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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.

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

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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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