Question

A researcher is analysing the impact of smoking during pregnancy on infant health. Using a survey of 2000 infants, data on birth weights, smoking and family income produce the following OLS estimates: bwght =116.97 -0.46cigs; + 0.09faminc + lli (Model 1) (1.05) (0.09) (0.02) where bwght is weight at birth measured in ounces, cigs is the average number of cigarettes smoked per day during pregnancy and faminc is the annual income of the family measured in thousands of dollars, and ûs is the residual. Standard errors are shown in parentheses beneath each coefficient and R2 =0.04 for this model. a) Interpret each of the OLS estimates. [3 marks] b) Test whether smoking has negative effect on infant health. [3 marks] c) Calculate the ceteris paribus effect of $10,000 increases in family income on birth weight [2 marks] d) Interpret the R2 of the regression and test the overall significance of the model. [4 marks] e) The model is re-estimated with faminc expressed in natural logarithms. The following estimates are obtained: bwght=113.99 -0.47cigs +1.851n(faminc;) + Ûi R2=0.0295 (Model 2) (1.94) (0.09) (0.59) Explain why transforming famincinto natural logarithms might be appropriate or useful. [4 marks] f) Imagine you are asked to advise the Minister for Health about the relationship between smoking and infant health. How would you summarise the evidence from your research? [4 marks]

I want to solve the branches e and f

Please, I would like to solve the last two subsections of the question

Answer 1

e) Logarithmically transforming variables in a regression model are a way to handle variables with skewed distribution as taking logarithmic form of the variable makes the distribution relatively normal or to capture the non-linear relationship between the dependent and independent variable preserving the Linear Model. Annual family income is usually skewed to income inequality creating a non-linear relationship between faminc and bwght . Log-lieanr mdel through logarithmic transformation helps in controlling the skewness and check the problem of hteroscedasticity.

f) The critical t-statistic at 5% level of significance and 1998 degrees of freedom since n=2000, is 1.96

t-statistic for average number of cigarettes smoked in a day is:

t_calculated = coefficent/standard error = - 0.46/ 0.09 (for equation 1) = 5.11

Since t_calculated > critical t-value, we reject the null and conclude that smoking is a statistically significant variable in infant's weight at birth. If average cigarette consumption per day goes up by one unit, it leads to a fall in infant's body weight at birth by 0.47 ounces.

State Ministry of Helath should promote awareness programmes to demotivate cigarette smoking among pregnant women to promote better infant health. Government advisories focussed at discouraging smoking among pregnant woman could be implemented through health workers, community health system and through awareness drives.