elasticity was
-0.5086. In other words, there is -50.86% change in Food for 1% change in PDI.

(ii) We conduct a t-test.

H0:
Ha:

We can compute the test statistic as follows. Given the standard error of the log(PRICE) to ...

#### Solution Summary

Going through the steps of hypothesis testing, this solution interprets the information in the regression, as well as calculates SSE and R squared. This solution is provided within a Word document which is attached.

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