Use data from the chemical dataset for your analysis. Consider the equation to express the sales of Chinese rms in the chemical industry in terms of their capital inputs (machinery, other equipment, etc). ln(sales) : 131 + gln(capital) + 81- Note that the variables are already given in terms of their logarithmic component in the dataset. For the year 2004: a ( (b Estimate the given equation Explain the meaning of the coefcients? d ) ) (c) How many degrees of freedom are present? ( ) How does this interpretation differ from a linear-linear model? ) (e Would we reject the null: implied from summary output for the slope at the 1% level? What does this mean in words? (f) Create a scatterplot of the variables and plot the model on top. (g) You suspect that a linearlinear model may work better for this data than a loglog model. For this new model: (i) Estimate its coeicients and give the interpretation. (ii) How many degrees of freedom are present? does it differ from the model above? Why or why not? (iii) What is the estimated sales if a company invests 23, 000 in capital? (iv) Give the 95% condence interval for the marginal effect of an additional dollar of capital using this new model. (v) How does this compare when using the z-distribution for the 95% condence interval? (vi) Which model is better? Why do you suspect that one model performs better than the other? What metric did you use to determine this and what does it mean to be better