Using a sample of 7006 observations, the following regression for consumption of
ID: 1199256 • Letter: U
Question
Using a sample of 7006 observations, the following regression for consumption of Diesel Jeans was estimated: q_i = -2.0 - 1.20 p_i + 0.40S_i + 2.0 m_i - 0.025m_i^2 + 0.05 p_i S_i, Where qi denotes quantity of Diesel Jeans purchased over a 3 year period by household i, pi is the price of Diesel Jeans, si is the price of Seven Jeans and mi is monthly household income. Quantity, prices and income are all measured in logarithms. Standard errors of the coefficient estimates are in parentheses. The total sum of squares is 1500 and the explained sum of squares is 800. Test the significance of the coefficients on pi and si. Test the hypothesis that the coefficient on pi equals -1 Describe the effect of pi on qi. Describe the effect of mi on qi. When m2 and pisi were removed from the model and the regression was re-estimated, the explained sum of squares dropped to 700. Would you include or exclude these variables from the regression? Justify your answer with a test.Explanation / Answer
e) decrease of explained sum of square means some part of the residuals is not explaining by the explanatory variable. So if sum of square increases that means that independent variable are capturing the random residuals... So we should keep those variables.
d) If mi increases by 1 unit then Qi will change by (2.0-0.025). but if the change is more than 1 then due to 2.0xmi, Qi will increase by 2 unit but for square of mi it will again decrease by one unit. So as mi increases qi increases linearly and decrease by square multiplied by 0.025 of change in Mi..
c)due to increase in Pi, Qi will decrease by 1.2 but it will lead another effect to yhe interaction term of Pi and Si.
a)generally we take 2xstandered error must be less than 5 fr 95% confidence limit.. So in thos case both the variable are statistically significant.
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