MGTSC 212 Fall 2024
Lab Assignment 4
Due by 11:59 PM, 06 Dec. 2024
Total points: 80
Perform. all calculations using Excel, when calculations are needed: no other source of answers requiring calculation will be permitted. Some of the answers will automatically appear in the Answer worksheet (except tables and graphs). Leave the table(s) and graph(s) within the respective worksheet unless instructed to copy-paste them to the Answer sheet. After calculating answers on the designated worksheet for each problem, if they do not automatically appear in the Answer sheet, Copy and Paste 123 (Values) to the Answer sheet without rounding. Rounded numbers will be treated as errors. Do not type values into the Answer sheet that you calculate elsewhere. Any numbers written directly without excel cell reference or formula into the answer cells will get 0 unless otherwise specified [e.g., you can type in the given x-values while calculatingY(̂)]. You can also type degrees of freedom whenever applicable (as there is no rounding involved).
[3 points] Put your student ID and name in the designated shaded cells in the Answer sheet.
Questions:
Use α = 5% for all hypothesis testing-related questions.
1. [7 points] In the Rand worksheet, you are given a set of two randomly generated numbers between 0 and 1 in cells A4 to A5. Treat these values as the cumulative probabilities under a standard Normal Distribution. Now simulate values in cells B4 to B5 from the Standard Normal distribution such that the area to the left reflects the values in cells A4 - A5. Copy the values from B4 to B5 as Paste Special in cells C9 to C10 of the Answer worksheet [paste as values 123, slide #45 from Lab-cycle1_data_summary]. Note that, failure to fulfill the instructions for the Rand portion, as outlined above, will result in a 15% deduction from your earned marks for Lab Assignment 4.
2. [12 points] The VIF worksheet contains data on Income tax (Y) and other related explanatory variables with an estimated regression model for the Income tax based on a list of explanatory variables as appeared in the regression output. We suspect that there maybe multicollinearity in the system and we would like to find the VIF value of Operating expenses.
a. [8 pts.] Run the VIF regression and save it either in the same worksheet or a separate worksheet
b. [4 pts.] Calculate the VIF value in the VIF worksheet (cell W19). You can also transfer the VIF (calculated elsewhere) without rounding in cell W19.
3. [33 points] The Regs worksheet contains summarized regression results for the CO2 emissions (metric tons per capita) for five different models. Here is a screenshot of the related data sample:
Bangladeshis the base country for the India and Malaysia dummy variables. MVA&IND and MVA&MYS are the interaction variables between Manufacturing, value-added and country dummies.
Based on the regression results answer the following questions (also included in the textbox within the Regs worksheet).
a. [2 pts.] What is the value of the Mean Square Error in Model 3?
b. [4 pts.] What is the value of the test statistic totest H0: βMVA = βTime_Year = βOil rents = βGDP growth = 0 vs. Ha: at least one βj ≠ 0 in Model 3?
c. [2 pts.] What is the sample standard deviation of CO2 emissions in Model 3?
d. [2 pts.] What is the estimated standard error of the error, i.e., what is the value ofσ(̂)? [in OLS regression, we assume that the error, ε~N(0, σ2)] in Model 3?
e. [1.5 pts.] In Model 3, what is the value of the test statistic to test that βoil rents is significantly different from zero?
f. [0.5 pts.] What is the Residual degrees of freedom in Model 3?
g. [2 pts.] What is the p-value of the test that βoil rents is significantly different from zero in Model 3?
h. [2 pts.] What is the correlation between CO2 emissions (Y) and GDP growth (X) based on the sample data utilized in these models?
i. [3 pts.] In Model 1, what will be the predicted CO2 emissions from a country with a 5.5% GDP growth?
j. [6 pts.] Using Model 4 estimates, what will be the predicted CO2 emissions in Malaysia with Manufacturing, value added = 15.72%, Time_Year=1, Oil rents = 0.5%, and a GDP growth of 6.18%?
k. [1 pt.] In Model 3, what is the value of β(̂)MVA?
l. [1 pt.] In Model 3, what is the value of the standard error of β(̂)MVA?
m. [4 pts.] In Model 3, you want to test if the predicted CO2 emissions is increased by less than 0.2 units due to a 1% increase in the Manufacturing, value added when the other variables are in the model and their values are held constant. Calculate the related test statistic value.
n. [2 pts.] In Model 3, calculate the p-value totest H0: βMVA ≥ 0. 2 Vs. Ha: βMVA < 0. 2.
4. [25 points] The LogReg worksheet contains data on university admission for a sample of 400 students with their respective GRE and GPA scores. A researcher is interested in how variables, such as GRE (Graduate Record Exam scores) and GPA (grade point average), affect admission into graduate school. The response variable, admit/do not admit, is a binary variable. Complete the necessary calculations to get the optimal value
of β(̂)0, β(̂)1, β(̂)2 in the logit function: β0 + β1GRE + β2GPA.
a. [8 pts.] Complete the column calculations for Logit, e^Logit, Probability, and Log-likelihood.
b. [3 pts.] Report the optimalβ(̂)0, β(̂)1, β(̂)2 values in cells K4 to K6
c. [2 pts.] Report the maximized log-likelihood value in cell K7
d. [3 pts.] What is the probability of getting admission with a GRE score of 750 and a GPA of 4?
e. [2 pts.] What is the Odds of getting admission with a GRE score of 750 and a GPA of 4?
f. [3 pts.] What is the probability of getting admission with a GRE score of 750 and a GPA of 3?
g. [2 pts.] What is the Odds of getting admission with a GRE score of 750 and a GPA of 3?
h. [2 pts.] What is the Odds ratio for getting admission with a fixed GRE score due to a 1-unit increase in the GPA?