DATA PROVIDED BELOW Consider the dataset LAWSCH85.dta (Link pasted below). We wi
ID: 3333252 • Letter: D
Question
DATA PROVIDED BELOW
Consider the dataset LAWSCH85.dta (Link pasted below). We will consider the following explanatory variables for the log of median salary (lsalary = log(salary)): LSAT , GP A, lcost (log(cost)) and rank
(a) Provide the three explanatory variable pairs that are the most correlated (in either direction)?
(b) Calculate R^2j for the rank variable given the four explanatory variables.
(c) Perform the multivariate regression of lsalary on the above explanatory variables and report the five coefficients.
(d) What is the interpretation of the lcost coefficient, and what is the statistical inference about it’s significance?
(e) Test the hypothesis that a hundred-point gain in your LSAT score produces a one-percent gain in your salary with a t-test.
(f) Suppose that we add rank2 to the set of explanatory variables above. Perform the regression for lsalary again. Given the regression results, what is the ceteris paribus effect on salary from decreasing the rank of the school attended by 1 from:
i. A school ranked 10?
ii. A school ranked 150?
https://docs.google.com/spreadsheets/d/1fKARIc2GvROGWF57jBoRi1fV2AwL4Q_bVLCE5IZezrc/edit?usp=sharing
Number refers to column the data is ordered in
Explanation / Answer
a)
The 4 explanatory variables under surveilance are rank, LSAT, GPA and lcost.
Take only those data for these 4 variables.
Remove the rows if any missing values present in any of these columns (as dots or blanks).
Use correlation option from Data Analysis addin in excel and find the correlation between these 4 variables.
The correlation table is
The three most correlated pair are
1. LSAT and GPA with correlation coeficient as 0.7672
2. LSAT and rank with correlation coefficient as -0.7065
3. GPA and rank with correlation coefficient as -0.7040
b) Peform multivariate regression using Regression option in Data Analysis toolpak in excel
lsalary is the response variable
The four explanatory variables are rank, LSAT, GPA and lcost
r square is 0.91 which is strong and hence the explanation of lsalary by these 4 variables is significant.
c)
The output coefficients table for the regression is
Thus the equation is lsalary = 8.56 - 0.004 rank + 0.007 LSAT + 0.26 GPA + 0.04 lcost
d)
lsalary is sightly negatively related with rank, as the rank increases the lsalary decreases slightly(0.004 times)
lsalary is slightly positively related with LSAT, as the LSAT increases the lsalary increases slightly (0.007 times)
lsalary is positively related with GPA, as the GPA increases the lsalary increases (0.25 times)
lsalary is positively related with lcost, as the lcost increases the lsalary increases (0.04 times)
The intercept is 8.56, mostly the lsalary hovers over the range of 10-11, out of which almost 8.5 is constant and cannot be explained by other explanatory variables.
rank LSAT GPA lcost rank 1 LSAT -0.70652 1 GPA -0.70405 0.767216 1 lcost -0.43813 0.445891 0.17645 1Related Questions
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