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Question 2 NAT · 0.5 marks
**(The following scenario is purely Imaginary)**
Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest
possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual
workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as
parameters to predict defaulters. The model is configured such that a “NOT DEFAULTER” is
categorised as the positive class. The final model had the parameters as specified in Table-1
below. To test the model, the data in Table-2 is used as test data. Given this information, answer
the given subquestions.
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
At a threshold of 0.6, how many “True Positives” is the model predicting?
Published solution
**1. Calculate the logistic probabilities:** The positive class is NOT DEFAULTER. Use \(z=3.20-1.70A+1.40I\) and \(p=1/(1+e^{-z})\). For CID01–CID06, the scores are −2.48,−1.61,2.11,1.17,−1.99,2.30 and the two-decimal probabilities are 0.08,0.17,0.89,0.76,0.12,0.91.
**2. Apply the 0.60 threshold:** CID03,CID04,CID06 are predicted positive; CID01,CID02,CID05 are predicted negative. Comparing with actual status gives TP=1 (CID06), TN=1 (CID02), FP=2 (CID03,CID04), FN=2 (CID01,CID05).
**3. Count true positives:** Only CID06 is both actually and predicted NOT DEFAULTER, so TP=1.
**Answer: 1.**
**(The following scenario is purely Imaginary)**
Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest
possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual
workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as
parameters to predict defaulters. The model is configured such that a “NOT DEFAULTER” is
categorised as the positive class. The final model had the parameters as specified in Table-1
below. To test the model, the data in Table-2 is used as test data. Given this information, answer
the given subquestions.
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
At a threshold of 0.6, how many “True Negatives” is the model predicting?
A published solution is not available for this question yet.
**(The following scenario is purely Imaginary)**
Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest
possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual
workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as
parameters to predict defaulters. The model is configured such that a “NOT DEFAULTER” is
categorised as the positive class. The final model had the parameters as specified in Table-1
below. To test the model, the data in Table-2 is used as test data. Given this information, answer
the given subquestions.
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
At a threshold of 0.6, how many “False Positives” is the model predicting?
A published solution is not available for this question yet.
**(The following scenario is purely Imaginary)**
Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest
possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual
workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as
parameters to predict defaulters. The model is configured such that a “NOT DEFAULTER” is
categorised as the positive class. The final model had the parameters as specified in Table-1
below. To test the model, the data in Table-2 is used as test data. Given this information, answer
the given subquestions.
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
At a threshold of 0.6, how many “False Negatives” is the model predicting?
Published solution
**1. Calculate the logistic probabilities:** The positive class is NOT DEFAULTER. Use \(z=3.20-1.70A+1.40I\) and \(p=1/(1+e^{-z})\). For CID01–CID06, the scores are −2.48,−1.61,2.11,1.17,−1.99,2.30 and the two-decimal probabilities are 0.08,0.17,0.89,0.76,0.12,0.91.
**2. Apply the 0.60 threshold:** CID03,CID04,CID06 are predicted positive; CID01,CID02,CID05 are predicted negative. Comparing with actual status gives TP=1 (CID06), TN=1 (CID02), FP=2 (CID03,CID04), FN=2 (CID01,CID05).
**3. Count false negatives:** CID01 and CID05 are actual NOT DEFAULTER customers predicted negative, so FN=2.
**Answer: 2.**
**(The following scenario is purely Imaginary)**
Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest
possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual
workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as
parameters to predict defaulters. The model is configured such that a “NOT DEFAULTER” is
categorised as the positive class. The final model had the parameters as specified in Table-1
below. To test the model, the data in Table-2 is used as test data. Given this information, answer
the given subquestions.
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
At a threshold of 0.6, what is the ACCURACY of the model? (Note: **Enter the answer in “%”** rounded
to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as
“1.23”)
A published solution is not available for this question yet.
**(The following scenario is purely Imaginary)**
Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest
possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual
workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as
parameters to predict defaulters. The model is configured such that a “NOT DEFAULTER” is
categorised as the positive class. The final model had the parameters as specified in Table-1
below. To test the model, the data in Table-2 is used as test data. Given this information, answer
the given subquestions.
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
At a threshold of 0.6, what is the PRECISION of the model for predicting the Negative Class? (Note:
**Enter the answer in “%”** rounded to two decimal places without the “%” symbol. For example, if the
answer is “1.234%”, then enter it as “1.23”)
A published solution is not available for this question yet.
**(The following scenario is purely Imaginary)**
Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest
possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual
workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as
parameters to predict defaulters. The model is configured such that a “NOT DEFAULTER” is
categorised as the positive class. The final model had the parameters as specified in Table-1
below. To test the model, the data in Table-2 is used as test data. Given this information, answer
the given subquestions.
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
At a threshold of 0.6, what is the SPECIFICITY of the model? (Note: **Enter the answer in “%”**
rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then
enter it as “1.23”)
A published solution is not available for this question yet.
**(The following scenario is purely Imaginary)**
Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest
possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual
workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as
parameters to predict defaulters. The model is configured such that a “NOT DEFAULTER” is
categorised as the positive class. The final model had the parameters as specified in Table-1
below. To test the model, the data in Table-2 is used as test data. Given this information, answer
the given subquestions.
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
At a threshold of 0.6, what is the SENSITIVITY of the model? (Note: **Enter the answer in “%”**
rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then
enter it as “1.23”)
Published solution
**1. Calculate the logistic probabilities:** The positive class is NOT DEFAULTER. Use \(z=3.20-1.70A+1.40I\) and \(p=1/(1+e^{-z})\). For CID01–CID06, the scores are −2.48,−1.61,2.11,1.17,−1.99,2.30 and the two-decimal probabilities are 0.08,0.17,0.89,0.76,0.12,0.91.
**2. Apply the 0.60 threshold:** CID03,CID04,CID06 are predicted positive; CID01,CID02,CID05 are predicted negative. Comparing with actual status gives TP=1 (CID06), TN=1 (CID02), FP=2 (CID03,CID04), FN=2 (CID01,CID05).
**3. Calculate sensitivity:** Among three actual NOT DEFAULTER customers, one is correctly predicted positive. Thus \(100TP/(TP+FN)=100(1/3)=33.33\%\).
**Answer: 33.33.**
**(The following scenario is purely Imaginary)**
A demand response curve has a constant elasticity of +0.4. If the price of the product is 100 and
the corresponding demand is 200, then answer the given subquestions.
What is the value for the constant term of the demand response curve? (Note: Enter the answer
rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Published solution
**1. Write the course’s constant-elasticity curve:** With elasticity magnitude ε=0.4, \(D(p)=ap^{-0.4}\).
**2. Use the known point:** \(200=a100^{-0.4}\), hence \(a=200(100^{0.4})\approx1261.914689\). Rounded constant: 1261.91.
**Answer: 1261.91.**
**Convention note:** The key treats +0.4 as the magnitude of downward-sloping demand elasticity. If +0.4 is a literal signed elasticity, D=ap^0.4 and the constant is 31.70 instead. Retain exponent precision before the final two-decimal rounding.
**(The following scenario is purely Imaginary)**
A demand response curve has a constant elasticity of +0.4. If the price of the product is 100 and
the corresponding demand is 200, then answer the given subquestions.
What should be the price to achieve a demand of 300? (Note: Enter the answer rounded to two
decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Published solution
**1. Use a demand ratio:** Under \(D=ap^{-0.4}\), \(300/200=(p/100)^{-0.4}\).
**2. Solve for price:** \[p=100(1.5)^{-1/0.4}=100(1.5)^{-2.5}\approx36.288737.\] Required price: 36.29.
**Answer: 36.29.**
**Convention note:** This follows the course’s elasticity-magnitude convention. A literal signed elasticity +0.4 would instead require p=100(1.5)^2.5≈275.57.
**(The following scenario is purely Imaginary)**
“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo
wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new
investments be made in oil industry, steel industry or government bonds. Specifically, the analyst
identified five investment opportunities and projected their annual rates of returns (which are
specified in Table-3). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has
specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be exactly 25% of the total steel industry investments
3. Government bonds can at most be 30% of the total oil industry investments
4. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than
60% of total oil industry investment
Given this information, answer the given subquestions
How many (count of) decision variable(s) is/are present in the standard (canonical) form of the
primal?
Published solution
**1. Define the five investments:** Let x1,x2 be oil investments, x3,x4 steel investments and x5 government bonds. Write O=x1+x2 and S=x3+x4.
**2. List the restrictions:** \(O+S+x_5=100000\), \(O\le50000\), \(S\le50000\), \(x_5=0.25S\), \(x_5\le0.30O\), and \(x_2\le0.60O\), with all xi nonnegative.
**3. Count original decisions:** One amount is chosen for each opportunity, giving five decision variables.
**Answer: 5.**
**Convention note:** The question uses “canonical” for an inequality formulation. Converting inequalities to equality standard form would introduce additional slack variables, but those are not original investment decisions.
**(The following scenario is purely Imaginary)**
“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo
wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new
investments be made in oil industry, steel industry or government bonds. Specifically, the analyst
identified five investment opportunities and projected their annual rates of returns (which are
specified in Table-3). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has
specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be exactly 25% of the total steel industry investments
3. Government bonds can at most be 30% of the total oil industry investments
4. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than
60% of total oil industry investment
Given this information, answer the given subquestions
How many constraints (count of constraints, excluding the non-negativity constraints) is present in
the standard (canonical) form of the primal?
Published solution
**1. Define the five investments:** Let x1,x2 be oil investments, x3,x4 steel investments and x5 government bonds. Write O=x1+x2 and S=x3+x4.
**2. List the restrictions:** \(O+S+x_5=100000\), \(O\le50000\), \(S\le50000\), \(x_5=0.25S\), \(x_5\le0.30O\), and \(x_2\le0.60O\), with all xi nonnegative.
**3. Convert equalities to paired inequalities:** The full-budget equality contributes two rows and the bond–steel equality contributes two rows. The two industry caps, bond–oil cap and Bongu cap contribute four more: \(2+2+4=8\).
**Answer: 8.**
**Convention note:** This counts the course’s all-≤ canonical form. A mixed equality/inequality formulation has six restriction rows instead.
**(The following scenario is purely Imaginary)**
“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo
wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new
investments be made in oil industry, steel industry or government bonds. Specifically, the analyst
identified five investment opportunities and projected their annual rates of returns (which are
specified in Table-3). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has
specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be exactly 25% of the total steel industry investments
3. Government bonds can at most be 30% of the total oil industry investments
4. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than
60% of total oil industry investment
Given this information, answer the given subquestions
How many (count of) decision variables are present in the dual (which is based on the standard
(canonical) form of the primal)?
Published solution
**1. Define the five investments:** Let x1,x2 be oil investments, x3,x4 steel investments and x5 government bonds. Write O=x1+x2 and S=x3+x4.
**2. List the restrictions:** \(O+S+x_5=100000\), \(O\le50000\), \(S\le50000\), \(x_5=0.25S\), \(x_5\le0.30O\), and \(x_2\le0.60O\), with all xi nonnegative.
**3. Count canonical primal rows:** Each of the two equalities becomes two inequalities, giving 8 primal restriction rows. One dual variable corresponds to each row, so this representation has 8 dual variables.
**Answer: 8.**
**Convention note:** Keeping the equalities would instead give six dual variables, two unrestricted in sign. Splitting equalities explains the exported answer of eight.
**(The following scenario is purely Imaginary)**
“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo
wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new
investments be made in oil industry, steel industry or government bonds. Specifically, the analyst
identified five investment opportunities and projected their annual rates of returns (which are
specified in Table-3). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has
specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be exactly 25% of the total steel industry investments
3. Government bonds can at most be 30% of the total oil industry investments
4. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than
60% of total oil industry investment
Given this information, answer the given subquestions
If FM has suggested the below distribution of investments, then how much money (total money) is
projected to be in hand at the end of the first year? (Note: **Enter the answer in “Rs.”** rounded to
two decimal places without the “Rs.” symbol. For example, if the answer is “Rs. 1.234”, then enter it as
“1.23”)
Published solution
**1. Calculate annual return:** For investments (20000,30000,15000,25000,10000), the returns are \(0.07(20000)+0.10(30000)+0.06(15000)+0.07(25000)+0.04(10000)=1400+3000+900+1750+400=7450\).
**2. Add the principal:** \(100000+7450=107450.00\) rupees at year end.
**Answer: 107450.00.**
**(The following scenario is purely Imaginary)**
“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo
wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new
investments be made in oil industry, steel industry or government bonds. Specifically, the analyst
identified five investment opportunities and projected their annual rates of returns (which are
specified in Table-3). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has
specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be exactly 25% of the total steel industry investments
3. Government bonds can at most be 30% of the total oil industry investments
4. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than
60% of total oil industry investment
Given this information, answer the given subquestions
If FM has suggested the below distribution of investments, then how many decision variables in
the dual will have a **“zero”** value?
A published solution is not available for this question yet.
**(The following scenario is purely Imaginary)**
“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo
wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new
investments be made in oil industry, steel industry or government bonds. Specifically, the analyst
identified five investment opportunities and projected their annual rates of returns (which are
specified in Table-3). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has
specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be exactly 25% of the total steel industry investments
3. Government bonds can at most be 30% of the total oil industry investments
4. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than
60% of total oil industry investment
Given this information, answer the given subquestions
If FM has suggested the below distribution of investments, then what is the objective function
value for the primal in the standard (canonical) form?
Published solution
**1. Write the return objective:** \(Z=0.07x_1+0.10x_2+0.06x_3+0.07x_4+0.04x_5\).
**2. Evaluate the proposed allocation:** \(Z=1400+3000+900+1750+400=7450.00\). This is annual interest, rather than principal plus interest.
**Answer: 7450.00.**
**(The following scenario is purely Imaginary)**
Milo’s Bakery is famous for three products “BA Biscuits (BAB)”, “TA Controversy Cake (TACC)” and
“Hot Argument Drink (HAD)”. Dr.Milo, the owner of the shop, is an aspiring data analyst. He has
collected 5 days of data. On each day, he captures the number of each product made and total
kilogram of cooking gas consumed. Using all the collected data, Dr.Milo has built a linear
regression model in excel, and the partial regression output is provided in Figure-2. Using this
information, answer the given subquestions
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
What is the sample size for building the model in Figure-2?
Published solution
**1. Identify one observation:** Each day supplies one response, total cooking gas consumed, and three predictor counts. Five days therefore give five observations, not fifteen.
**Answer: 5.**
**(The following scenario is purely Imaginary)**
Milo’s Bakery is famous for three products “BA Biscuits (BAB)”, “TA Controversy Cake (TACC)” and
“Hot Argument Drink (HAD)”. Dr.Milo, the owner of the shop, is an aspiring data analyst. He has
collected 5 days of data. On each day, he captures the number of each product made and total
kilogram of cooking gas consumed. Using all the collected data, Dr.Milo has built a linear
regression model in excel, and the partial regression output is provided in Figure-2. Using this
information, answer the given subquestions
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
What is the value of Q1?
Published solution
**1. Count fitted coefficients:** Three product predictors plus one intercept give four estimated regression coefficients.
**2. Subtract from sample size:** With n=5, residual degrees of freedom are \(Q1=5-3-1=1\).
**Answer: 1.**
**(The following scenario is purely Imaginary)**
Milo’s Bakery is famous for three products “BA Biscuits (BAB)”, “TA Controversy Cake (TACC)” and
“Hot Argument Drink (HAD)”. Dr.Milo, the owner of the shop, is an aspiring data analyst. He has
collected 5 days of data. On each day, he captures the number of each product made and total
kilogram of cooking gas consumed. Using all the collected data, Dr.Milo has built a linear
regression model in excel, and the partial regression output is provided in Figure-2. Using this
information, answer the given subquestions
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
What is the value of Q2? (Note: Enter your answer rounded to two decimal places. For example, if your
answer is “1.235” then enter it as “1.24”)
Published solution
**1. Recover residual sum of squares:** Residual df=5−3−1=1. The standard error is 3.36, so \(SSE=3.36^2(1)\approx11.29\).
**2. Use adjusted R² directly:** \[0.97=1-\frac{SSE/1}{SST/4}\quad\Rightarrow\quad SST=\frac{4(11.29)}{0.03}\approx1505.33.\]
**3. Subtract unexplained variation:** \(Q2=SSR=SST-SSE=1505.33-11.29=1494.04\).
**Answer: 1494.04.**
**Convention note:** The displayed adjusted R² and standard error are rounded summaries, so reconstructed ANOVA values are approximate. Keep the small ratio 0.0075 unrounded; rounding it to 0.01 mid-calculation causes a large distortion despite the passage’s blanket two-decimal instruction.
**(The following scenario is purely Imaginary)**
Milo’s Bakery is famous for three products “BA Biscuits (BAB)”, “TA Controversy Cake (TACC)” and
“Hot Argument Drink (HAD)”. Dr.Milo, the owner of the shop, is an aspiring data analyst. He has
collected 5 days of data. On each day, he captures the number of each product made and total
kilogram of cooking gas consumed. Using all the collected data, Dr.Milo has built a linear
regression model in excel, and the partial regression output is provided in Figure-2. Using this
information, answer the given subquestions
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
What is the value of Q3? (Note: Enter your answer rounded to two decimal places. For example, if your
answer is “1.235” then enter it as “1.24”)
Published solution
**1. Use the residual degrees of freedom:** With five observations and three predictors plus intercept, dfE=1.
**2. Square the standard error:** \(Q3=SSE=s^2df_E=3.36^2(1)=11.2896\), rounding to 11.29.
**Answer: 11.29.**
**(The following scenario is purely Imaginary)**
Milo’s Bakery is famous for three products “BA Biscuits (BAB)”, “TA Controversy Cake (TACC)” and
“Hot Argument Drink (HAD)”. Dr.Milo, the owner of the shop, is an aspiring data analyst. He has
collected 5 days of data. On each day, he captures the number of each product made and total
kilogram of cooking gas consumed. Using all the collected data, Dr.Milo has built a linear
regression model in excel, and the partial regression output is provided in Figure-2. Using this
information, answer the given subquestions
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
What is the value of Q4? (Note: Enter your answer rounded to two decimal places. For example, if your
answer is “1.235” then enter it as “1.24”)
Published solution
**1. Find residual variation:** \(df_E=1\) and \(SSE\approx3.36^2=11.29\). Total df is n−1=4.
**2. Invert adjusted R²:** \(1-0.97=(SSE/1)/(SST/4)\). Thus \(Q4=SST=4(11.29)/0.03\approx1505.33\).
**Answer: 1505.33.**
**Convention note:** The displayed adjusted R² and standard error are rounded summaries, so reconstructed ANOVA values are approximate. Keep the small ratio 0.0075 unrounded; rounding it to 0.01 mid-calculation causes a large distortion despite the passage’s blanket two-decimal instruction.
**(The following scenario is purely Imaginary)**
Milo’s Bakery is famous for three products “BA Biscuits (BAB)”, “TA Controversy Cake (TACC)” and
“Hot Argument Drink (HAD)”. Dr.Milo, the owner of the shop, is an aspiring data analyst. He has
collected 5 days of data. On each day, he captures the number of each product made and total
kilogram of cooking gas consumed. Using all the collected data, Dr.Milo has built a linear
regression model in excel, and the partial regression output is provided in Figure-2. Using this
information, answer the given subquestions
Note: For all computations (both final and those done in the middle), **round your answer to two**
**decimal places**. Do not use single decimal values for any computation or comparisons.
What is the value of Q5? (Note: Enter your answer rounded to two decimal places. For example, if your
answer is “1.235” then enter it as “1.24”)
Published solution
**1. Obtain the mean squares:** From s=3.36, \(MSE\approx11.29\). Adjusted R²=0.97 implies \(SST\approx1505.33\) and \(SSR\approx1494.04\).
**2. Divide by regression df:** Three predictors give \(MSR=1494.04/3\approx498.01\).
**3. Form the overall F statistic:** \(Q5=MSR/MSE=498.01/11.29\approx44.11\).
**Answer: 44.11.**
**Convention note:** The displayed adjusted R² and standard error are rounded summaries, so reconstructed ANOVA values are approximate. Keep the small ratio 0.0075 unrounded; rounding it to 0.01 mid-calculation causes a large distortion despite the passage’s blanket two-decimal instruction.
